(2) Two AlertsCurrent Trading View free plan allows only ONE active alert.
This simple indicator Allows to trigger this ONE and ONLY alert when price reaches Higher, or Lower price level.
You can set levels and turn alerts for them on/off in settings, or by just drag-n-dropping Horizontal lines on the chart.
To set the only alert you need to create new alert, and change it's following parameters :
condition : 2alerts
Any alert function() call
Feel free to modify it on your needs.
Options
[ChasinAlts] A New Beginning[MO]Hello Tradeurs, firstly let me say this… Please do not think that this dump is over (so I want to gift you one of the best gifts I CAN gift you at the PERFECT TIME...which is now) but I believe it to be the final one before a New Beginning is upon us. I hope that anybody that sees this within the next day or so listens to me when I tell you this… Follow the instructions below, IF ANYTHING, just to set the alert to be notify you so you can see why I’m about to tell you everything that I’m about to tell you. That being that this indicator is pure magic…..BUT you must stay in your lane when using it (ie. ultimately, understand its use case) and most importantly, how many people you expose it to. The good thing about it is it produces very few alerts. In fact, it was built SOLELY to find the very tips of MAJOR dumps/pumps (with its current default settings). I honestly cannot remember where I acquired the code so if anyone recognizes it please direct me to the source so I can give a shoutout. In the past it has been so astonishingly accurate that I didn’t want to publish it but I've just been...in the mood I suppose recently.
Now…it is SPECIFICALLY meant for the 1min TF. I’ll say it again… It is meant for ONE MINUTE CHARTS…it was built for 1min charts, it will only work as well as I’m describing to you on the…you guessed it…ONE MINUTE CHART (again, with the default settings how they are, that is). If any of you use it for this present dump (November 8, 2022) and want to thank me for it or speak very highly about it or give it a bunch of likes… DO NOT!!! I will reword this so you fully comprehend my urgency on this matter. I do not want this indicator getting out for every Joe Schmoe (or stupid YouTuber) to use and spread because the manipulators will see to it that it will no longer work. Things that will happen that will cause it to gain the popularity that I do not want it to have are the following:
1) You "like" the indicator in TradingView to show appreciation/that your using it so that it will show up in your indicators list (to get past this you need to select all of the text of the script on the indicator's page and copy and paste it into the “Pine Editor”. Then select "save" and name it as you wish. Now, it is in your indicator list under the name that you saved it as.
2) You *favorite* the indicator in TradingView
3) You leave comments in the comments section on the indicators page in TradingView (I really do love hearing comments about anything regarding my indicators(positive or negative..though I haven't gotten any negative yet SO BRING IT ON), even though I don’t get too many of them, so if you are grateful (or hateful) PLEASE message me privately (and really I truly truly do appreciate getting comments/messages so if it has benefited you make sure to message me as I might have more for those that do express their gratitude) and tell me anything that you want to tell me or ask me anything that you wanna ask me there).
One major thing that will help to suppress its popularity will be that if anybody goes back on historical charts to see its accuracy they most likely will not be able to go far back enough on the 1min TF to be able to Witness its efficacy so I'm banking on that helping to keep a lid on things.
The settings used (as well as the TF used) really should not be changed if using it for its intended purpose. On little dumps that last for a few hours os so will produce points somewhere in the 40 to 60 range at the dumps/pumps peak. Each coin is worth one point and there are 40 coins per set and 2 sets (that you will have to link together) and when the under the hood indicator is triggered for that coin it will add a point to the score. With the settings how they are and on the 1min TF(if I hadn't mentioned it yet. lol) a good point alert threshold to use to catch the apex of heavy pumps/dumps would be between 70 to 80 points(80 is max). Ultimately is the users choice to input the alert threshold of points in the indicators settings(default is 72). If you’re trying to nail the very bottom of a hard pump/dump, DO NOT fall for times where it peaks at 50 to 60. You’re looking for 70 or above.
*** This is the most important thing to do as you will not receive an alert if you do not do this correctly. You have to add the indicator two times to the chart. One of the indicators needs to be under “Coin Set 1“ and the other under “Coin Set 2“. Now, in “Set 1“ you need to go to the setting entitled “Select New Beginning Count Plot from drop-down“ and you need to open the drop-down and select the plot entitled “A New Beginning Count Plot”. This will link both the indicators and since there are 40 coins per iteration of the script, when you link them it could give you a max of 80 points total at the very peak of a very strong dump...which will obviously be rare. You CAN use only one copy of the script (but need to change the alert setting to a MAX of 40) but in my experience it's best to use both of them and to link them. It gives you a more well-rounded outcome. Good luck my people and always remember...Much love...Much Love. May the force be with your trades. -ChasinAlts out.
4C Expected Move (Weekly Options)This indicator plots the Expected Move (EM) calculated from weekly options pricing, for a quick visual reference.
The EM is the amount that a stock is predicted to increase or decrease from its current price, based on the current level of implied volatility.
This range can be viewed as support and resistance, or once price gets outside of the range, institutional hedging actions can accelerate the move in that direction.
The EM range is based on the Weekly close of the prior week.
It can be useful to know what the weekly EM range is for a stock to understand the probabilities of the overall distance, direction and volatility for the week.
To use this indicator you must have access to a broker with options data (not available on Tradingview).
Look at the stock's option chain and find the weekly expected move. You will have to do your own research to find where this information is displayed depending on your broker.
See screenshot example on the chart. This is the Thinkorswim platform's option chain, and the Implied Volatility % and the calculated EM is circled in red. Use the +- number in parentheses, NOT the % value.
Input that number into the indicator on a weekly basis, ideally on the weekend sometime after the cash market close on Friday, and before the Market open at the beginning of the trading week.
The indicator must be manually updated each week.
It will automatically start over at the beginning of the week.
