A Krylov Subspace Method for Option Pricing

22 Pages Posted: 30 Mar 2011

See all articles by Jitse Niesen

Jitse Niesen

School of Mathematics, University of Leeds

Will M. Wright

University of Melbourne - Centre for Actuarial Studies

Date Written: March 30, 2011

Abstract

We consider the pricing of financial contracts that are based on two or three underlyings and are modelled using time dependent linear parabolic partial differential equations (PDEs). To provide accurate and efficient numerical approximations to the financial contract's value, we decompose the numerical solution into two parts. The first part involves the spatial discretization, using finite difference methods of the governing PDE. From this a large system of ordinary differential equations (ODEs) with a special affine structure is obtained. On the second part, we develop highly efficient numerical methods to approximate the exact solution of the system of ODEs with a high level of accuracy. We compare our approach, which is based of Krylov subspace methods, with the Crank-Nicolson and Alternating Direct Implicit (ADI) methods on Rainbow and Basket options, European call options using Heston stochastic volatility, and power reverse dual currency (PRDC) swaps with Bermudan and knockout features.

Keywords: Option pricing, Exponential integrator, Krylov subspace method, Heston stochastic volatility, PRDC swaps

Suggested Citation

Niesen, Jitse and Wright, Will M., A Krylov Subspace Method for Option Pricing (March 30, 2011). Available at SSRN: https://ssrn.com/abstract=1799124 or http://dx.doi.org/10.2139/ssrn.1799124

Jitse Niesen

School of Mathematics, University of Leeds ( email )

Leeds LS2 9JT
United Kingdom

HOME PAGE: http://www.maths.leeds.ac.uk/~jitse/

Will M. Wright (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Centre for Actuarial Studies
Melbourne, 3010
Australia

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