Numerical Valuation of Cross-Currency Swaps and Swaptions

30 Pages Posted: 6 Dec 1997

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

J.P. Hutton

Nomura Holdings, Inc. (NHI)

Date Written: October 24, 1996

Abstract

We investigate numerical valuation of cross-currency interest rate-based derivatives under Babbs' extended Vasicek-style model by numerical solution of the associated partial differential equation (PDE), in particular, we consider the terminable differential (diff) swap. Firstly we precisely formulate, in terms of their cash ows, various types of single and cross-currency swaps and swaptions. We describe Babbs' model for the domestic and foreign term structures and the exchange rate, its formulation in terms of three correlated driftless Gaussian processes and the associated three state variable parabolic PDE. We then formulate nine difference approximations to the PDE, and discuss explicit and implicit methods. With this discrete approximation to the valuation problem in a period, we proceed to value the terminable diff swap and other deals numerically by backwards recursion through the payment dates, and investigate the solutions found graphically. We conclude that it is certainly practical, on a fast workstation, to solve for the value function of a wide range of cross-currency derivative securities by solution of explicit nite difference approximations of the PDE.

JEL Classification: G13

Suggested Citation

Dempster, M. A. H. and Hutton, J.P., Numerical Valuation of Cross-Currency Swaps and Swaptions (October 24, 1996). Available at SSRN: https://ssrn.com/abstract=40872 or http://dx.doi.org/10.2139/ssrn.40872

M. A. H. Dempster (Contact Author)

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

J.P. Hutton

Nomura Holdings, Inc. (NHI)

1 St. Martins-le-Grand
Nomura Research Inst Nomura House
London EC1A 4NP
United Kingdom
0171 521 2000 (Phone)

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