RedK Magic Ribbon JeetendraGaurCross Over Strategy
Moving average Cross Over Strategy
Please use in 1 minute Expiry
Moving Averages SelectionHello everyone, I present my first script. In it I collect a group of fully configurable moving averages, both in color, value and selection of the ones we want to observe.
The moving averages I collect are 3 of each of the following types:
EMA: An exponential moving average ( EMA ) is a type of moving average (MA) that places a greater weight and significance on the most recent data points.
SMA: It is simply the average price over the specified period. The average is called "moving" because it is plotted on the chart bar by bar, forming a line that moves along the chart as the average value changes.
HMA: The Hull Moving Average ( HMA ) attempts to minimize the lag of a traditional moving average while retaining the smoothness of the moving average line. Developed by Alan Hull in 2005, this indicator makes use of weighted moving averages to prioritize more recent values and greatly reduce lag.
RMA: The Rolling Moving Average, sometimes referred to as "Smoothed Moving Average", gives the recent prices most weighting, though the historic prices are also weighted, each given less weighting further back in time.
WMA: The weighted moving average ( WMA ) is a technical indicator that traders use to generate trade direction and make a buy or sell decision. It assigns greater weighting to recent data points and less weighting on past data points.
I am open to any opinion and advice for improvement, greetings, I hope you find it useful :)
LazyScalp BoardThis indicator allows you to quickly view all important parameters in the table.
The table consists of a daily volume indicator, an average volume for a certain period, a volatility indicator (normalized ATR) and a correlation coefficient.
All parameters can be flexibly customized. You can also customize the table display, styles, and more.
This indicator is primarily useful for intraday traders and scalpers to quickly select an instrument to trade.
Volatility Cone [Loxx]When it comes to forecasting volatility, it seems that the old axiom about weather is applicable: "Everyone talks about it, but no one can do much about it!" Volatility cones are a tool that may be useful in one’s attempt to do something about predicting the future volatility of an asset.
A "volatility cone" is a plot of the range of volatilities within a fixed probability band around the true parameter, as a function of sample length. Volatility cone is a visualization tool for the display of historical volatility term structure. It was introduced by Burghardt and Lane in early 1990 and is popular in the option trading community. This is mostly a static indicator due to processor load and is restricted to the daily time frame.
Why cones?
When we enter the options arena, in an effort to "trade volatility," we want to be able to compare current levels of implied volatility with recent historical volatility in an effort to assess the relative value of the option(s) under consideration Volatility cones can be an effective tool to help us with this assessment. A volatility cone is an analytical application designed to help determine if the current levels of historical or implied volatilities for a given underlying, its options, or any of the new volatility instruments, such as VolContractTM futures, VIX futures, or VXX and VXZ ETNs, are likely to persist in the future. As such, volatility cones are intended to help the user assess the likely volatility that an underlying will go on to display over a certain period. Those who employ volatility cones as a diagnostic tool are relying upon the principle of "reversion to the mean." This means that unusually high levels of volatility are expected to drift or move lower (revert) to their average (mean) levels, while relatively low volatility readings are expected to rise, eventually, to more "normal" values.
How to use
Suppose you want to analyze an options contract expiring in 3-months and this current option has an current implied volatility 25.5%. Suppose also that realized volatility (y-axis) at the 3-month mark (90 on the x-axis) is 45%, median in 35%, the 25th percentile is 30%, and the low is 25%. Comparing this range to the implied volatility you would maybe conclude that this is a relatively "cheap" option contract. To help you visualize implied volatility on the chart given an expiration date in bars, the indicator includes the ability to enter up to three expirations in bars and each expirations current implied volatility
By ascertaining the various historical levels of volatility corresponding to a given time horizon for the options futures under consideration, we’re better prepared to judge the relative "cheapness" or "expensiveness" of the instrument.
Volatility options
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility .
Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.
Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility .
Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.
Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.
The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility. One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility. That drawback is taken into account in the Garman-Klass's volatility estimator.
Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.
Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.
The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.
A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.
Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.
We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility ) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility . It considered being 14 times more efficient than the close-to-close estimator.
Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.
Standard Deviation of Log Returns
This is the simplest calculation of volatility . It's the standard deviation of ln(close/close(1))
Sampling periods used
5, 10, 20, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360
Historical Volatility plot
Purple outer lines: High and low volatility values corresponding to x-axis time
Blue inner lines: 25th and 75th percentiles of volatility corresponding to x-axis time
Green line: Median volatility values corresponding to x-axis time
White dashed line: Realized volatility corresponding to x-axis time
Additional things to know
Due to UI constraints on TradingView it will be easier to visualize this indicator by double-clicking the bottom pane where it appears and then expanded the y- and x-axis to view the entire chart.
You can click on each point on the graph to see what the volatility of that point is.
Option expiration dates will show up as large dots on the graph. You can input your own values in the settings.
Variety Distribution Probability Cone [Loxx]Variety Distribution Probability Cone forecasts price within a range of confidence using Geometric Brownian Motion (GBM) calculated using selected probability distribution, volatility, and drift. Below is detailed explanation of the inner workings of the indicator and the math involved. While normally this indicator would be used by options traders, this can also be used by regular directional traders who wish to observe a forecast of the confidence interval of possible prices over time.
What is a Random Walk
A random walk is a path which consists of a set of random steps. The starting point is zero and following movement may be one step to the left or to the right with equal probability. In the random walk process, there is no observable trend or pattern which are followed by the objects that is the movements are completely random. That is why the prices of a stock as it moves up and down can be modeled by random a walk process.
Stock Prices and Geometric Brownian Motion
Brownian motion, as first conceived by the botanist Robert Brown (1827), is a mathematical model used to describe random movements of small particles in a fluid or gas. These random movements are observed in the stock markets where the prices move up and down, randomly; hence, Brownian motion is considered as a mathematical model for stock prices.
