Recently academic researchers and practitioners have use the asymptotic expansion method to examine a variety of financial issues under high-dimensional stochastic environments. This methodology is mathematically justified by Watanabe theory (Watanabe, 1987), and Malliavin calculus (Yoshida,...

The stochastic volatility model of Heston (Rev Financ Stud 6(2):327–343, <CitationRef CitationID="CR19">1993</CitationRef>) has found difficulty in describing some of the important features of implied volatility dynamics, leading to a quest for multifactor extensions as well as the incorporation of time-dependent model parameters. In...</citationref>

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with...

The quasi-likelihood estimator and the Bayesian type estimator of the volatility parameter are in general asymptotically mixed normal. In case the limit is normal, the asymptotic expansion was derived by Yoshida [28] as an application of the martingale expansion. The expansion for the...

This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. The asymptotic expansion method in finance initiated by Kunitomo and Takahashi (1992), Yoshida (1992b) and Takahashi (1995, 1999) is a widely applicable methodology for an analytic...