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

Masaaki Fujii
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Masaaki Fujii: Faculty of Economics, The University of Tokyo

No CIRJE-F-931, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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 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 λ-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.

Pages: 36 pages
Date: 2014-05
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