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On the difference between the volatility swap strike and the zero vanna implied volatility

Author

Listed:
  • Elisa Alos
  • Frido Rolloos
  • Kenichiro Shiraya

Abstract

In this paper, Malliavin calculus is applied to arrive at exact formulas for the difference between the volatility swap strike and the zero vanna implied volatility for volatilities driven by fractional noise. To the best of our knowledge, our estimate is the first to derive the rigorous relationship between the zero vanna implied volatility and the volatility swap strike. In particular, we will see that the zero vanna implied volatility is a better approximation for the volatility swap strike than the ATMI.

Suggested Citation

  • Elisa Alos & Frido Rolloos & Kenichiro Shiraya, 2019. "On the difference between the volatility swap strike and the zero vanna implied volatility," Papers 1912.05383, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:1912.05383
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    References listed on IDEAS

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    1. Peter Friz & Jim Gatheral, 2005. "Valuation of volatility derivatives as an inverse problem," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 531-542.
    2. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675, arXiv.org, revised Mar 2019.
    3. 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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