In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners...

In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners...

This paper proposes a general approximation method for the solutions to second-order parabolic partial differential equations (PDEs) widely used in finance through an extension of L'eandre's approach(L'eandre (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 [9], Yoshida [34] and Takahashi [20], [21] is a widely applicable methodology for an analytic approximation of...

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...

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...

<i>Recent Advances in Financial Engineering 2012</i> is the Proceedings of the International Workshop on Finance 2012, which was held at the University of Tokyo on October 30 and 31, 2012. This workshop was organized by the Center for Advanced Research in Finance (CARF), Graduate School of Economics,...

This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion with multidimensional Malliavin weights to compute...

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...