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Heston Option Pricer

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

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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

*******************************************************************************

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

Comments and Ratings (1)

Daniel

Daniel (view profile)

Hi Rodolph,
Quick question, where does rho fit in, in all of this?

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