A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option Pricing
38 Pages Posted: 3 May 2014 Last revised: 22 Dec 2014
Date Written: December 22, 2014
Abstract
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed. The perturbation parameter “ϵ” 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 λ-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.
Keywords: stochastic control, asymptotic expansion, BSDE, Heston, SABR
JEL Classification: C61, G11, G12
Suggested Citation: Suggested Citation
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