A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model

This paper studies the approximation accuracy of a singular perturbation method for option pricing up to the second order under a stochastic volatility model. First, numerical experiments confirm that the first order approximation provides sufficiently accurate option prices in a fast mean-reversion volatility case. On the other hand, it creates relatively large errors in a non-fast mean-reversion volatility environment. Then, the second order approximation formula is derived and the improvement of the approximation is investigated