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?
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2 Answers
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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.
answered Dec 12, 2019 at 10:26
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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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$\begingroup$ My question was more related to the antithetic variable. I did the discretization for both the stock and volatility, but I was unsure if I want to use antithetic variables to reduce the variance of the processes, if I needed to implement it in both processes too or is it enough if I just use it in the stock price process. $\endgroup$ Commented Dec 12, 2019 at 11:09