P(exp(lnS0 + (mu + 1/2*sigma^2)t - z(0.05)*sigma*t^0.5) <= St <= exp(lnS0 + (mu + 1/2*sigma^2)t + z(0.05)*sigma*t^0.5)) = 0.95
Probability Distributions
Typically the normal distribution is used, but for our purposes here we extend this to Student t-distribution, Cauchy, Gaussian KDE, and Laplace
Student's t-Distribution
The probability density function of the Student’s t distribution is given by
g(x) = (L(v+1)/2) / L(v/2) * 1 / L(sqrt(v)) * (1 + x^2/v) ^ (-(v+1)/2)
with v degrees of freedom and v >= 0, denoted by X ~ t(v). The mean is 0 and the variance is v/(v-2). It is known that as v tends to infinity, the Student’s t-distribution tends to a standard normal probability density function, which has a variance of one. Blattberg and Gonedes were the first to propose that stock returns could be modeled by this distribution. (Blattberg and Gonedes, 1974) Platen and Sidorowicz later reaffirmed these findings.(Platen and Rendek, 2007) Finally, Cassidy, Hamp, and Ouyed used these findings to derive the Gosset formula, which is the Student t version of the Black-Scholes model.(Cassidy et al., 2010) They found that v = 2.65 provides the best fit when looking at the past 100 years of returns. They realized that as markets become more turbulent, the degrees of freedom should be adjusted to a smaller value.(Cassidy et al., 2010)
Cauchy Distribution
The probability density function of the Cauchy distribution is given by
f(x) = 1 / (theta*pi*(1 + ((x-n)/v)))
where n is the location parameter and theta is the scale parameter, for -infinity < x < infinity and is denoted by X ~ CAU(L,v). This model is similar to the normal distribution in that it is symmetric about zero, but the tails are fatter. This would mean that the probability of an extreme event occurring lies far out in the distributions tail. Using a crude example, if the normal distribution gave a probability of an extreme event occurring of 0.05% and the “best case” scenario of this event occurring 300 years, then using the Cauchy distribution one would find that the probability of occurring would be around 5% and now the “best case” scenario might have been reduced to only 63 years. Thus giving extreme events more of a likelihood of occurring. The mean, variance, and higher order moments are not defined (they are infinite); this implies that n and theta cannot be related to a mean and standard deviation. The Cauchy distribution is related to the Student’s t distribution T ~ CAU(1,0) when v = 1. In 1963, Benoit Mandelbrot was the first to suggest that stock returns follow a stable distribution, in particular, the Cauchy distribution.(Mandelbrot, 1963) His work was validated by Eugene Fama in 1965.(Fama, 1965) Recent research by Nassim Taleb came to the same conclusion as Mandelbrot, saying that stock returns follow a Cauchy distribution, as reported in his New York Times best-seller book “The Black Swan”.(Taleb, 2010)
Laplace Distribution
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.
The probability density function of the Cauchy distribution is given by
f(x) = 1/2b * exp(-|x-µ|/b)
Here, µ is a location parameter and b > 0, which is sometimes referred to as the "diversity", is a scale parameter. If µ = 0 and b=1, the positive half-line is exactly an exponential distribution scaled by 1/2.
The probability density function of the Laplace distribution is also reminiscent of the normal distribution; however, whereas the normal distribution is expressed in terms of the squared difference from the mean µ, the Laplace density is expressed in terms of the absolute difference from the mean. Consequently, the Laplace distribution has fatter tails than the normal distribution.
Gaussian Kernel Density Estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.
Let (x1, x2, ..., xn) be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is:
f(x) = 1/nh * sum(k(x-xi)/h, n)
where K is the kernel—a non-negative function—and h > 0 is a smoothing parameter called the bandwidth. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance.
The probability density function of Gaussian Kernel Density Estimation is given by
f(x) = 1 / (v * 2*pi)^0.5 * exp(-(x - m)^2 / (2 * v))
where v is the bandwidth component h squared
KDE Bandwidth Estimation
Bandwidth selection strongly influences the estimate obtained from the KDE (much more so than the actual shape of the kernel). Bandwidth selection can be done by a "rule of thumb", by cross-validation, by "plug-in methods" or by other means. The default is Scott's Rule.
Scott's Rule
n ^ (-1/(d+4))
with n the number of data points and d the number of dimensions.
In the case of unequally weighted points, this becomes
neff^(-1/(d+4))
with neff the effective number of datapoints.
Silverman's Rule
(n * (d + 2) / 4)^(-1 / (d + 4))
or in the case of unequally weighted points:
(neff * (d + 2) / 4)^(-1 / (d + 4))
With a set of weighted samples, the effective number of datapoints neff
is defined by:
neff = sum(weights)^2 / sum(weights^2)
Manual input
You can provide your own bandwidth input. This is useful for those who wish to run external to TradingView Grid Search Machine Learning algorithms to solve for the bandwidth per ticker.
Inverse CDF of KDE Calculation
1. Create an array of random normalized numbers, using an inverse CDF of a normal distribution of mean of zero
and standard deviation one
2. Create a line space range of values -3 to 3
3. Create a Gaussian Kernel Density Estimate CDF by iterating over the line space array created in step 2. For each line space item, find the mean difference between the line space and the random variable divided by the bandwidth.
4. Derive test statistics from the resulting KDE inverse CDF, we use cubic spline interpolation to solve for line space value for a given alpha computed using the user selected probability percent value in the settings.
Volatility
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility.
Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.
Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility.
Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.
Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.
The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility.
One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility. That drawback is taken into account in the Garman-Klass's volatility estimator.
Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.
Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.
The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.
A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.
Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.
We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility. It considered being 14 times more efficient than the close-to-close estimator.
Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.
Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.
Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.
Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.
Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.
Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.
Standard Deviation of Log Returns
This is the simplest calculation of volatility. It's the standard deviation of ln(close/close(1))
Pseudo GARCH(2,2)
This is calculated using a short- and long-run mean of variance multiplied by θ.
