English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In a multi-dimensional diffusion framework, the price of a financialderivative can be expressed as an iterated conditional expectation, where theinner conditional expectation conditions on the future of an auxiliary processthat enters into the dynamics for the spot. Inspired by results from non-linearfiltering theory, we show that this inner conditional expectation solves abackward SPDE (a so-called 'conditional Feynman-Kac formula'), therebyestablishing a connection between SPDE and derivative pricing theory. Unlikesituations considered previously in the literature, the problem at handrequires conditioning on a backward filtration generated by the noise of theauxiliary process and enlarged by its terminal value, leading us to search fora backward Brownian motion in this filtration. This adds an additional sourceof irregularity to the associated SPDE which must be tackled with newtechniques. Moreover, through the conditional Feynman-Kac formula, we establishan alternative class of so-called mixed Monte-Carlo PDE numerical methods forpricing financial derivatives. Finally, we provide a simple demonstration ofthis method by pricing a European put option.

On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula