In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The wellknown decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise...

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...

The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literature treats the MVH problem by the duality method, here we study an equivalent system...

This paper studies impacts of imperfect collateralization on derivatives values. Firstly, we present a general framework for the analysis in a multi-dimensional diffusion setting, and then calclate pre-default values of forwards and options for the numerical experiments. In particular, we...

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in best approximation in an inner product space. Moreover, we apply "Dykstra's cyclic projections algorithm" for its implementation. Numerical examples for...

This paper develops a new approximation formula for pricing basket options in a local-stochastic volatility model with jumps. In particular, the model admits local volatility functions and jump components in not only the underlying asset price processes, but also the volatility processes. To the...