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

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.