θavg(var ;M) + (1 − θ)avg(var ;N) = 2θvar/(M+1-(M-1)L) + 2(1-θ)var/(M+1-(M-1)L)
Solving for θ can be done by minimizing the mean squared error of estimation; that is, regressing L^-1var - avg(var; N) against avg(var; M) - avg(var; N) and using the resulting beta estimate as θ.
Manual
User input % value
Drift
Cost of Equity / Required Rate of Return (CAPM)
Standard Capital Asset Pricing Model used to solve for Cost of Equity of Required Rate of Return. Due to the processor overhead required to compute CAPM, the user must plug in values for beta, alpha, and expected market return using Loxx's CAPM indicator series. Used for stocks.
Mean of Log Returns
Average of the log returns for the underlying ticker over the user selected period of evaluation. General purpose use.
Risk-free Rate (r)
10, 20, or 30 year bond yields for the user selected currency. Under equilibrium the drift of the empirical GBM must be the risk-free rate. If the price process is a GBM under the empirical measure, then a consequence of viability is that it is also a GBM under an equivalent (risk-neutral) measure.
Risk-free Rate adjusted for Dividends (r-q)
This is the Risk-free Rate minus the Dividend Yield.
Forex (r-rf)
This is derived from the Garman and Kohlhagen (1983) modified Black-Scholes model can be used to price European currency options. This is simply the diffeence between Risk-free Rate of the Forex currency in question. This is used for Forex pricing.
Martingale (0)
When the drift parameter is 0, geometric Brownian motion is a martingale. In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Typically used for futures or margined futures.
Manual
User input % value
Additional notes
Indicator can be used on any timeframe. The T (time) variable used to annualize volatility and inside the GBM formula is automatically calculated based on the timeframe of the chart.
Confidence interval of volatility is calculated using an inverse CDF of a Chi-Squared Distribution. You change the volatility input used to create the probability cones from from realized volatility to upper or lower confidence levels of volatility to better visualize extremes of range. Generally, you'd stick with realized volatility.
Days per year should be 252 for everything but Cryptocurrency. These are days trader per year. Maximum future forecast bars is 365. Forecast bars are limited to the maximum of selected days per year.
Includes the ability to overlay option expiration dates by bars to see the range of prices for that date at that bar
You can select confidence % you wish for both the cone in general and the volatility. There are three levels for the cones, this will show on the three different levels up and down on the chart.
The table on the right displays important calculated values so you don't have to remember what they are or what settings you selected
All values are annualized no matter the timeframe.
Additional distributions and measures of volatility and drift will be added in future releases.
Higher Time Frame Average True RangesPurpose: This script will help an options trader asses risk and determine good entry and exit strategies
Background Information: The true range is the greatest of: current high minus the current low; the absolute value of the current high minus the previous close; and the absolute value of the current low minus the previous close. The Average True Range (ATR) is a 14-day moving average of the true range. Traders use the ATR indicator to assess volatility in stocks and decide when to enter and exit trades. It is important to note the limitations of using True Range and ATR: These indications cannot tell you the direction of your options trade (call vs. put) and they cannot tell you whether a particular trend is about to reverse. However, it can be used to assess if volatility has peaked for a particular direction and time period.
How this script works: This indicator calculates true range for the daily (DTR), weekly (WTR), and monthly (MTR) time frames and compares it to the Average True Range (ATR) for each of those time frames (DATR, WATR, and MATR). The comparison is displayed into a colored table in the upper right-hand corner of the screen. When a daily, weekly, or monthly true range reaches 80% of its respective ATR, the row for that time frame will turn Orange indicating medium risk for staying in the trade. If the true range goes above 100% of the respective ATR, then the row will turn Red indicating high risk for staying in the trade. When the row for a time period turns red, volatility for the time period has likely peaked and traders should heavily consider taking profits. It is important to note these calculations start at different times for each time frame: Daily (Today’s Open), Weekly (Monday’s Open), Monthly (First of the Month’s Open). This means if it’s the 15th of the month then the Monthly True Range is being calculated for the trading days in the first half of the month (approximately 10 trade days).
The script also plots three sets of horizontal dotted lines to visually represent the ATR for each time period. Each set is generated by adding and subtracting the daily, weekly, and monthly ATRs from that time periods open price. For example, the weekly ATR is added and subtracted from Mondays open price to visually represent the true range for that week. The DATR is represented by red lines, the WATR is represented by the green lines, and the MATR is represented by the blue lines. These plots could also be used to assess risk as well.
How to use this script: Use the table to assess risk and determine potential exit strategies (Green=Low Risk, Orange=Medium Risk, Red=High Risk. Use the dotted lines to speculate what a stock’s price could be in a given time period (Daily=Red, Weekly=Green, and Monthly=Blue). And don’t forget the true range’s calculation and plots starts at the beginning of each time period!
MINI SPXThis is the XSP version of SPX, basically it's just the price of SPX divided by 10 and shown using labels.
Should only be used on SPX to watch the price of XSP since XSP doesn't have real-time data ATM.
Can be used on any time frames.
This script allows you to view the Daily (O, H, L, C) and Yesterday's (O, H, L, C) with a non intrusive price line.
Allows for extra customization of the price lines and labels.
APIBridge Nifty Options Algo StrategyUsing Pinescript, we will use charts of Cash/Future to trade in Options. Note this strategy works well with even the free version of TradingView.
The Relative Strength Index ( RSI ). Is a momentum oscillator that measures the speed and change of price movements. The RSI oscillates between zero and 100. Increasing RSI shows increasing bullish momentum. Decreasing RSI shows increasing bearish momentum. We take RSI upper bound as 80 to indicate bullish momentum and RSI lower bound as 20 to indicate bearish momentum.
We use the above premise to create options buy-only strategy which trades in ATM strikes by default. This strategy requires very less margin (Minimum Rs . 15000).
