An Efficient Numerical PDE Approach for Pricing Foreign Exchange Interest Rate Hybrid Derivatives

38 Pages Posted: 26 Mar 2012 Last revised: 5 May 2013

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: March 24, 2012

Abstract

We discuss efficient pricing methods via a Partial Differential Equation (PDE) approach for long dated foreign exchange (FX) interest rate hybrids under a three-factor multi-currency pricing model with FX volatility skew. The emphasis of the paper is on Power-Reverse Dual-Currency (PRDC) swaps with popular exotic features, namely knockout and FX Target Redemption (FX-TARN). Challenges in pricing these derivatives via a PDE approach arise from the high-dimensionality of the model PDE, as well as from the complexities in handling the exotic features, especially in the case of the FX-TARN provision, due to its path-dependency. Our proposed PDE pricing framework for FX-TARN PRDC swaps is based on partitioning the pricing problem into several independent pricing sub-problems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these pricing sub-problems can be viewed as equivalent to a knockout PRDC swap with a known time-dependent barrier, and requires a solution of the model PDE, which, in our case, is a time-dependent parabolic PDE in three space dimensions. Finite difference schemes on non-uniform grids are used for the spatial discretization of the model PDE, and the Alternating Direction Implicit (ADI) timestepping methods are employed for its time discretization. Numerical examples illustrating the convergence properties and efficiency of the numerical methods are provided.

Keywords: Power-Reverse Dual-Currency (PRDC) swaps, Target Redemption (TARN), knockout, Partial Differential Equation (PDE), finite differences,non-uniform grids

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

Suggested Citation

Dang, Duy-Minh and Christara, Christina and Jackson, Kenneth R. and Lakhany, Asif, An Efficient Numerical PDE Approach for Pricing Foreign Exchange Interest Rate Hybrid Derivatives (March 24, 2012). Available at SSRN: https://ssrn.com/abstract=2028519 or http://dx.doi.org/10.2139/ssrn.2028519

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

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