Using the Stock Price as a Heston Monte Carlo Control Variate

Summary

The document asks how to reduce Monte Carlo estimation error when pricing vanilla options under the Heston stochastic volatility model. The questioner reports that Black–Scholes controls using implied, average, or long-term volatility have not worked well, and asks for alternatives.

The accepted response recommends the stock price as a control variate, citing a standard Monte Carlo reference and a paper on efficient simulation of Heston. A control variate uses a related quantity with known expectation to reduce estimator variance; the cited sources are said to report that the stock-price approach works well in this setting. The document does not provide implementation details, numerical comparisons, or conditions under which the approach is most effective, so readers would need to consult those references to assess performance for a particular simulation scheme.

Key ideas

• A control variate can reduce Monte Carlo pricing variance by using a related quantity with known expectation.
• The response recommends the stock price as a control variate for vanilla options in Heston.
• The questioner reports limited success with several Black–Scholes volatility-based controls.
• The supporting references are cited, but the document gives no implementation or comparative results.

Tags

# Control variate for Heston model


# Control variate for Heston model












Does anyone have suggestions for potential control variates for vanillas in a Heston model? I've tried black scholes with implied volatility, average volatility and long term volatility all without great success, so I'm hoping you guys got an idea.

## Answer by user1157 (score 3, accepted)

https://quant.stackexchange.com/a/10045

Glassermans's book suggests the stock price as the default idea for a control variate. In this paper, "Efficient, almost exact simulation of the Heston stochastic volatility model", by Haastrecht and Pelsser, (2008) the authors claim that this approach also works well for the Heston model (see appendix A2).

The book is very approachable and available online: Monte Carlo Methods in Financial Engineering, Paul Glasserman, 2003.

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