Black-Scholes Probability Model with Time-Based Volatility

I developed this tool to automate probability calculations and to verify if Polymarkets accurately reflects Bitcoin's value. The indicator uses a modified Black-Scholes model to estimate the likelihood of Bitcoin exceeding or falling below a $97,000 strike price by a specified end date, providing a "fair value" probability.

Key Features:

- Timeframe Control: Displays data only between a defined start and end date, ensuring relevance during the prediction period.

- Dynamic Volatility Calculation: Offers a choice between manual input and auto-calculated annualized volatility. The auto-calculation derives historical volatility from recent price data over a selected lookback period and adjusts it based on the time remaining until expiration. More time implies greater expected price movement; less time indicates a narrower expected range.

- Probability Estimation: Calculates an adjusted parameter (d1) and applies a normal cumulative distribution function (CDF) to determine:
- "Yes" (Green Line): Probability that Bitcoin will exceed $97,000.
- "No" (Red Line): Probability that Bitcoin will remain below $97,000.

When Bitcoin's price is exactly $97,000, the tool sets the probabilities to a balanced 50/50 split, indicating fair value.

- Fair Value Indicator: Includes a static white reference line at 50% probability. A 50/50 probability suggests Bitcoin is fairly valued at $97,000; deviations indicate potential overvaluation or undervaluation.

- Polymarkets Tracking & Trading Strategy: I use Polymarkets to access cost-effective, high-leverage long call options on Bitcoin. However, these options don't always mirror Bitcoin's price movements precisely. For instance, if I anticipate Bitcoin rising from $95,000 to $97,000 by day's end, the tool might show a fair value probability of 50%. If Polymarkets quotes a 50% chance, the alignment indicates a fair trade. In such cases, I can avoid an unfavorable trade or exploit the difference as an arbitrage opportunity.

- Personal Motivation: This indicator eliminates the need for manual calculations and ensures I can quickly assess when Polymarkets' pricing aligns with Bitcoin's actual value, leading to more informed trading decisions.

This tool automates probability and fair value assessments, serving as a practical resource for verifying and potentially capitalizing on discrepancies in Polymarkets' Bitcoin pricing. It helps identify when there's a mismatch between the market's implied probability and the calculated fair value, allowing me to avoid unnecessary premiums on high-leverage options.