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A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing

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  • Masaaki Fujii

Abstract

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. Although it requires a special form of the quadratic covariation terms of the continuous part, it allows rather generic drift as well as jump components to exist. The resultant approximation is given by a polynomial function in terms of the unperturbed forward variables whose coefficients are uniquely specified by the solution of the recursive system of linear ODEs. Applications to a jump-extended Heston and lambda-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.

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  • Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," Papers 1405.0378, arXiv.org, revised Dec 2014.
    • Handle: RePEc:arx:papers:1405.0378
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    References listed on IDEAS

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    6. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," Papers 1401.2314, arXiv.org, revised Jul 2014.
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    8. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CIRJE F-Series CIRJE-F-891, CIRJE, Faculty of Economics, University of Tokyo.
    9. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," CARF F-Series CARF-F-348, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," CARF F-Series CARF-F-321, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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