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On the Equivalence of Floating and Fixed-Strike Asian Options

Author

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  • Vicky Henderson
  • Rafal Wojakowski

Abstract

There are two types of Asian options in the financial markets which differ according to the role of the average price. We give a symmetry result between the floating and fixed-strike Asian options. The proof involves a change of numeraire and time reversal of the Brownian motion. Symmetries are very useful in option valuation and in this case, the result allows the use of more established fixed-strike pricing methods to price floating-strike Asian options.

Suggested Citation

  • Vicky Henderson & Rafal Wojakowski, 2001. "On the Equivalence of Floating and Fixed-Strike Asian Options," OFRC Working Papers Series 2001mf08, Oxford Financial Research Centre.
    • Handle: RePEc:sbs:wpsefe:2001mf08
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2001mf08.pdf
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    Citations

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    Cited by:

    1. Vicky Henderson & David Hobson & William Shaw & Rafal Wojakowski, 2007. "Bounds for in-progress floating-strike Asian options using symmetry," Annals of Operations Research, Springer, vol. 151(1), pages 81-98, April.
    2. Dan Pirjol & Lingjiong Zhu, 2018. "Sensitivities Of Asian Options In The Black–Scholes Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-25, February.
    3. C. Brown & J. C. Handley & C.-T. Lin & K. J. Palmer, 2016. "Partial differential equations for Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 447-460, March.
    4. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    5. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
    6. Eberlein, Ernst & Papapantoleon, Antonis, 2005. "Equivalence of floating and fixed strike Asian and lookback options," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 31-40, January.
    7. Dan Pirjol & Jing Wang & Lingjiong Zhu, 2017. "Short Maturity Forward Start Asian Options in Local Volatility Models," Papers 1710.03160, arXiv.org.
    8. Jan Vecer, 2013. "Asian options on the harmonic average," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1315-1322, September.
    9. Hideharu Funahashi & Masaaki Kijima, 2017. "A unified approach for the pricing of options relating to averages," Review of Derivatives Research, Springer, vol. 20(3), pages 203-229, October.
    10. Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.
    11. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    12. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    13. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    14. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    15. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.

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