On Numerical Methods for Spread Options

31 Pages Posted: 16 Jan 2018

See all articles by Mesias Alfeus

Mesias Alfeus

Department of Statistics and Actuarial Science - Stellenbosch University

Erik Schlögl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management; Faculty of Science, Department of Statistics, University of Johannesburg; Financial Research Network (FIRN)

Date Written: January 11, 2018

Abstract

Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial variables. In most cases, analytically closed form solutions for pricing such payoffs are not available, and the application of numerical pricing methods turns out to be non-trivial. We consider several such non-trivial cases and explore the performance of the highly efficient numerical technique of Hurd and Zhou (2010), comparing this with Monte Carlo simulation and the lower bound approximation formula of Caldana and Fusai (2013). We show that the former is in essence an application of the two–dimensional Parseval Identity.

As application examples, we price spread options in a model where asset prices are driven by a multivariate normal inverse Gaussian (NIG) process, in a threefactor stochastic volatility model, as well as in examples of models driven by other popular multivariate Lévy processes such as the variance Gamma process, and discuss the price sensitivity with respect to volatility. We also consider examples in the fixed–income market, specifically, on cross–currency interest rate spreads and on LIBOR/OIS spreads. In terms of FFT computation, we have used the FFTW library (see Frigo and Johnson (2010)) and we document appropriate usage of this library to reconcile it with the MATLAB ifft2 counterpart.

Keywords: spread options, numerical methods, Fourier transform, option pricing

JEL Classification: G13, C63

Suggested Citation

Alfeus, Mesias and Schloegl, Erik, On Numerical Methods for Spread Options (January 11, 2018). FIRN Research Paper, Available at SSRN: https://ssrn.com/abstract=3099902 or http://dx.doi.org/10.2139/ssrn.3099902

Mesias Alfeus

Department of Statistics and Actuarial Science - Stellenbosch University ( email )

Matieland
m
Stellenbosch, 7602
South Africa
0633236629 (Phone)
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Erik Schloegl (Contact Author)

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

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Sydney, NSW 2007
Australia
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HOME PAGE: http://www.schlogl.com

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

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Cape Town, Western Cape 7700
South Africa

Faculty of Science, Department of Statistics, University of Johannesburg ( email )

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South Africa

Financial Research Network (FIRN)

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Queensland
Australia

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