On stochastic partial differential equations and their applications to derivative pricing through a conditional Feynman-Kac formula
Abstract
The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a 'conditional Feynman-Kac formula'). The problem requires conditioning on a backward filtration generated by the noise of the auxiliary process and enlarged by its terminal value, leading us to search for a backward Brownian motion here. This adds a source of irregularity to the SPDE which we tackle with new techniques. Lastly, we establish a new class of mixed Monte-Carlo PDE numerical methods.
Fields of Study & Subjects
Stochastic processes and financial applications
Stochastic processes and statistical mechanics
Complex Systems and Time Series Analysis
Publication details
- Journal / source
- Stochastic Processes and their Applications
- Volume
- 195
- Pages
- 104886–104886
- Publication date
- 16 January 2026
- Language
- EN