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Sensitivities Of Asian Options In The Black–Scholes Model

Author

Listed:
  • DAN PIRJOL

    (J. P. Morgan, 277 Park Avenue, New York, NY-10172, USA)

  • LINGJIONG ZHU

    (Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL-32306, USA)

Abstract
We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black–Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit, obtained using large deviations theory. Numerical tests demonstrate good agreement of the proposed approximation with alternative numerical simulation results for cases of practical interest. We also study the qualitative properties of Asian Greeks, including new results for Rho, the sensitivity with respect to changes in the risk-free rate, and Psi, the sensitivity with respect to the dividend yield. In particular, we show that the Rho of a fixed-strike Asian option and the Psi of a floating-strike Asian option can change sign.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:01:n:s0219024918500085
    DOI: 10.1142/S0219024918500085
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    References listed on IDEAS

    as
    1. Vicky Henderson & Rafal Wojakowski, 2001. "On the Equivalence of Floating and Fixed-Strike Asian Options," OFRC Working Papers Series 2001mf08, Oxford Financial Research Centre.
    2. Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
    3. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    4. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    5. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
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    7. Carr, Peter & Ewald, Christian-Oliver & Xiao, Yajun, 2008. "On the qualitative effect of volatility and duration on prices of Asian options," Finance Research Letters, Elsevier, vol. 5(3), pages 162-171, September.
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    9. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    10. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    11. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
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    Citations

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    Cited by:

    1. Dan Pirjol, 2024. "Subleading correction to the Asian options volatility in the Black-Scholes model," Papers 2407.05142, arXiv.org, revised Aug 2024.
    2. Jaehyun Kim & Hyungbin Park & Jonghwa Park, 2019. "Pricing and hedging short-maturity Asian options in local volatility models," Papers 1911.12944, arXiv.org, revised Apr 2024.
    3. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.

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