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....

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....

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [6] and Yoshida [29] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. Mathematically, this methodology is justified by Watanabe...

Recently, not only academic researchers but also many practitioners have used the methodology so-called "an asymptotic expansion method" in their proposed techniques for a variety of financial issues. e.g. pricing or hedging complex derivatives under high-dimensional stochastic environments....

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional...

This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. An asymptotic expansion method in finance initiated by Kunitomo and Takahashi[9], Yoshida[34] and Takahashi [20], [21] is a widely applicable methodology for an analytic approximation of the...

This paper derives an approximation formula for average options under two stochastic volatility models such as Heston and ă(Lambda)-SABR models by using an asymptotic expansion method. Moreover, numerical examples with various parameters some of which are obtained by calibration to WTI...