Using Antithetic Sampling for Both Heston Model Processes

Summary

The document asks how to apply antithetic sampling when simulating the Heston stochastic volatility model with a discretized process. The central issue is whether to reverse the random draws only for the stock price or for both the price and variance processes.

The responses recommend using antithetic draws for both processes because the model samples normal variables for price and volatility, and the underlying’s movement depends on the volatility state. They also point out that the variance process follows a CIR process and that discretization schemes more suitable than basic Euler may be available. The discussion offers implementation guidance but provides no derivation, comparison of variance reduction, or quantitative evidence; results will depend on the discretization and simulation setup.

Key ideas

• Antithetic sampling pairs simulations using opposite random draws to reduce estimator variance.
• The Heston simulation includes randomness in both the underlying price and its variance process.
• The responses recommend applying antithetic sampling to both processes.
• The price process depends on the variance process, so treating them separately may miss their relationship.
• The variance process follows CIR dynamics, for which alternatives to basic Euler discretization may be considered.

Tags

# Heston Model and antithetic variables


# Heston Model and antithetic variables












I was implementing some variance reduction techniques for the heston model and came up with a question when implementing the antithetic variable technique. Namely, I was not sure if I had to implement it into the stochastic process (discretized process with the Euler scheme for the underlying and the volatility process) for the underlying and also for the volatility or would it be enough just to implement it in the stock price process?

## Answer by Dhruv Mahajan (score 1)

https://quant.stackexchange.com/a/50251

Antithetic Sampling is used to reduce variance in simulation by sampling from two 'opposite' set of distributions. Since in Heston models you require sampling from normal for both the price and volatility, it would be better to use antithetic sampling for both.

## Answer by siou0107 (score 0)

https://quant.stackexchange.com/a/50250

Not sure I understand well your question, but in a stochastic volatility model you have to implement your discretised process for both underlying and volatility since the underlying's move are conditional on the volatility process value.

Note that more efficient discretisation schemes as Euler exist for the CIR process followed by variance in Heston's model :)

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