Nonlinear Option Pricing

Chapter 13

Marked Branching Diffusions

Les arbres tardifs sont ceux qui portent les meilleurs fruits.

1

— Moli`ere, in Le Malade Imaginaire

In Chapter 7, we introduced first and second order (Markovian) backward

stochastic differential equations (BSDEs). They provide a generalization of

the Feynman-Kac theorem for nonlinear PDEs. Unfortunately, in practice,

numerically solving BSDEs requires the computation of conditional expecta-

tions, typically using regression methods. Finding regressors of good quality

is difficult, notably for multi-asset portfolios. This leads us to introduce a

new promising method based on branching diffusions describing a marked

Galton-W ...