Option Pricing under GARCH models with Generalized Hyperbolic innovations (I) : Methodology
In this paper, we present an alternative to the Black Scholes model for a discrete time economy using GARCH-type models for the underlying asset returns with Generalized Hyperbolic (GH) innovations that are potentially skewed and leptokurtic. Assuming that the stochastic discount factor is an exponential affine function of the states variables, we show that this class of distributions is stable under the Risk neutral change of probability.
|Date of creation:||May 2008|
|Date of revision:|
|Publication status:||Published in Documents de travail du Centre d'Economie de la Sorbonne 2008.37 - ISSN : 1955-611X. 2008|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00281585|
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- Christophe Chorro & Dominique Guegan & Florian Ielpo, 2008. "Option pricing under GARCH models with generalized hyperbolic innovations (II) : data and results," Documents de travail du Centre d'Economie de la Sorbonne b08047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Bertholon, H. & Monfort, A. & Pegoraro, F., 2007.
"Pricing and Inference with Mixtures of Conditionally Normal Processes,"
188, Banque de France.
- Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Centre de Recherche en Economie et Statistique.
- 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.
- Franses,Philip Hans & Dijk,Dick van, 2000.
"Non-Linear Time Series Models in Empirical Finance,"
Cambridge University Press, number 9780521770415.
- Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- 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.
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Kevin Fergusson & Eckhard Platen, 2006.
"On the Distributional Characterization of Daily Log-Returns of a World Stock Index,"
Applied Mathematical Finance,
Taylor & Francis Journals, vol. 13(1), pages 19-38.
- Kevin Fergusson & Eckhard Platen, 2005. "On the Distributional Characterization of Log-returns of a World Stock Index," Research Paper Series 153, Quantitative Finance Research Centre, University of Technology, Sydney.
- Rosenberg, Joshua V. & Engle, Robert F., 2002.
"Empirical pricing kernels,"
Journal of Financial Economics,
Elsevier, vol. 64(3), pages 341-372, June.
- Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
- 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,"
157, Federal Reserve Bank of Minneapolis.
- 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.
- Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Brown, David P & Gibbons, Michael R, 1985. " A Simple Econometric Approach for Utility-based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 40(2), pages 359-81, June.
- Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152.
- repec:adr:anecst:y:2006:i:82:p:01 is not listed on IDEAS
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