Implied Volatility and the Risk-Free Rate of Return in Options Markets
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.
|Date of creation:||2014|
|Contact details of provider:|| Postal: Medford, MA 02155, USA|
Phone: (617) 627-3560
Fax: (617) 627-3917
Web page: http://ase.tufts.edu/economics
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Fischer Black, 1989. "How To Use The Holes In Black-Scholes," Journal of Applied Corporate Finance, Morgan Stanley, vol. 1(4), pages 67-73.
- 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.
- Shawkat Hammoudeh & Michael McAleer, 2012.
"Risk Management and Financial Derivatives: An Overview,"
Working Papers in Economics
12/10, University of Canterbury, Department of Economics and Finance.
- 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.
- Michael McAleer & Shawkat Hammoudeh, 2012. "Risk Management and Financial Derivatives:An Overview," KIER Working Papers 816, Kyoto University, Institute of Economic Research.
- Hammoudeh, S.M. & McAleer, M.J., 2012. "Risk Management and Financial Derivatives: An Overview," Econometric Institute Research Papers EI 2012-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Shawkat Hammoudeh & Michael McAleer, 2012. "Risk Management and Financial Derivatives: An Overview," Documentos de Trabajo del ICAE 2012-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
- 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 1173-1186, December.
- Diebold, Francis X & Mariano, Roberto S, 1995.
"Comparing Predictive Accuracy,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 13(3), pages 253-263, July.
- Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
- Tom Doan, . "DMARIANO: RATS procedure to compute Diebold-Mariano Forecast Comparison Test," Statistical Software Components RTS00055, Boston College Department of Economics.
- 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 637-654, May-June.
- 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.
- George M. Constantinides & Jens Carsten Jackwerth & Alexi Savov, 2012. "The Puzzle of Index Option Returns," Working Paper Series of the Department of Economics, University of Konstanz 2012-35, Department of Economics, University of Konstanz.
- 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..
- Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
- 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.
- Hentschel, Ludger, 2003. "Errors in Implied Volatility Estimation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(04), pages 779-810, December.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:tuf:tuftec:0777. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Caroline Kalogeropoulos)
If references are entirely missing, you can add them using this form.