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Exotic Geometric Average Options Pricing under Stochastic Volatility

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  • Nabil Tahani

Abstract

This article derives semi-analytical pricing formulae for geometric average options (GAOs) within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, the cross-moment generating function is derived and the cumulative probabilities are recovered using the Gauss--Laguerre quadrature rule. Fixed and floating strikes as well as other exotic GAO on different assets such as stocks, currency exchange rates and interest rates are derived. The approach is found to be very accurate and efficient.

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  • Nabil Tahani, 2013. "Exotic Geometric Average Options Pricing under Stochastic Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 229-245, July.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:229-245
    DOI: 10.1080/1350486X.2012.678735
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    Cited by:

    1. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    2. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.

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