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Implied Volatility and the Risk-Free Rate of Return in Options Markets

Author

Listed:
  • Marcelo Bianconi
  • Scott MacLachlan
  • Marco Sammon

Abstract

This paper implements an algorithm that can be used to solve systems of Black-Scholes equations for implied volatility and implied risk-free rate of return. After using a seemingly unrelated regressions (SUR) model to obtain point estimates for implied volatility and implied risk-free rate, the options are re-priced using these parameters in the Black-Scholes formula. Given this re-pricing, we find that the difference between the market and model price is increasing in moneyness, and decreasing in time to expiration and the size of the bid ask spread. We ask whether the new information gained by the simultaneous solution is useful. We find that after using the SUR model, and re-pricing the options, the varying risk-free rate model yields Black-Scholes prices closer to market prices than the fixed risk-free rate model. We also find that the varying risk-free rate model is better for predicting future evolutions in model-free implied volatility as measured by the VIX. Finally, we discuss potential trading strategies based both on the model-based Black-Scholes prices and on VIX predictability.

Suggested Citation

  • Marcelo Bianconi & Scott MacLachlan & Marco Sammon, 2014. "Implied Volatility and the Risk-Free Rate of Return in Options Markets," Discussion Papers Series, Department of Economics, Tufts University 0777, Department of Economics, Tufts University.
  • Handle: RePEc:tuf:tuftec:0777
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    File URL: http://ase.tufts.edu/econ/research/documents/2014/bianconiImpliedVolatility.pdf
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    References listed on IDEAS

    as
    1. Hammoudeh, Shawkat & McAleer, Michael, 2013. "Risk management and financial derivatives: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 109-115.
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    4. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    6. Becker, Ralf & Clements, Adam E. & White, Scott I., 2007. "Does implied volatility provide any information beyond that captured in model-based volatility forecasts?," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2535-2549, August.
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    Cited by:

    1. Arısoy, Yakup Eser & Altay-Salih, Aslıhan & Akdeniz, Levent, 2015. "Aggregate volatility expectations and threshold CAPM," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 231-253.
    2. Lin, Shin-Hung & Huang, Hung-Hsi & Li, Sheng-Han, 2015. "Option pricing under truncated Gram–Charlier expansion," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 77-97.

    More about this item

    Keywords

    re-pricing options; forecasting volatility; seemingly unrelated regression; implied volatility;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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