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On the implied volatility of Asian options under stochastic volatility models

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  • Elisa Al`os
  • Eulalia Nualart
  • Makar Pravosud

Abstract

In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating Ito's formula we first compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find and short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We apply our general results to the SABR model and the rough Bergomi model, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew.

Suggested Citation

  • Elisa Al`os & Eulalia Nualart & Makar Pravosud, 2022. "On the implied volatility of Asian options under stochastic volatility models," Papers 2208.01353, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2208.01353
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    References listed on IDEAS

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    1. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    2. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124, September.
    3. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986, September.
    4. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    5. Elisa Alòs & Kenichiro Shiraya, 2019. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," Finance and Stochastics, Springer, vol. 23(2), pages 423-447, April.
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    Cited by:

    1. Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity Asian options in local-stochastic volatility models," Papers 2409.08377, arXiv.org.
    2. Elisa Al`os & Eulalia Nualart & Makar Pravosud, 2023. "On the implied volatility of Inverse options under stochastic volatility models," Papers 2401.00539, arXiv.org, revised Sep 2024.

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