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Option Pricing using Realized Volatility

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  • Lars Stentoft

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate dynamics to be used for option pricing purposes in this framework, and we show that our model explains some of the mispricings found when using traditional option pricing models based on interdaily data. We then show explicitly that a Generalized Autoregressive Conditional Heteroskedastic model with Normal Inverse Gaussian distributed innovations is the corresponding benchmark model when only daily data is used. Finally, we perform an empirical analysis using stock options for three large American companies, and we show that in all cases our model performs significantly better than the corresponding benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-13.

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Length: 38
Date of creation: 03 Mar 2008
Date of revision:
Handle: RePEc:aah:create:2008-13

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Option Pricing; Realized Volatility; Stochastic Volatility; GARCH;

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References

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  1. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
  2. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 10.
  3. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  4. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
  5. Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, School of Economics and Management, University of Aarhus.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  9. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  10. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  12. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  13. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
  14. 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.
  15. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  17. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 143-151, June.
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Citations

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Cited by:
  1. Julien Chevallier & Benoît Sévi, 2009. "On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting," Working Papers halshs-00387286, HAL.
  2. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
  3. Benoît Sévi, 2014. "Forecasting the volatility of crude oil futures using intraday data," Working Papers 2014-053, Department of Research, Ipag Business School.
  4. Michel Beine & Bertrand Candelon & Jan Piplack, 2009. "Comovements of returns and volatility in international stock markets: a high-frequency approach," Working Papers 09-10, Utrecht School of Economics.
  5. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," PIER Working Paper Archive 11-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.
  7. Yow-Jen Jou & Chih-Wei Wang & Wan-Chien Chiu, 2013. "Is the realized volatility good for option pricing during the recent financial crisis?," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 171-188, January.
  8. Peter Christoffersen & Bruno Feunou & Kris Jacobs & Nour Meddahi, 2012. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Working Papers 12-34, Bank of Canada.
  9. Asuka Takeuchi-Nogimori, 2012. "An Empirical Analysis of the Nikkei 225 Put Options Using Realized GARCH Models," Global COE Hi-Stat Discussion Paper Series gd12-241, Institute of Economic Research, Hitotsubashi University.

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