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Forward And Future Implied Volatility

Author

Listed:
  • PAUL GLASSERMAN

    (Columbia Business School, USA)

  • QI WU

    (Department of APAM, Columbia University, 200 S.W. Mudd Building, New York, NY 10027, USA)

Abstract

We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu (forthcoming) allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free" measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons.

Suggested Citation

  • Paul Glasserman & Qi Wu, 2011. "Forward And Future Implied Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 407-432.
  • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:03:n:s0219024911006590
    DOI: 10.1142/S0219024911006590
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    Citations

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    Cited by:

    1. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    2. Li, Xingyi & Zakamulin, Valeriy, 2020. "The term structure of volatility predictability," International Journal of Forecasting, Elsevier, vol. 36(2), pages 723-737.
    3. Byström, Hans, 2016. "Credit-implied forward volatility and volatility expectations," Finance Research Letters, Elsevier, vol. 16(C), pages 132-138.
    4. Antoine Jacquier & Patrick Roome, 2013. "The Small-Maturity Heston Forward Smile," Papers 1303.4268, arXiv.org, revised Aug 2013.
    5. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    6. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.

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