A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model
Posted: 18 Jun 2009 Last revised: 10 Nov 2009
Date Written: July 8, 2009
Abstract
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.
Keywords: option pricing, stochastic volatility, partial differential equation, singular perturbation, approximation accuracy
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