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Applied Mathematical Finance Volume 30, 2023 - Issue 5
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Research Article

On the Implied Volatility of Asian Options Under Stochastic Volatility Models

Elisa AlòsDepartment of Economics and Business, Universitat Pompeu Fabra and Barcelona School of Economics, Barcelona, SpainORCID Iconhttps://orcid.org/0000-0003-4234-0671View further author information
ORCID Icon,
Eulalia NualartDepartment of Economics and Business, Universitat Pompeu Fabra and Barcelona School of Economics, Barcelona, SpainORCID Iconhttps://orcid.org/0000-0002-3319-3545View further author information
ORCID Icon &
Makar PravosudDepartment of Economics and Business, Universitat Pompeu Fabra and Barcelona School of Economics, Barcelona, SpainCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-8591-7904View further author information
ORCID Icon
Pages 249-274 | Received 10 Mar 2023, Accepted 09 Mar 2024, Published online: 12 May 2024

References

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  • Alòs E., García-Lorite D., and Muguruza A.. 2022. “On Smile Properties of Volatility Derivatives: Understanding the VIX Skew.” SIAM Journal on Financial Mathematics 13 (1): 32–69. https://doi.org/10.1137/19M1269981.
  • Alòs E., and León J. A.. 2017. “On the Curvature of the Smile in Stochastic Volatility Models.” SIAM Journal on Financial Mathematics 8 (1): 373–399. https://doi.org/10.1137/16M1086315.
  • Alòs E., and León J. A.. 2019. “A Note on the Implied Volatility for Floating Strike Asian Options.” Decisions in Economics and Finance 42 (2): 743–758. https://doi.org/10.1007/s10203-019-00239-w.
  • Alòs E., León J. A., and Vives J.. 2007. “On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models with Stochastic Volatility.” Finance and Stochastics 11 (3): 373–397. https://doi.org/10.1007/s00780-007-0043-7.
  • Alòs E., and Shiraya J. A.. 2019. “Estimating the Hurst Parameter From Short Term Volatility Swaps: A Maliiavin Calculus Approach.” Finance and Stochastics 23 (2): 423–447. https://doi.org/10.1007/s00780-019-00384-5.
  • Chatterjee R., Cui Z., Fan J., and Liu M.. 2018. “An Efficient and Stable Method for Short Maturity Asian Options.” Journal of Futures Markets 38 (12): 1470–1486. https://doi.org/10.1002/fut.v38.12.
  • Forde M., and Jacquier A.. 2010. “Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility.” Applied Mathematical Finance 17 (3): 241–259. https://doi.org/10.1080/13504860903335348.
  • Fouque J.-P., and Han C.-H.. 2003. “Pricing Asian Options with Stochastic Volatility.” Quantitative Finance 3 (5): 353–362. https://doi.org/10.1088/1469-7688/3/5/301.
  • Jäckel P. 2015. “Let's Be Rational.” Wilmott 2015 (75): 40–53. https://doi.org/10.1002/wilm.2015.2015.issue-75.
  • Lee R. W. 2005. Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation. In Recent Advances in Applied Probability edited by R. Baeza-Yates, J. Glaz, H. Gzyl, J. Hüsler, J. L. Palacios. Boston, MA: Springer.
  • Nualart D., and Nualart E.. 2018. Introduction to Malliavin Calculus. Cambridge: Cambridge University Press.
  • Pirjol D. 2023. “Subleading Correction to the Asian Volatility in the Black-Scholes Model.” International Journal of Theoretical and Applied Finance 26 (02n03): 2350005. https://doi.org/10.1142/S021902492350005X.
  • Pirjol D., and Zhu L.. 2016. “Short Maturity Asian Options in Local Volatility Models.” SIAM Journal on Financial Mathematics 7 (1): 947–992. https://doi.org/10.1137/15M1047568.
  • Pirjol D., and Zhu L.. 2019. “Short Maturity Asian Options in the CEV Model.” Probability in the Engineering and Informational Sciences 33 (2): 258–290. https://doi.org/10.1017/S0269964818000165.
  • Yang Z., and Ewald C.-O.. 2009. “Implied Volatility From Asian Options Via Monte Carlo Methods.” International Journal of Theoretical and Applied Finance 12 (02): 153–178. https://doi.org/10.1142/S021902490900518X.

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