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

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  • Marcelo Bianconi
  • Scott MacLachlan
  • Marco Sammon
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    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.

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    File URL: http://ase.tufts.edu/econ/research/documents/2014/bianconiImpliedVolatility.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, Tufts University in its series Discussion Papers Series, Department of Economics, Tufts University with number 0777.

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    Date of creation: 2014
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    Handle: RePEc:tuf:tuftec:0777

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    Related research

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

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    1. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
    2. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    3. Fischer Black, 1989. "How To Use The Holes In Black-Scholes," Journal of Applied Corporate Finance, Morgan Stanley, vol. 1(4), pages 67-73.
    4. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
    5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    6. Hentschel, Ludger, 2003. "Errors in Implied Volatility Estimation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(04), pages 779-810, December.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    8. MacBeth, James D & Merville, Larry J, 1979. "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance, American Finance Association, vol. 34(5), pages 1173-86, December.
    9. Swidler, Steve, 1986. "Simultaneous option prices and an implied risk-free rate of interest: A test of the Black-Scholes models," Journal of Economics and Business, Elsevier, vol. 38(2), pages 155-164, May.
    10. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
    11. 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.
    12. George M. Constantinides & Jens Carsten Jackwerth & Alexi Savov, 2011. "The Puzzle of Index Option Returns," Working Paper Series of the Department of Economics, University of Konstanz 2011-17, Department of Economics, University of Konstanz.
    13. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
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