Partial Differential Equation Pricing of Contingent Claims Under Stochastic Correlation

SIAM Journal on Scientific Computing, Forthcoming

32 Pages Posted: 27 Nov 2017 Last revised: 8 Dec 2017

See all articles by Nat Leung

Nat Leung

University of Toronto - Department of Computer Science

Christina Christara

University of Toronto - Department of Computer Science

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Date Written: October 1, 2017

Abstract

In this paper, we study a partial differential equation (PDE) framework for option pricing where the underlying factors exhibit stochastic correlation, with an emphasis on computation. We derive a multi-dimensional time-dependent PDE for the corresponding pricing problem, and present a numerical PDE solution. We prove a stability result, and study numerical issues regarding the boundary conditions used. Moreover, we develop and analyze an asymptotic analytical approximation to the solution, leading to a novel computational asymptotic approach based on quadrature with a perturbed transition density. Numerical results are presented to verify second order convergence of the numerical PDE solution and to demonstrate its agreement with the asymptotic approximation and Monte Carlo simulations. The effect of certain problem parameters to the PDE solution, as well as to the asymptotic approximation solution, is also studied.

Keywords: Stochastic Correlation, Option Pricing, Numerical Solution, Asymptotic Solution, Partial Differential Equation

JEL Classification: C63

Suggested Citation

Leung, Nat and Christara, Christina and Dang, Duy-Minh, Partial Differential Equation Pricing of Contingent Claims Under Stochastic Correlation (October 1, 2017). SIAM Journal on Scientific Computing, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3075837 or http://dx.doi.org/10.2139/ssrn.3075837

Nat Leung

University of Toronto - Department of Computer Science ( email )

Sandford Fleming Building
King’s College Road, Room 3302
Toronto, Ontario M5S 3G4
Canada

Christina Christara

University of Toronto - Department of Computer Science ( email )

Department of Computer Science
University of Toronto
Toronto, Ontario M5S 3G4
Canada

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

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