Pricing Barrier and Average Options under Stochastic Volatility Environment

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.Revised version of CIRJE-F-682 (2009); subsequently published in the Journal of Computational Finance, Volume 14/Number 2, Winter 2011/12.本文フィルはリンク先を参照のこ