## Variance Reduction for Monte Carlo Simulation

Control Variates Technique

Posted by Yu-Ting Chen  •  Filed under Derivatives Pricing

Call Option Calculators Under the Heston Model

$$dS_t = S_t(r dt + \sqrt{V_t} dW_t^S),$$ $$dV_t = \kappa(\theta-V_t)dt+\sigma\sqrt{V_t}d W_t^V,$$ $$dW_t^S dW_t^V =\rho dt.$$
 Input: Initial underlying asset price Initial volatility (annulized) Strike price Time to maturity Years $r:$ Risk free interest rate (annulized) $\kappa:$ Rate of mean reversion of $V$ $\theta:$ Long term mean level of $V$ $\sigma:$ Volatility of V (annulized) $\rho:$ Correlation of underlying asset and $V$ Number of partitions Number of paths
 Output: Call Option Price Standard Error Computational Time (sec.) Crude Monte Carlo Monte Carlo with Control Variates

The calculation is based on Monte Carlo method with and without Control Variates technique.

Go Back to Heston Pricer Collection implemented by Yu-Ting Chen

Tagged: Monte Carlo, Exotic Option

•  June 13, 2016  •

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