In this paper, we propose an efficient Monte Carlo implementation of a non-linear FBSDE as a system of interacting particles inspired by the idea of the branching diffusion method of McKean. It will be particularly useful to investigate large and complex systems, and hence it is a good...

This paper provides a survey on an asymptotic expansion approach to valuation and hedging problems in nance. The asymptotic expansion is a widely applicable methodology for analytical approximations of expectations of certain Wiener functionals. Hence not only academic researchers but also...

This study proposes a new scheme for static hedging of European path‐independent derivatives under stochastic volatility models. First, we show that pricing European path‐independent derivatives under stochastic volatility models is transformed to pricing those under one‐factor local...

This study proposes a new approximation formula for pricing average options on commodities under a stochastic volatility environment. In particular, it derives an option pricing formula under Heston and an extended λ‐SABR stochastic volatility models (which includes an extended SABR model as...

This study proposes a new scheme for the static replication of European options and their portfolios. First, a general approximation formula for efficient static replication as an extension of Carr P. and Chou A. (1997, 2002) and Carr P. and Wu L. (2002) is derived. Second, a concrete procedure...

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

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 applies "Dykstra's cyclic projections algorithm" for its implementation. Numerical examples for...

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,...

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...