A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives with Target Redemption Features

International Conference of Numerical Analysis and Applied Mathematics, Symposium on Computational Finance, 2010

4 Pages Posted: 19 Jul 2010

See all articles by Christina Christara

Christina Christara

University of Toronto - Department of Computer Science

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Asif Lakhany

Algorithmics Inc.

Date Written: July 19, 2010

Abstract

We propose a general framework for efficient pricing via a partial differential equation (PDE) approach for exotic cross-currency interest rate (IR) derivatives, with strong emphasis on long-dated foreign exchange (FX) IR hybrids, namely Power Reverse Dual Currency (PRDC) swaps with a FX Target Redemption (FX-TARN) provision. The FX-TARN provision provides a cap on the FX-linked PRDC coupon amounts, and once the accumulated coupon amount reaches this cap, the underlying PRDC swap terminates.

Our PDE pricing framework is based on an auxiliary state variable to keep track of the total accumulated PRDC coupon amount. Finite differences on uniform grids and the Alternating Direction Implicit (ADI) method are used for the spatial and time discretizations, respectively, of the model-dependent PDE corresponding to each discretized value of the auxiliary variable. Numerical examples illustrating the convergence properties of the numerical methods are provided.

Keywords: Alternating Direction Implicit, ADI, Power Reverse Dual Currency Swap, PRDC

Suggested Citation

Christara, Christina and Dang, Duy-Minh and Jackson, Kenneth R. and Lakhany, Asif, A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives with Target Redemption Features (July 19, 2010). International Conference of Numerical Analysis and Applied Mathematics, Symposium on Computational Finance, 2010. Available at SSRN: https://ssrn.com/abstract=1645308

Christina Christara (Contact Author)

University of Toronto - Department of Computer Science ( email )

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

Duy-Minh Dang

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

Asif Lakhany

Algorithmics Inc. ( email )

Toronto, Ontario M5T 2C6
Canada

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