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

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• 作者：Akihiko Takahashi ; Toshihiro Yamada
• 关键词：Forward–backward stochastic differential equations (FBSDEs) ; Asymptotic expansion ; Malliavin calculus ; CVA ; Local volatility model ; Stochastic volatility model
• 刊名：Asia-Pacific Financial Markets
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：23
• 期：4
• 页码：337-373
• 全文大小：634 KB
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Finance and Banking
  Financial Economics
  International Economics
  Econometrics
  Economic Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-6946
• 卷排序：23

文摘

This paper proposes a new analytical approximation scheme for the representation of the forward–backward stochastic differential equations (FBSDEs) of Ma and Zhang (Ann Appl Probab, 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 is taken into account.