Since this strategy uses underlying data (cash/future) to place trades in Options, please ignore the backtest of this strategy given by TradingView. TradingView does not provide options data but this strategy bypasses it.
Strategy Premise
The Relative Strength Index (RSI) is a momentum oscillator that measures the speed and change of price movements. The RSI oscillates between zero and 100. Increasing RSI shows increasing bullish momentum. Decreasing RSI shows increasing bearish momentum. We take RSI upper bound as 80 to indicate bullish momentum and RSI lower bound as 20 to indicate bearish momentum.
We use the above premise to create options buy-only strategy which trades in ATM strikes by default. This strategy requires very less margin (Rs. 15000 should be sufficient).
NSE Options Algo Strategy Logic
Long Entry: When RSI goes above 80, send LE in an auto-calculated option strike Call. When RSI goes below 20, send LE in auto-calculated option strike Put.
Long Exit: When we hit Stop loss or Target. In case SL/TGT does not hit and reverse RSI goes above 80 send Long Exit in auto-calculated option. Put as per last trade; RSI goes below 20, send LX in auto-calculated option call as per last trade.
For Long and Short entry the order is fired in the option buying side with auto strike price selection.
Option Strategy Parameters for TraingView Charts
RSI Length(Mandatory): Number of bars used to calculated RSI.
Upper Band(Mandatory): To specify upper band of RSI.
Lower Band(Mandatory): For specifying lower band of RSI.
Use reversal from Upper Band (Optional): This will enable short entry when RSI is falling below 80 from upper band. Recommended to keep unchecked initially.
Use reversal from Lower Band (Optional): This will enable long entry when RSI is raising above 20 from lower band. Recommended to keep unchecked initially.
Quantity: We use this specify the trade quantity (for Nifty min 75)
Custom Stop Loss in Points: Movement in chart price against the momentum which will trigger exit in options positions
Custom Target in Points: Movement in chart price against the momentum which will trigger exit in options positions
Base symbol: This is the base instrument symbol like NIFTY or BANK NIFTY.
Strike distance from ATM: Our default strike selection is considered as first ATM option (with nearest distance, only 100s are considered ). This strike distance allows to calculate ATM options which are at fixed distance.
Expiry: Expiry of option. Weekly and monthly both expiry are allowed.
Instrument: For index instrument will be OPTIDX, for stock instrument will be OPTSTK
Strategy Tag: The Strategy of Nifty options configured in Api bridge.
Setting Up Alert
Before setting up the alert make sure that you have selected desired script, time frame, strategy settings, and APIbridge configuration. Click in settings add alert and paste {{strategy.order.comment}} in message box.
Important: Do not change any settings during live trading. It may break the sequence of exit for the correct call/put.
Ichi-Price WaveWelcome to the Ichi-Price Wave. This indicator is designed for day trading options contracts for any ticker, using a number of indicators — Ichimoku Cloud, Volume-Weighted Average Price, Stochastic Relative Strength Index, Exponential Moving Average (13/48) — and calculating how they interact with each other to provide entry and exit signals for both Calls and Puts on normal days. ****Read the Important Information section before opening any positions based on this indicator. (Also *NFA)
The general concept is that you, the trader, are a Surfer 🏄🏾 who rides the best waves in deep water until it gets dangerous.
Emoji storyline: The 🏄🏾 emoji (Call or Put, depending on the color of its Green or Red label, respectively) indicates an upcoming *potential* entry that, for a number of reasons, may be disregarded. (See: Important Information section below). And just as there are no certainties in the stock market itself, the tiered exit signals are ranked by low 🐬, medium 🦈 and high risk 🦑 tolerance. (In other words, it's relatively safe to surf with dolphins around, but there's the off chance they even strike trainers and become aggressive. It's more dangerous to swim with sharks. And on the unlikely, rare occasion you see a literal, giant, mythical, ship destroying Kraken 😬 ... you definitely need to get out of the water.
Surfing for as long as possible reaps the greatest rewards — but risk/reward are to be considered for entries and exits. Exiting every time you see a 🐬 (E1) should secure profits nearly 100% of the time, but they'll be very minimal. Whereas surfing til you reach a Kraken 🦑 (which will not even appear on most Price Wave cycles) would reap the most rewards. (NFA: I recommend considering sharks 🦈 as an exit point for the majority of positions, and perhaps only keeping a few runners open with the hopes of finding that shiny Kraken. (On the non-Emoji chart, the low, medium and high risk exits are named E1, E2 and E3, respectively. Got to the indicator's Settings > Inputs > then toggle EMOJIs ON/OFF)
Boring stuff: The entry 🏄🏾 signals are triggered by multiple conditions that must be all true. For Call entries, one of the necessary conditions is that the RSI's K must be maximum 10 (this can be changed in default). This, along with another condition where current price must be below the VWAP Lower Bound 1, serves as a great reference point showing the stock price is currently uncomfortable where it is and may likely soon snap back closer to the VWAP, perhaps even to the other side due to a pendulum effect.
Important information
Relying on those two factors for setting entry and exit points are great for normal days. (Normal, as in the ticker price bounces within a channel (e.g., ≤3% + or -) that's trending slightly bullish or bearish depending on greater market trend). But there are abnormal days where news catalysts (e.g., CPI data, CEO scandals, unexpected company data release, etc.) trigger FOMO and FUD, ultimately rendering the logic behind most indicators non applicable (e.g., RSI's "buy when oversold"). On the chart, this indicator accounts for this with two measures:
One, you should only "Surf" in the water. That is, there are two bands — Shallow and Deep Water. Any "Surf" emojis where price action is outside of the water should be ignored**. Two, there are additional EMOJIs that show you "Bearish trend" ⛈ and "Bullish trend ☀️. (Story time again: You obviously shouldn't surf in thunder and lightning. But also, surfing in the blistering sun with no clouds in the sky during a heatwave is also dangerous to your health.)
