Library "FunctionBlackScholes" Some methods for the Black Scholes Options Model, which demonstrates several approaches to the valuation of a European call.
asset_path(s0, mu, sigma, t1, n) Simulates the behavior of an asset price over time. Parameters: s0: float, asset price at time 0. mu: float, growth rate. sigma: float, volatility. t1: float, time to expiry date. n: int, time steps to expiry date. Returns: option values at each equal timed step (0 -> t1)
binomial(s0, e, r, sigma, t1, m) Uses the binomial method for a European call. Parameters: s0: float, asset price at time 0. e: float, exercise price. r: float, interest rate. sigma: float, volatility. t1: float, time to expiry date. m: int, time steps to expiry date. Returns: option value at time 0.
bsf(s0, t0, e, r, sigma, t1) Evaluates the Black-Scholes formula for a European call. Parameters: s0: float, asset price at time 0. t0: float, time at which the price is known. e: float, exercise price. r: float, interest rate. sigma: float, volatility. t1: float, time to expiry date. Returns: option value at time 0.
forward(e, r, sigma, t1, nx, nt, smax) Forward difference method to value a European call option. Parameters: e: float, exercise price. r: float, interest rate. sigma: float, volatility. t1: float, time to expiry date. nx: int, number of space steps in interval (0, L). nt: int, number of time steps. smax: float, maximum value of S to consider. Returns: option values for the european call, float array of size ((nx-1) * (nt+1)).
mc(s0, e, r, sigma, t1, m) Uses Monte Carlo valuation on a European call. Parameters: s0: float, asset price at time 0. e: float, exercise price. r: float, interest rate. sigma: float, volatility. t1: float, time to expiry date. m: int, time steps to expiry date. Returns: confidence interval for the estimated range of valuation.