A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives

11 Pages Posted: 10 Nov 2009 Last revised: 2 May 2010

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Christina Christara

University of Toronto - Department of Computer Science

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Asif Lakhany

Algorithmics Inc.

Date Written: November 8, 2009

Abstract

We propose a general framework for efficient pricing via a Partial Differential Equation (PDE) approach of cross-currency interest rate derivatives under the Hull-White model. In particular, we focus on pricing long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. We formulate the problem in terms of three correlated processes that incorporate FX skew via a local volatility function. This formulation results in a time dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE. The Crank-Nicolson (CN) method and the Alternating Direction Implicit (ADI) method are considered for the time discretization. In the former case, the preconditioned Generalized Minimal Residual (GMRES) method is employed for the solution of the resulting block banded linear system at each time step, with the preconditioner solved by Fast Fourier Transform (FFT) techniques. Numerical results indicate that the numerical methods considered are second-order convergent, and, asymptotically, as the discretization granularity increases, almost optimal, with the ADI method being modestly more efficient than CN-GMRES-FFT. An analysis of the impact of the FX volatility skew on the PRDC swaps' prices is presented, showing that the FX volatility skew results in lower prices (i.e. profits) for the payer of PRDC coupons.

Keywords: Power Reverse Dual Currency swaps, Bermudan cancelable, Partial Differential Equation PDE, Alternating Direction Implicit, Generalized Minimal Residual GMRES, Fast Fourier Transform FFT

JEL Classification: E40, E43, G12, G13, C61, C63

Suggested Citation

Dang, Duy-Minh and Christara, Christina and Jackson, Kenneth R. and Lakhany, Asif, A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives (November 8, 2009). Available at SSRN: https://ssrn.com/abstract=1502302 or http://dx.doi.org/10.2139/ssrn.1502302

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/

Christina Christara

University of Toronto - Department of Computer Science ( email )

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

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

Asif Lakhany

Algorithmics Inc. ( email )

Toronto, Ontario M5T 2C6
Canada

Register to save articles to
your library

Register

Paper statistics

Downloads
1,180
Abstract Views
4,058
rank
16,906
PlumX Metrics