A change of measure formula for recursive conditional expectations

TL;DR

This paper develops a change of measure formula for recursive conditional expectations in jump-diffusion models, enabling advanced financial pricing techniques involving multiple interest rates and collateralization.

Contribution

It introduces a novel representation for the value process of FBSDEs under multiple measures, generalizing the change of numéraire method for complex financial settings.

Findings

Derived a new representation for FBSDE solutions in jump-diffusion models

Extended change of numéraire technique to multiple interest rates

Facilitated recursive pricing formulas in collateralized markets

Abstract

In this paper, we derive a representation for the value process associated to the solutions of FBSDEs in a jump-diffusion setting under multiple probability measures. Motivated by concrete financial problems, the latter representations are then applied to devise a generalization of the change of num\'eraire technique allowing to obtain recursive pricing formulas in the presence of multiple interest rates and collateralization.