Of Smiles and Smirks: A Term-Structure Perspective

44 Pages Posted: 2 Jun 1998 Last revised: 17 Nov 2015

See all articles by Sanjiv Ranjan Das

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business

Rangarajan K. Sundaram

New York University (NYU) - Department of Finance

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Abstract

Empirical anamolies in the Black-Scholes model have been widely documented in the Finance literature. Patterns in these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities) have also been widely documented. Theoretical efforts in the literature at addressing these anamolies have largely centered around extensions of the basic Black-Scholes model. Two approaches have become especially popular in this context -- introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonly-used versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We focus especially on the possible "term-structures": of skewness, kurtosis, and the implied volatility smile that can arise under each model. Our central finding is that each model exhibits moment patterns and implied volatility smiles that are consistent with some of the observed anamolies, but not with others. In sum, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.

JEL Classification: G13

Suggested Citation

Das, Sanjiv Ranjan and Sundaram, Rangarajan K., Of Smiles and Smirks: A Term-Structure Perspective. Journal of Financial and Quantitative Analysis (JFQA), Vol. 34, No. 2, 1999. Available at SSRN: https://ssrn.com/abstract=91648 or http://dx.doi.org/10.2139/ssrn.91648

Sanjiv Ranjan Das (Contact Author)

Santa Clara University - Leavey School of Business ( email )

Department of Finance
316M Lucas Hall
Santa Clara, CA 95053
United States

HOME PAGE: http://algo.scu.edu/~sanjivdas/

Rangarajan K. Sundaram

New York University (NYU) - Department of Finance ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States
212-998-0308 (Phone)
212-995-4233 (Fax)

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