Discussion Papers 2016

CIRJE-F-1009

"An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach"

Author Name

Takahashi, Akihiko and Toshihiro Yamada

Date

April 2016

Full Paper

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Remarks

Revised in September 2016; forthcoming in Asia-Pacific Financial Markets, December 2016, Volume 23, Issue 4, Pages 337-373.

Abstract

This paper proposes a new analytical approximation scheme for the representation of the forward- backward stochastic differential equations (FBSDEs) of Ma and Zhang (2002). In particular, we obtain an error estimate for the scheme applying Malliavin calculus method for the forward SDEs combined with the Picard iteration scheme for the BSDEs. We also show numerical examples for pricing option with counterparty risk under local and stochastic volatility models, where the credit value adjustment (CVA) is taken into account.

Keywords: Forward-Backward Stochastic Differential Equations (FBSDEs), Asymptotic expansion, Malliavin calculus, CVA, Local volatility model, Stochastic volatility model