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JDOI Variance Reduction Method and the Pricing of American-Style Options

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  • Johan Auster
  • Ludovic Mathys
  • Fabio Maeder

Abstract

The present article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under (time-homogeneous) L\'evy stochastic differential equations. The resulting Jump Diffusion Operator Integral (JDOI) method can be combined with numerous Monte Carlo based stopping-time algorithms, including the ubiquitous least-squares Monte Carlo (LSMC) algorithm of Longstaff and Schwartz (cf. Carriere (1996), Longstaff and Schwartz (2001)). We exemplify the usefulness of our theoretical derivations under a concrete, though very general jump-diffusion stochastic volatility dynamics and test the resulting LSMC based version of the JDOI method. The results provide evidence of a strong variance reduction when compared with a simple application of the LSMC algorithm and proves that applying our technique on top of Monte Carlo based pricing schemes provides a powerful way to speed-up these methods.

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  • Johan Auster & Ludovic Mathys & Fabio Maeder, 2021. "JDOI Variance Reduction Method and the Pricing of American-Style Options," Papers 2104.01365, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:2104.01365
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    3. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps: Parity Relations, PIDEs, and Semi-Analytical Pricing," Swiss Finance Institute Research Paper Series 20-11, Swiss Finance Institute.
    4. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 362-369.
    5. Ludovic Goudenège & Andrea Molent & Antonino Zanette, 2020. "Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models," Quantitative Finance, Taylor & Francis Journals, vol. 20(4), pages 573-591, April.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    8. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
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