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Of Smiles and Smirks: A Term Structure Perspective

Published online by Cambridge University Press:  06 April 2009

Sanjiv Ranjan Das  and
Rangarajan K. Sundaram
Sanjiv Ranjan Das
Affiliation:
Department of Finance, Harvard Business School, Harvard University, Boston, MA 02163
Rangarajan K. Sundaram
Affiliation:
Department of Finance, Stern School of Business, New York University, New York, NY 10012
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Abstract

An extensive empirical literature in finance has documented not only the presence of anomalies in the Black-Scholes model, but also the term structures of these anomalies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anomalies have largely focused on two extensions of the Black-Scholes model: introducing jumps into the return process, and allowing volatility to be stochastic. We employ commonly used versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anomalies. We find that each model exhibits some term structure patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare somewhat better than jumps.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 34 , Issue 2 , June 1999 , pp. 211 - 239
Copyright
Copyright © School of Business Administration, University of Washington 1999

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