You can use these two measures to disregard the "surfers" suggesting you join them in opening a position in the suggested direction. And surfers followed by Cloud EMOJIs — 🌤️ (Put) or 🌧️ (Call) — can be used as "perfect entry" points. (The clouds represent weather being less extreme and better for surfing).
(**While these should mostly be ignored, these have not been muted because there is the possibility of a very strong turn around if you happen to catch the last one (which is not ideal for risk-averse traders). Use other indicators, such as the MACD and trend lines, to find potential bottoms (or tops) as price action plunges (or soars) due to abnormal news circumstances.)
Entry and exit buffers
At the beginning of each day, most indicators usually are not immediately calibrated correctly due to premarket trading and open market (at least to the degree that the day's sentiment can be best read from them due to the amount of volatility). What I recommend when using this indicator is disregarding signals during the first 15 minutes (or possibly 30 minutes) of market open to get the best results. And also, considering this indicator is meant for day trading (i.e., not holding positions overnight), disregarding ENTRY signals for the last 45 minutes of the trading day could give yourself enough buffer on the back end for exiting comfortably.
RSI entry
Preparing for an entry when you see a surfer is recommended, but actually opening the position when you see a 🌤️ (Put) or 🌧️ (Call) would yield best results and avoid misfires — particularly when those two cloud EMOJIs are signaled when the RSI is overbought and K is at least 95 (Puts), or oversold and K at maximum 5 (Calls). (Story time logic: The cloud eclipsing the Sun means it's cooling off and better for surfing. And the rain cloud no longer having lightning means the "bearish" storm is possibly soon over).
Delta and the Greeks
You should experiment yourself, but keep in mind that this is for capitalizing off of a day's minor price swings (≤3% + or -). Entering a same day expiry contract that's deep OTM is not going to work with this indicator (even if you enter at a surfer 🏄🏾 and exit at a Kraken 🦑) because the price wave from one end to the other won't be enough to compensate for the other Greeks working against you. Use another indicator (or insider knowledge ... Just kidding, that's illegal, don't do that) if you want to buy those kind of contracts.
I personally purchase contracts w/ minimum 80% Implied Volatility and somewhere between 20-40 Delta. Having a nice range for yourself with these factors, depending also on the size of your own portfolio and the risk tolerance you have, will determine how much you're able to capitalize off successful entry and exits.
Tips
• I set stop losses 5-10% depending on the ticker. (e.g., $TSLA's volatility may require SL closer to 10% whereas using it on $SPY, a 5% could suffice). This is in addition to ignoring entry signals that don't meet the aforementioned two requirements (i.e., it's risky to Surf in shallow water, and you shouldn't try to Surf at all outside of the water, ref. Band 2 and outside of Band 2). Remember, this is the stock market — not the casino. We rely on strategy and risk management — not hope.
• It's recommended you use time intervals ≤ 5 min. (I use 1 minute and 5 min)
• Liquidity . Using these signals on a ticker with low liquidity (particularly if you enter on the Ask side), can reduce your profits to 0% or even to a loss even if you have a perfect entry and exit. I always point to SPY as the optimal bid-ask spread, but keep that in mind.
What's with the name "Ichi-Price Wave"?
The "Ichi" gives credit to Japanese journalist Goichi Hosoda, whose indicator I used in conjunction with the 13/48 Exponential Moving Averages to create some of the exit signal conditions (e.g., E2🦈). That E2 condition is: Signal the first time the price intersects the Ichimoku conversion line *after* it has entered the VWAP UB/LB channel on one end and has exited on the opposite end). And it's named "Price Wave" because it's a literal price wave, which is where the fun surf narrative comes in. Also, "Price" doubles as me naming it after myself (in a less pretentious way). It's actually convenient that my last name is literally Price. Almost as if I was born for this. Nonetheless, this indicator is far more accurate in spotting directional changes than the free 13/48 cross, which oddly enough, influencers are charging for access. It's free, but the code is protected, for now at least.
Try it out on any ticker and look at how accurately it catches the tops and bottoms (keeping in mind to ignore misfires according to the two measures and also setting ~5-10% stop losses). And of course, use this in conjunction with other indicators. Ignoring all of my other emojis and simply setting surfer 🏄🏾 alerts could serve as additional confirmations for your personal strategy. Or you could simply enter at a surfer 🏄🏾 and exit when it reaches VWAP (or at least increase your Stop Loss to sell at break even if it doesn't reach). That strategy is the most conservative and would secure consistent gains). AND AGAIN, use your stop losses. Either it makes a move or it doesn't. Simply re-enter at a better point if necessary.
Reset Strike Options-Type 2 (Gray Whaley) [Loxx]For a reset option type 2, the strike is reset in a similar way as a reset option 1. That is, the strike is reset to the asset price at a predetermined future time, if the asset price is below (above) the initial strike price for a call (put). The payoff for such a reset call is max(S - X, 0), and max(X - S, 0) for a put, where X is equal to the original strike X if not reset, and equal to the reset strike if reset. Gray and Whaley (1999) have derived a closed-form solution for the price of European reset strike options. The price of the call option is then given by (via "The Complete Guide to Option Pricing Formulas")
c = Se^(b-r)T2 * M(a1, y1; p) - Xe^(-rT2) * M(a2, y2; p) - Se^(b-r)T1 * N(-a1) * N(z2) * e^-r(T2-T1) + Se^(b-r)T2 * N(-a1) * N(z1)
p = Se^(b-r)T1 * N(a1) * N(-z2) * e^-r(T2-T1) + Se^(b-r)T2 * N(a1) * N(-z1) + Xe^(-rT2) * M(-a2, -y2; p) - Se^(b-r)T2 * M(-a1, -y1; p)
where b is the cost-of-carry of the underlying asset, a is the volatility of the relative price changes in the asset, and r is the risk-free interest rate. K is the strike price of the option, T1 the time to reset (in years), and T2 is its time to expiration. N(x) and M(a,b; p) are, respectively, the univariate and bivariate cumulative normal distribution functions. Further
a1 = (log(S/X) + (b+v^2/2)T1) / v*T1^0.5 ... a2 = a1 - v*T1^0.5
z1 = ((b+v^2/2)(T2-T1)) / v*(T2-T1)^0.5 ... z2 = z1 - v*(T2-T1)^0.5
y1 = (log(S/X) + (b+v^2/2)T1) / v*T1^0.5 ... y2 = a1 - v*T1^0.5
and p = (T1/T2)^0.5. For reset options with multiple reset rights, see Dai, Kwok, and Wu (2003) and Liao and Wang (2003).
