ON SPREAD OPTION PRICING USING TWO-DIMENSIONAL FOURIER TRANSFORM

Mesias Alfeus and Erik Schlogl
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Mesias Alfeus: University of Technology Sydney, Sydney, New South Wales 2007, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 05, 1-20

Abstract: Spread options are multi-asset options with payoffs dependent 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 nontrivial. We consider several such nontrivial cases and explore the performance of the highly efficient numerical technique of Hurd & Zhou[(2010) A Fourier transform method for spread option pricing, SIAM J. Financial Math. 1(1), 142–157], comparing this with Monte Carlo simulation and the lower bound approximation formula of Caldana & Fusai[(2013) A general closed-form spread option pricing formula, Journal of Banking & Finance 37, 4893–4906]. We show that the former is in essence an application of the two-dimensional Parseval’s 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 three-factor 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.

Keywords: Spread options; Fourier transform; numerical methods; two-dimensional Parseval’s identity; FFTW (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024919500237

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