Stochastic Volatility and Epsilon-Martingale Decomposition

We address the problems of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. We show that when volatility is stochastic but fast mean reverting Black-Scholes pricing theory can be corrected. The correction accounts for the effect of stochastic volatility and the associated market price of risk. For European derivatives it is given by explicit formulas which involve parsimonous parameters directly calibrated from the implied volatility surface. The method presented here is based on a martingale decomposition result which enables us to treat nonMarkovian models as well. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.