Of smiles and smirks: A term structure perspective

An extensive empirical literature in finance has documented not only the pr esence of anomalies in the Black-Scholes model, but also the term structure s 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 ex tensions of the Black-Scholes model: introducing jumps into the return proc ess, and allowing volatility to be stochastic. We employ commonly used vers ions of these two classes of models to examine the extent to which the mode ls are theoretically capable of resolving the observed anomalies. We find t hat each model exhibits some term structure patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither cl ass of models constitutes an adequate explanation of the empirical evidence , although stochastic volatility models fare somewhat better than jumps.