Multiscale Asymptotics of Partial Hedging

We consider the problem of partial hedging of an European derivative under the assumption that the volatility is stochastic, driven by two diffusion processes, one fast mean reverting and the other varying slowly. For options with long maturities typically beyond 90 days, the singular perturbation analysis in [Partial Hedging in a Stochastic Volatility Environment, M. Jonsson and K.R. Sircar, Mathematical Finance, 12, pp. 375-409, 2002] ignores the slow factor. In this paper, we investigate the full two factors model and show how an additional term can be included in the approximate value functions and strategies.