We shall propose a new computational scheme for the evaluation of the optimal portfolio for investment.Our method is based on an extension of the asymptotic expansion approach which has been recently developed for pricing problems of the contingent claims' analysis by Kunitomo-Takahashi (1992,...

This paper presents a new approximation formula for pricing swaptions and caps/floors under the LIBOR market model of interest rates (LMM) with the local and affine-type stochastic volatility. In particular, two approximation methods are applied in pricing, one of which is so called...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin...

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the...

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation...

This paper proposes a general approximation method for the solution to a second-order parabolic partial differential equation(PDE) widely used in finance through an extension of Leandre's approach (Leandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997)) in Malliavin...

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...

In this work, we have presented a simple analytical approximation scheme for the generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out recursive...

In the forthcoming ISDA Standard Credit Support Annex (SCSA), the trades denominated in non-G5 currencies as well as those include multiple currencies are expected to be allocated to the USD silo, where the contracts are collateralized by USD cash, or a different currency with an appropriate...