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.
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.