Analytical Approximations of BSDEs with Non-Smooth Driver
Gobet E., Pagliarani S., SIAM J. Finan. Math., 6(1), 919–958. DOI:10.1137/14100021X
40 Pages Posted: 12 Jun 2014 Last revised: 17 Nov 2016
Date Written: December 15, 2014
We provide and analyze analytical approximations of BSDEs in the limit of small non-linearity and short time, in the case of non-smooth drivers. We identify the first and the second order approximations within this asymptotics and consider two topical financial applications: the two interest rates problem and the Funding Value Adjustment. In high dimensional diffusion setting, we show how to compute explicitly the first order formula by taking advantage of recent proxy techniques. Numerical tests up to dimension 10 illustrate the efficiency of the numerical schemes.
Keywords: backward stochastic differential equation, asymptotic expansion
JEL Classification: C30, E10
Suggested Citation: Suggested Citation