A Shannon Wavelet Method for Pricing Foreign Exchange Options under the Heston Multi-Factor CIR Model

30 Pages Posted: 9 Sep 2017

See all articles by Edouard Berthe

Edouard Berthe

University of Queensland; École Centrale Paris

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Luis Ortiz-Gracia

University of Barcelona

Date Written: August 24, 2017

Abstract

We present a robust and highly efficient Shannon wavelet pricing method for plain-vanilla foreign exchange European options under the jump-extended Heston model with multi-factor CIR interest rate dynamics. Under a Monte Carlo and partial differential equation hybrid computational framework, the option price can be expressed as an expectation, conditional on the variance factor, of a convolution product that involves the densities of the time-integrated domestic and foreign multi-factor CIR interest rate processes. We propose an efficient treatment to this convolution product that effectively results in a significant dimension reduction, from two multi-factor interest rate processes to only a one-factor process. By means of a state-of-the-art Shannon wavelet inverse Fourier technique, the resulting convolution product is approximated analytically and the conditional expectation can be computed very efficiently. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and impressive efficiency of the method.

Keywords: hybrid Monte Carlo Partial Differential Equation approach, Shannon wavelet, foreign exchange, multi-factor Cox-Ingersoll-Ross, dimension reduction

Suggested Citation

Berthe, Edouard and Dang, Duy-Minh and Ortiz-Gracia, Luis, A Shannon Wavelet Method for Pricing Foreign Exchange Options under the Heston Multi-Factor CIR Model (August 24, 2017). Available at SSRN: https://ssrn.com/abstract=3033003 or http://dx.doi.org/10.2139/ssrn.3033003

Edouard Berthe

University of Queensland ( email )

St Lucia
Brisbane, Queensland 4072
Australia

École Centrale Paris ( email )

Paris
France

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/

Luis Ortiz-Gracia

University of Barcelona ( email )

Diagonal, 690
08034 Barcelona
Spain

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