Review of Derivatives Research

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

A tale of two volatilities

  • Dilip B. Madan


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.


Levy process Stochastic volatility Skewness Time changes Scaling 

JEL Classifications

G10 G12 G13 


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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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