An Asymptotic Expansion for Forward-Backward SDEs; A Malliavin Calculus Aproach

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

No CIRJE-F-865, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper proposes a new closed-form approximation scheme for the forward-backward stochastic differential equations (FBSDEs). In particular, we obtain an error estimate for the scheme applying an asymptotic expansion in Malliavin calculus for the forward SDEs combined with the Picard iteration scheme for the BSDEs. We also show a numerical example for pricing options with counterparty risk under Heston model, where the credit value adjustment (CVA) is taken into account.

Pages: 28 pages
Date: 2012-10
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Citations: View citations in EconPapers (6)

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