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Efficient Pricing of Spread Options with Stochastic Rates and Stochastic Volatility

Author

Listed:
  • Alexis Levendis

    (Department of Actuarial Science, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
    These authors contributed equally to this work.)

  • Eben Maré

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
    These authors contributed equally to this work.)

Abstract

Spread options are notoriously difficult to price without the use of Monte Carlo simulation. Some strides have been made in recent years through the application of Fourier transform methods; however, to date, these methods have only been applied to specific underlying processes including two-factor geometric Brownian motion (gBm) and three-factor stochastic volatility models. In this paper, we derive the characteristic function for the two-asset Heston–Hull–White model with a full correlation matrix and apply the two-dimensional fast Fourier transform (FFT) method to price equity spread options. Our findings suggest that the FFT is up to 50 times faster than Monte Carlo and yields similar accuracy. Furthermore, stochastic interest rates can have a material impact on long-dated out-of-the-money spread options.

Suggested Citation

  • Alexis Levendis & Eben Maré, 2022. "Efficient Pricing of Spread Options with Stochastic Rates and Stochastic Volatility," JRFM, MDPI, vol. 15(11), pages 1-12, October.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:11:p:504-:d:959392
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    References listed on IDEAS

    as
    1. 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..
    2. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
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