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On Spread Option Pricing Using Two-Dimensional Fourier Transform

Author

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  • MESIAS ALFEUS

    (University of Technology Sydney, Sydney, New South Wales 2007, Australia)

  • ERIK SCHLÖGL

    (Quantitative Finance Research Centre, University of Technology Sydney, 15 Broadway, Sydney, New South Wales 2007, Australia3Department of Statistics, Faculty of Science, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa)

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.

Suggested Citation

  • Mesias Alfeus & Erik Schlögl, 2019. "On Spread Option Pricing Using Two-Dimensional Fourier Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-20, August.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:05:n:s0219024919500237
    DOI: 10.1142/S0219024919500237
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    References listed on IDEAS

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    1. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    4. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Hainaut, Donatien, 2022. "Pricing of spread and exchange options in a rough jump-diffusion market," LIDAM Discussion Papers ISBA 2022012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Mesias Alfeus & James Collins, 2023. "A novel stochastic modeling framework for coal production and logistics through options pricing analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-19, December.

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