• Corpus ID: 235658042

On Stochastic PDEs for the pricing of derivatives in a multi-dimensional diffusion framework

  title={On Stochastic PDEs for the pricing of derivatives in a multi-dimensional diffusion framework},
  author={Kaustav Das and Ivan Guo and Gr{\'e}goire 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. Inspired by results from non-linear filtering theory, we show that this inner conditional expectation solves a backward SPDE (a so-called ‘conditional Feynman-Kac formula’), thereby establishing a connection between SPDE and… 

Tables from this paper



A mixed PDE/Monte-Carlo method for stochastic volatility models

Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results

This paper uses the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develops a closed-form series expansion in powers of correlation, to propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas.

Mixing monte-carlo and partial differential equations for pricing options

There is a need for very fast option pricers when the financial objects are modeled by complex systems of stochastic differential equations. Here the authors investigate option pricers based on mixed

Mixing LSMC and PDE Methods to Price Bermudan Options

We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated

Stochastic partial differential equations and filtering of diffusion processes

We establish basic results on existence and uniqueness for the solution of stochastic PDE's. We express the solution of a backward linear stochastic PDE in terms of the conditional law of a partially

A Mixed Monte Carlo and Partial Differential Equation Variance Reduction Method for Foreign Exchange Options Under the Heston–Cox–Ingersoll–Ross Model

In this paper, we consider the valuation of European and path-dependent options in foreign exchange markets when the currency exchange rate evolves according to the Heston model combined with the

quations du filtrage non linaire de la prdiction et du lissage

We establish equations of non linear filtering, prediction (extrapolation) and smoothing (interpolation) in the case where the signal is a non degenerate diffusion process, and the observation is a

Grossissement d'une filtration et retournement du temps d'une diffusion

Notre m6thode consiste ~ identifier {Wt } ,en r6solvant un probl~me de grossissement de filtration . On pourrait probablement d6duire le r@sultat ci-dessous de ceux de Jeulin [4] et de Jacod [3] ,

Stochastic partial differential equations and diffusion processes

CONTENTS § 1. Introduction § 2. Solubility of the direct and inverse Cauchy problems § 3. The direct equation of inverse diffusion. The method of variation of constants § 4. The method of