This paper proposes a new approximation method of pricing barrier and average options under stochastic
volatility environment by applying an asymptotic expansion approach. In particular, a high-order expansion
scheme for general multi-dimensional diffusion processes is effectively applied. Moreover, the paper combines
a static hedging method with the asymptotic expansion method for pricing barrier options. Finally,
numerical examples show that the fourth or fifth-order asymptotic expansion scheme provides sufficiently
accurate approximations under the λ-SABR and SABR models.
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