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

no code implementations • 28 Jun 2021 • Kaustav Das, Ivan Guo, Grégoire Loeper

In a multi-dimensional diffusion framework, the price of a financial derivative can be expressed as an iterated conditional expectation, where the inner conditional expectation conditions on the future of an auxiliary process that enters into the dynamics for the spot.

Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework

no code implementations • 2 Jun 2020 • Kaustav Das, Nicolas Langrené

We obtain an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters.

Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility

no code implementations • 19 Dec 2018 • Kaustav Das, Nicolas Langrené

We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters.