FunctionBlackScholes

17 janv. 2022

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/Burkardt/py_src/black_scholes/black_scholes.html
// people.math.sc.edu/Burkardt/py_src/black_scholes/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.

17 janv. 2022

Notes de version

v2 fixed some issues.