Date of Award
Doctor of Philosophy (PhD)
Garland B Durham
Michael J Stutzer
Essay I: The Roles of Short-Run and Long-Run Volatility Factors in Options Market: A Term Structure Perspective
This paper examines the option pricing implications of short-run and long-run volatility factors, which are assumed to be driven by short-run and long-run news events, respectively. Using a comprehensive dataset of S&P 500 index options over 1993-2008, I find that the proposed two-factor volatility models have two desirable properties that help capture the term structures of option-implied volatility and skewness. First, the options data show evidence of time-variation in the long-run expectation of volatility, which may be caused by long-run news events. While this feature is inconsistent with a single-factor volatility assumption, the two-factor volatility models do a good job of matching the entire term structure of implied volatility. Second, the options data reveal that the term structure of implied skewness is nearly flat on average. This feature is hard to reconcile with single-factor volatility models and jumps in returns. In contrast, I find that the two-factor volatility models can generate flat term structures much like those seen in the data. In particular, the short-run volatility factor is dominant in generating short-term skewness, while the long-run volatility factor plays a pivotal role in generating long-term skewness.
Essay II: Beyond Stochastic Volatility and Jumps in Returns and Volatility
While a great deal of attention has been focused on stochastic volatility in stock returns, there is strong evidence suggesting that return distributions have time-varying skewness and kurtosis as well. This can be seen, for example, from variation across time in the shape of Black-Scholes implied volatility smiles. This paper investigates model characteristics that are consistent with variation in the shape of return distributions using a standard stochastic volatility model with a regime-switching feature to allow for random changes in the parameters governing volatility of volatility and leverage effect. The analysis consists of two steps. First, the models are estimated using only information from observed returns and option-implied volatility. Standard model assessment tools indicate a strong preference in favor of the proposed models. Since the information from option-implied skewness and kurtosis is not used in fitting the models, it is available for diagnostic purposes. In the second step of the analysis, regressions of option-implied skewness and kurtosis on the filtered state variables (and some controls) suggest that the models have strong explanatory power. This is important because it suggests that variation in the shape of risk-neutral return distributions (and of the Black-Scholes implied volatility smile) is not just due, for example, to changes in risk premia, but is associated with changes in related characteristics of the physical dynamics.
Park, Yang-Ho, "Two Essays on Options Market" (2011). Finance Graduate Theses & Dissertations. 2.