Inputs
Asset price ( S )
Strike price ( K )
Reset time ( T1 )
Time to maturity ( T2 )
Risk-free rate ( r )
Cost of carry ( b )
Volatility ( s )
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Numerical Greeks Outputs
Delta D
Elasticity L
Gamma G
DGammaDvol
GammaP G
Vega
DvegaDvol
VegaP
Theta Q (1 day)
Rho r
Rho futures option r
Phi/Rho2
Carry
DDeltaDvol
Speed
Strike Delta
Strike gamma
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Writer Extendible Option [Loxx]These options can be exercised at their initial maturity date /I but are extended to T2 if the option is out-of-the-money at ti. The payoff from a writer-extendible call option at time T1 (T1 < T2) is (via "The Complete Guide to Option Pricing Formulas")
c(S, X1, X2, t1, T2) = (S - X1) if S>= X1 else cBSM(S, X2, T2-T1)
and for a writer-extendible put is
c(S, X1, X2, T1, T2) = (X1 - S) if S< X1 else pBSM(S, X2, T2-T1)
Writer-Extendible Call
c = cBSM(S, X1, T1) + Se^(b-r)T2 * M(Z1, -Z2; -p) - X2e^-rT2 * M(Z1 - vT^0.5, -Z2 + vT^0.5; -p)
Writer-Extendible Put
p = cBSM(S, X1, T1) + X2e^-rT2 * M(-Z1 + vT^0.5, Z2 - vT^0.5; -p) - Se^(b-r)T2 * M(-Z1, Z2; -p)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
Asset price ( S )
Initial strike price ( X1 )
Extended strike price ( X2 )
Initial time to maturity ( t1 )
Extended time to maturity ( T2 )
Risk-free rate ( r )
Cost of carry ( b )
Volatility ( s )
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Numerical Greeks Output
Delta
Elasticity
Gamma
DGammaDvol
GammaP
Vega
DvegaDvol
VegaP
Theta (1 day)
Rho
Rho futures option
Phi/Rho2
Carry
DDeltaDvol
Speed
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Reset Strike Options-Type 1 [Loxx]In a reset call (put) option, the strike is reset to the asset price at a predetermined future time, if the asset price is below (above) the initial strike price. This makes the strike path-dependent. The payoff for a call at maturity is equal to max((S-X)/X, 0) where is equal to the original strike X if not reset, and equal to the reset strike if reset. Similarly, for a put, the payoff is max((X-S)/X, 0) Gray and Whaley (1997) x have derived a closed-form solution for such an option. For a call, we have
c = e^(b-r)(T2-T1) * N(-a2) * N(z1) * e^(-rt1) - e^(-rT2) * N(-a2)*N(z2) - e^(-rT2) * M(a2, y2; p) + (S/X) * e^(b-r)T2 * M(a1, y1; p)
and for a put,
p = e^(-rT2) * N(a2) * N(-z2) - e^(b-r)(T2-T1) * N(a2) * N(-z1) * e^(-rT1) + e^(-rT2) * M(-a2, -y2; p) - (S/X) * e^(b-r)T2 * M(-a1, -y1; p)
where b is the cost-of-carry of the underlying asset, a is the volatil- ity of the relative price changes in the asset, and r is the risk-free interest rate. X is the strike price of the option, r the time to reset (in years), and T is its time to expiration. N(x) and M(a, b; p) are, respec- tively, the univariate and bivariate cumulative normal distribution functions. The remaining parameters are p = (T1/T2)^0.5 and
a1 = (log(S/X) + (b+v^2/2)T1) / vT1^0.5 ... a2 = a1 - vT1^0.5
z1 = (b+v^2/2)(T2-T1)/v(T2-T1)^0.5 ... z2 = z1 - v(T2-T1)^0.5
y1 = log(S/X) + (b+v^2)T2 / vT2^0.5 ... y2 = y1 - vT2^0.5
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
Asset price ( S )
Initial strike price ( X1 )
Extended strike price ( X2 )
Initial time to maturity ( t1 )
Extended time to maturity ( T2 )
Risk-free rate ( r )
Cost of carry ( b )
Volatility ( s )
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Numerical Greeks Ouput
Delta
Elasticity
Gamma
DGammaDvol
GammaP
Vega
DvegaDvol
VegaP
Theta (1 day)
Rho
Rho futures option
Phi/Rho2
Carry
DDeltaDvol
Speed
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Fade-in Options [Loxx]A fade-in call has the same payoff as a standard call except the size of the payoff is weighted by how many fixings the asset price were inside a predefined range (L, U). If the asset price is inside the range for every fixing, the payoff will be identical to a plain vanilla option. More precisely, for a call option, the payoff will be max(S(T) - X, 0) X 1/n Sum(n(i)), where n is the total number of fixings and n(i) = 1 if at fixing i the asset price is inside the range, and n(i) = 0 otherwise. Similarly, for a put, the payoff is max(X - S(T), 0) X 1/n Sum(n(i)).
