A Dimension and Variance Reduction Monte-Carlo Method for Option Pricing under Jump-Diffusion Models

35 Pages Posted: 9 Sep 2017

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Scott Sues

University of Queensland - School of Mathematics and Physics

Date Written: April 8, 2016

Abstract

We develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (i) the analytical tractability of the conditional PIDE is fully determined by that of the Black-Scholes-Merton model augmented with the same jump component as in our model, and (ii) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient.

Keywords: conditional Monte Carlo, variance reduction, dimension reduction, partial-integro~differential~equations, jump diffusions, fast Fourier transform, normal, double-exponential

Suggested Citation

Dang, Duy-Minh and Jackson, Kenneth R. and Sues, Scott, A Dimension and Variance Reduction Monte-Carlo Method for Option Pricing under Jump-Diffusion Models (April 8, 2016). Available at SSRN: https://ssrn.com/abstract=3032980 or http://dx.doi.org/10.2139/ssrn.3032980

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/

Kenneth R. Jackson

University of Toronto - Department of Computer Science ( email )

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

Scott Sues

University of Queensland - School of Mathematics and Physics

Brisbane
St Lucia, QLD 4072
Australia

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