Of Smiles and Smirks: A Term Structure Perspective
检验了跳跃模型和随机波动率模型能否解释Black-Scholes模型中的异常现象（如波动率微笑的期限结构），发现两类模型的理论期限结构与实证数据不一致，随机波动率模型表现稍好但仍不充分。
An extensive empirical literature in finance has documented not only the presence of anamolies in the Black-Scholes model, but also the "term-structures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anamolies have largely focussed on two extensions of the Black-Scholes model: 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 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 better than jumps in this regard.