Brockhaus, Ferraris, Gallus, Long, Martin, and Overhaus (1999) describe a closed-form formula for fade-in options. For a call the value is given by
max(X - S(T), 0) X 1/n Sum(n(i))
describe a closed-form formula for fade-in options. For a call the value is given by
c = 1/n * Sum(S^((b-r)*T) * (M(-d5, d1; -p) - M(-d3, d1; -p)) - Xe^(-rT) * (M(-d6, d2; -p) - M(-d4, d2; -p))
where n is the number of fixings, p = (t1^0.5/T^0.5), t1 = iT/n
d1 = (log(S/X) + (b + v^2/2)*T) / (v * T^0.5) ... d2 = d1 - v*T^0.5
d3 = (log(S/L) + (b + v^2/2)*t1) / (v * t1^0.5) ... d4 = d3 - v*t1^0.5
d5 = (log(S/U) + (b + v^2/2)*t1) / (v * t1^0.5) ... d6 = d5 - v*t1^0.5
The value of a put is similarly
p = 1/n * Sum(Xe^(-rT) * (M(-d6, -d2; -p) - M(-d4, -d2; -p))) - S^((b-r)*T) * (M(-d5, -d1; -p) - M(-d3, -d1; -p)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
Asset price ( S )
Strike price ( K )
Lower barrier ( L )
Upper barrier ( U )
Time to maturity ( T )
Risk-free rate ( r )
Cost of carry ( b )
Volatility ( s )
Fixings ( n )
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
cbnd3() = Cumulative Bivariate Distribution
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Log Contract Ln(S/X) [Loxx]A log contract, first introduced by Neuberger (1994) and Neuberger (1996), is not strictly an option. It is, however, an important building block in volatility derivatives (see Chapter 6 as well as Demeterfi, Derman, Kamal, and Zou, 1999). The payoff from a log contract at maturity T is simply the natural logarithm of the underlying asset divided by the strike price, ln(S/ X). The payoff is thus nonlinear and has many similarities with options. The value of this contract is (via "The Complete Guide to Option Pricing Formulas")
L = e^(-r * T) * (log(S/X) + (b-v^2/2)*T)
The delta of a log contract is
delta = (e^(-r*T) / S)
and the gamma is
gamma = (e^(-r*T) / S^2)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Log Option [Loxx]A log option introduced by Wilmott (2000) has a payoff at maturity equal to max(log(S/X), 0), which is basically an option on the rate of return on the underlying asset with strike log(X). The value of a log option is given by: (via "The Complete Guide to Option Pricing Formulas")
e^−rT * n(d2)σ√(T − t) + e^−rT*(log(S/K) + (b −σ^2/2)T) * N(d2)
where N(*) is the cumulative normal distribution function, n(*) is the normal density function, and
d = ((log(S/X) + (b - v^2/2)*T) / (v*T^0.5)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Log Contract Ln(S) [Loxx]A log contract, first introduced by Neuberger (1994) and Neuberger (1996), is not strictly an option. It is, however, an important building block in volatility derivatives (see Chapter 6 as well as Demeterfi, Derman, Kamal, and Zou, 1999). The payoff from a log contract at maturity T is simply the natural logarithm of the underlying asset divided by the strike price, ln(S/ X). The payoff is thus nonlinear and has many similarities with options. The value of this contract is (via "The Complete Guide to Option Pricing Formulas")
L = e^(-r * T) * (log(S/X) + (b-v^2/2)*T)
The delta of a log contract is
delta = (e^(-r*T) / S)
and the gamma is
gamma = (e^(-r*T) / S^2)
An even simpler version of the log contract is when the payoff simply is ln(S). The payoff is clearly still nonlinear in the underlying asset. It follows that the value of this contract is:
L = e^(-r * T) * (log(S) + (b-v^2/2)*T)
The theta/time decay of a log contract is
theta = - 1/T * v^2
and its exposure to the stock price, delta, is
delta = - 2/T * 1/S
This basically tells you that you need to be long stocks to be delta- neutral at any time. Moreover, the gamma is
gamma = 2 / (T * S^2)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = volatility of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Powered Option [Loxx]At maturity, a powered call option pays off max(S - X, 0)^i and a put pays off max(X - S, 0)^i . Esser (2003 describes how to value these options (see also Jarrow and Turnbull, 1996, Brockhaus, Ferraris, Gallus, Long, Martin, and Overhaus, 1999). (via "The Complete Guide to Option Pricing Formulas")
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = volatility of the underlying asset price
i = power
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
combin(x) = Combination function, calculates the number of possible combinations for two given numbers
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Capped Standard Power Option [Loxx]Power options can lead to very high leverage and thus entail potentially very large losses for short positions in these options. It is therefore common to cap the payoff. The maximum payoff is set to some predefined level C. The payoff at maturity for a capped power call is min . Esser (2003) gives the closed-form solution: (via "The Complete Guide to Option Pricing Formulas")
c = S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * (N(e1) - N(e3)) - e^(-r*T) * (X*N(e2) - (C + X) * N(e4))
while the value of a put is
e1 = (log(S/X^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e3 = (log(S/(C + X)^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e4 = e3 - i * v * T^0.5
In the case of a capped power put, we have
p = e^(-r*T) * (X*N(-e2) - (C + X) * N(-e4)) - S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * (N(-e1) - N(-e3))
where e1 and e2 is as before. e3 and e4 has to be changed to
e3 = (log(S/(X - C)^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e4 = e3 - i * v * T^0.5
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
i = power
c = Capped on pay off
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Standard Power Option [Loxx]Standard power options (aka asymmetric power options) have nonlinear payoff at maturity. For a call, the payoff is max(S^i - X, 0), and for a put, it is max(X - S^i , 0), where i is some power (i > 0). The value of this power call is given by (see Heynen and Kat, 1996c; Zhang, 1998; and Esser, 2003). (via "The Complete Guide to Option Pricing Formulas")
c = S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * N(d1) - X*e^(-r*T) * N(d2)
while the value of a put is
p = X*e^(-r*T) * N(-d2) - S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * N(-d1)
where
d1 = (log(S/X^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
d2 = d1 - i * v * T^0.5
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
pwr = power
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
