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

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Toshihiro Yamada: Graduate School of Economics, Hitotsubashi University

No CIRJE-F-1009, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 27 pages
Date: 2016-04
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2016cf1009

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