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Discrete time option pricing with flexible volatility estimation

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  • Härdle, Wolfgang
  • Hafner, Christian M.

Abstract

By extending the GARCH option pricing model of Duan (1995) to more flexible volatility estimation 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 pronounced 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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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1997,56.

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Date of creation: 1997
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Handle: RePEc:zbw:sfb373:199756

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  1. Peter Bossaerts & Pierre Hillion, 1993. "A Test Of A General Equilibrium Stock Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 3(4), pages 311-347.
  2. 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, Econometric Society, vol. 55(2), pages 391-407, March.
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  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  5. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 13-32.
  6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 145-166.
  7. Wolfgang HÄRDLE & H. LÜTKEPOHL & R. CHEN, 1996. "A Review of Nonparametric Time Series Analysis," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1996,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. E. Platen & M. Schweizer, 1997. "On Feedback Effects from Hedging Derivatives," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. Bossaerts, P. & Hillion, P., 1995. "Local Parametric Analysis of Hedging in Discrete Time," Discussion Paper, Tilburg University, Center for Economic Research 1995-23, Tilburg University, Center for Economic Research.
  10. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
  11. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(2), pages 351-372, December.
  12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  13. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
  14. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 159-199.
  15. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 48(5), pages 1749-78, December.
  16. L. YANG & Wolfgang HÄRDLE, 1996. "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1996,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  17. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  18. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
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  20. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 239-265.
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Cited by:
  1. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, Elsevier, vol. 8(1), pages 1-34, March.
  2. 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.
  3. 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.
  4. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 13(1), pages 113-128, January.
  5. M, El Babsiri & Jean-Michel Zakoïan, 1997. "Contemporaneous Asymmetry in GARCH Processes," Working Papers, Centre de Recherche en Economie et Statistique 97-03, Centre de Recherche en Economie et Statistique.
  6. 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.
  7. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers, CIRANO 2002s-33, CIRANO.
  8. Härdle, Wolfgang & Sperlich, Stefan, 1997. "Financial calculations on the net," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. 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.
  10. Duan, Jin-Chuan & Wei, Jason, 2005. "Executive stock options and incentive effects due to systematic risk," Journal of Banking & Finance, Elsevier, Elsevier, vol. 29(5), pages 1185-1211, May.
  11. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Paper, Federal Reserve Bank of Cleveland 0619, Federal Reserve Bank of Cleveland.
  12. 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, Taylor & Francis Journals, vol. 6(2), pages 225-239.

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