When volatility is stochastic the market is incomplete and there is an infinite number of equivalent martingale measures. This paper analyzes the situation where we have a sequence of stochastic volatility models which converge in the limit to a complete market model with deterministic volatility. We examine the convergence of derivative prices as the stochastic volatility model converges to its deterministic limit. Using some recent results from large deviation theory we are able to identify the speed of convergence and establish some theoretical results which will be used to analyze the hedging risk in stochastic volatility models.
(Joint work with Phelim Boyle and Feng Shui)