Heston Option Pricer

Compute European call option price using the Heston model and a conditional Monte-Carlo method

Compute European call option price using the Heston model and a conditional Monte-Carlo method

[call_prices, std_errs] = Heston(S0, r, V0, eta, theta, kappa, strike, T, M, N)

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INPUTS:

S0 - Current price of the underlying asset.
r - Annualized continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number.

Heston Parameters:
V0 - Current variance of the underlying asset
eta - volatility of volatility
theta - long-term mean
kappa - rate of mean-reversion

strike - Vector of strike prices of the option
T - Time to expiration of the option, expressed in years.
N - Number of time steps per path
M - Number of paths (Monte-Carlo simulations)

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OUTPUTS:

call_prices - Prices (i.e., value) of a vector of European call options.

std_err - Standard deviation of the error due to the Monte-Carlo simulation:
(std_err = std(sample)/sqrt(length(sample)))

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Example:

S0 = 100; r = 0.02;
V0 = 0.04; eta = 0.7; theta = 0.06; kappa = 1.5;
strike = 85:5:115; T = 0.25
M = 2000; % Number of paths.
N = 250; % Number of time steps per path

[call_prices, std_errs] = Heston(S0, r, V0, eta, theta, kappa, strike, T, M, N)

call_prices =
15.9804 11.4069 7.2125 3.9295 2.1213 1.2922 0.8625

std_errs =
0.0198 0.0263 0.0329 0.0367 0.0357 0.0315 0.0268

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I thank Roger Lee for his MSFM course at the University of Chicago