Variance Reduction for Monte Carlo Simulation

A Combined Method: Importance Sampling + Control Variates

Posted by Yu-Ting Chen  •  Filed under Derivatives Pricing

Call Option Calculators Under the Heston Model

$$ dS_t = S_t(r dt + \sqrt{V_t} dW_t^S), $$ $$ dV_t = \kappa(\theta-V_t)dt+\sigma\sqrt{V_t}d W_t^V, $$ $$ dW_t^S dW_t^V =\rho dt.$$
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
Call Option PriceStandard ErrorComputational Time (sec.)
Crude Monte Carlo
Monte Carlo with Importance Sampling and Control Variates

The calculation is based on Monte Carlo method with and without our combined technique (Importance Sampling + Control Variates).

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

Tagged: Monte Carlo, Exotic Option

 •  June 13, 2016  • 

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