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Option Valuation with Conditional Heteroskedasticity and Nonnormality

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  • Peter Christoffersen
  • Redouane Elkamhi
  • Bruno Feunou
  • Kris Jacobs

Abstract

We provide results for the valuation of European-style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state space setup using the no-arbitrage principle and an equivalent martingale measure (EMM). Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional nonnormal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of EMMs for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and nonnormal innovations. We provide extensions of these results to more general EMMs and to discrete-time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous-time models. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 23 (2010)
Issue (Month): 5 ()
Pages: 2139-2183

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Handle: RePEc:oup:rfinst:v:23:y:2010:i:5:p:2139-2183

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Citations

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Cited by:
  1. Monfort, A. & Pegoraro, F., 2012. "Asset Pricing with Second-Order Esscher Transforms," Working papers 397, Banque de France.
  2. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
  3. Ederington, Louis H. & Guan, Wei, 2013. "The cross-sectional relation between conditional heteroskedasticity, the implied volatility smile, and the variance risk premium," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3388-3400.
  4. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
  5. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
  6. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
  7. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
  8. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, School of Economics and Management, University of Aarhus.
  9. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
  10. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
  11. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
  12. Fuh, Cheng-Der & Luo, Sheng-Feng & Yen, Ju-Fang, 2013. "Pricing discrete path-dependent options under a double exponential jump–diffusion model," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2702-2713.
  13. Peter Christoffersen & Kris Jacobs & Bo Young Chang, 2011. "Forecasting with Option Implied Information," CREATES Research Papers 2011-46, School of Economics and Management, University of Aarhus.

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