Solving backward stochastic differential equations using the cubature method. Application to nonlinear pricing

摘要

We propose a new algorithm for the numerical solution of backward stochastic differential equations (BSDEs) with the terminal condition being a function of X_T, where X = {X_t, t∈ [0,T]} is the solution to a standard stochastic differ-ential equation. Using the property that the solution of a BSDE can be written as an integral of a certain functional against the law of the underlying diffu-sion, this new algorithm combines the Bouchard-Touzi~1-Zhang~2 discretization of BSDEs with a weak approximation method known as cubature on Wiener space, constructed by Lyons and Victoir.3 The main results concerning the propagation of the error are reported and a numerical example is included.