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Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets

Author

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  • Fusai, Gianluca
  • Marena, Marina
  • Roncoroni, Andrea

Abstract

We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61-73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.

Suggested Citation

  • Fusai, Gianluca & Marena, Marina & Roncoroni, Andrea, 2008. "Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2033-2045, October.
  • Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2033-2045
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    References listed on IDEAS

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    Cited by:

    1. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    2. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    3. Fred Espen Benth & Paul Kettler, 2010. "Dynamic copula models for the spark spread," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 407-421.
    4. Pun, Chi Seng & Chung, Shing Fung & Wong, Hoi Ying, 2015. "Variance swap with mean reversion, multifactor stochastic volatility and jumps," European Journal of Operational Research, Elsevier, vol. 245(2), pages 571-580.
    5. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    6. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Empirical Pricing Performance in Long-Dated Crude Oil Derivatives: Do Models with Stochastic Interest Rates Matter?," Research Paper Series 367, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. repec:uts:finphd:37 is not listed on IDEAS
    8. repec:eee:eneeco:v:64:y:2017:i:c:p:415-437 is not listed on IDEAS
    9. Cartea, Álvaro & González-Pedraz, Carlos, 2012. "How much should we pay for interconnecting electricity markets? A real options approach," Energy Economics, Elsevier, vol. 34(1), pages 14-30.
    10. repec:eee:ejores:v:266:y:2018:i:3:p:1134-1139 is not listed on IDEAS
    11. repec:kap:revdev:v:20:y:2017:i:3:d:10.1007_s11147-017-9128-4 is not listed on IDEAS
    12. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.

    More about this item

    Keywords

    C63 G13 Asian options Discrete monitoring Laplace transform Fourier transform Commodity markets Energy markets;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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