Abstract
We study the problem of pricing arithmetic Asian options when the underlying is driven by stochastic volatility models with two well-separated characteristic time scales. The inherently path-dependent feature of Asian options can be efficiently treated by applying a change of numeraire, introducedby Vercer. In our previous work on pricing Asian options, the volatility is modeled by a fast mean-reverting process. A singular perturbation expansionis used to derive an approximation for option prices. In this paper, we consider an additional slowly varying volatility factor so that the pricing partialdifferential equation becomes four-dimensional. Using the singular-regular perturbation technique introduced by Fouque-Papanicolaou-Sircar-Solna, weshow that the four-dimensional pricing partial differential equation can be approximated by solving a pair of one-dimensional partial differential equations,which takes into account the full term structure of implied volatility.