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

　　 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 <em>small-diffusion</em> 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 <em> unperturbed</em> 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.