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.-SABR and SABR models.
|