# FunctionBlackScholes

Library "FunctionBlackScholes"
Some methods for the Black Scholes Options Model, which demonstrates several approaches to the valuation of a European call.

// reference:
// people.math.sc.edu/B...s/black_scholes.html
// people.math.sc.edu/B...les/black_scholes.py

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.

v2 fixed some issues.
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