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Review of Derivatives Research

, Volume 12, Issue 3, pp 213–230 | Cite as

A tale of two volatilities

  • Dilip B. Madan
Article

Abstract

We show that there are two distinct ways to make volatility stochastic that are differentiated by their consequences for skewness. Most models in the literature have adopted the relatively tractable methodology of using stochastic time changes to engineer stochastic volatility. Unfortunately, this is also the one that can conflict with the relationship occasionally observed in markets between volatility and skewness. Research enhancing the tractability of the second approach to stochastic volatility based on scaling is called for.

Keywords

Levy process Stochastic volatility Skewness Time changes Scaling 

JEL Classifications

G10 G12 G13 

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References

  1. Bakshi G., Cao C., Chen Z. (1997) Empirical performance of alternative option pricing models. Journal of Finance 52: 2003–2049CrossRefGoogle Scholar
  2. Breeden D.T., Litzenberger R.H. (1978) Prices of state contingent claims implicit in option prices. Journal of Business 51: 621–652CrossRefGoogle Scholar
  3. Barndorff-Nielsen O.E., Shephard N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society, Series B 63: 167–241CrossRefGoogle Scholar
  4. Carr P., Geman H., Madan D., Yor M. (2003) Stochastic volatility for Lévy processes. Mathematical Finance 13: 345–382CrossRefGoogle Scholar
  5. Duffie D., Pan J., Singleton K. (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68: 1343–1376CrossRefGoogle Scholar
  6. Eberlein E., Kallsen J., Kristin J. (2002) Risk Management based on stochastic volatility. Journal of Risk 5: 19–44Google Scholar
  7. Engle R. (1982) Autoregressive conditional heteroskedestacity with estimates of the variance of U.K. inflation. Econometrica 50: 987–1008CrossRefGoogle Scholar
  8. Gatheral J. (2006) The volatility surface: A practioner’s guide. Wiley, Hoboken, NJGoogle Scholar
  9. Heston S. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6: 327–343CrossRefGoogle Scholar
  10. Konikov M., Madan D. (2002) Stochastic volatility via Markov Chains. Review of Derivatives Research 5: 81–115CrossRefGoogle Scholar
  11. Kou S.G. (2002) A jump diffusion model for option pricing. Management Science 48: 1088–1101CrossRefGoogle Scholar
  12. Niccolato E., Venardos E. (2003) Option pricing in stochastic volatility models of the Ornstein-Uhlenbeck type with a leverage effect. Mathematical Finance 13: 445–466CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Robert H. Smith School of Business, Van Munching HallUniversity of MarylandCollege ParkUSA

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