Sanjiv R Das, Rangarajan K Sundaram
ABSTRACT
Empirical anamolies in the Black-Scholes model have been widely documented
in the Finance literature. Pattern 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 rise 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 and adequate explanation
of the empirical evidence, although the stochastic volatility models fair
better than jumps in this regard.
Subject: Investments/Derivatives (Theoretical and Empirical)
Das: 617 495-6080 sdas@hbs.edu
Sundaram: 212 998-0308 rsundara@stern.nyu.edu
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