Summary: 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, introduced by Vercer. In our previous work on pricing Asian options, the volatility is modeled by a fast mean-reverting process. A singular perturbation expansion is used to derive an approximation for option prices. In this paper, we consider an additional slowly varying volatility factor so that the pricing partial differential equation becomes four-dimensional. Using the singular-regular perturbation technique introduced by Fouque-Papanicolaou-Sircar-Solna, we show 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.
For the entire collection see [Zbl 1048.91001].