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Discrete time option pricing with flexible volatility estimation

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  • HÄRDLE, Wolfgang

    (Institut für Statistik und Ökonometrie; Humboldt-Universität Zu Berlin, Germany)

  • HAFNER, Christian

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium and Humboldt-Universität Zu Berlin, Germany)

Abstract

By extending the GARCH option pricing model of Duan (1995) to more flexible volatility es- timation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in the case of a threshold GARCH model. For a stock index series with a pro- nounced leverage effect, simulated threshold GARCH option prices are substantially closer to observed market prices than the Black/Scholes and simulated GARCH prices.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1997047.

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Date of creation: 01 Jun 1997
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Handle: RePEc:cor:louvco:1997047

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  1. Gourieroux Christian & Monfort Alain, 1991. "Qualitative threshold arch models," CEPREMAP Working Papers (Couverture Orange) 9109, CEPREMAP.
  2. Bossaerts, P. & Hillion, P., 1995. "Local Parametric Analysis of Hedging in Discrete Time," Discussion Paper 1995-23, Tilburg University, Center for Economic Research.
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  4. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  5. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  6. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  7. L. YANG & Wolfgang HÄRDLE, 1996. "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," SFB 373 Discussion Papers 1996,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
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  10. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  11. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  12. 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.
  13. E. Platen & M. Schweizer, 1997. "On Feedback Effects from Hedging Derivatives," SFB 373 Discussion Papers 1997,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  14. Wolfgang HÄRDLE & H. LÜTKEPOHL & R. CHEN, 1996. "A Review of Nonparametric Time Series Analysis," SFB 373 Discussion Papers 1996,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  16. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  17. Peter Bossaerts & Pierre Hillion, 1993. "A Test Of A General Equilibrium Stock Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 311-347.
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  20. 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.
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Cited by:
  1. 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.
  2. Lars Stentoft, 2011. "What we can learn from pricing 139,879 Individual Stock Options," CREATES Research Papers 2011-52, School of Economics and Management, University of Aarhus.
  3. Badescu, Alexandru M. & Kulperger, Reg J., 2008. "GARCH option pricing: A semiparametric approach," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 69-84, August.
  4. Ignacio Mauleon & Javier Perote, 2000. "Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 225-239.
  5. Jacobi, Frank, 2005. "ARCH-Prozesse und ihre Erweiterungen - Eine empirische Untersuchung für Finanzmarktzeitreihen -," Arbeitspapiere des Instituts für Statistik und Ökonometrie 31, Johannes Gutenberg-Universität Mainz, Institut für Statistik und Ökonometrie.
  6. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Paper 0619, Federal Reserve Bank of Cleveland.
  7. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
  8. Duan, Jin-Chuan & Wei, Jason, 2005. "Executive stock options and incentive effects due to systematic risk," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1185-1211, May.
  9. M, El Babsiri & Jean-Michel Zakoïan, 1997. "Contemporaneous Asymmetry in GARCH Processes," Working Papers 97-03, Centre de Recherche en Economie et Statistique.
  10. Härdle, Wolfgang & Sperlich, Stefan, 1997. "Financial calculations on the net," SFB 373 Discussion Papers 1997,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
  12. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.

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