Conditional moment matching approximations by stochastic bridges for exponential Brownian functionals

Nicolas Privault
Nanyang Technological Univ., Singapore

Abstract: Using Doob transform techniques we will derive closed-form expectations for exponential functionals of Brownian motion in several settings, including Brownian motion on matrix Lie groups. We will also propose numerical approximations constructed by conditional moment matching and stochastic bridges, which turn out to be numerically more stable than closed form expressions.
Applications to option pricing will be mentioned.