Essays on Fine Structure of Asset Returns, Jumps, and Stochastic Volatility

There has been an on-going debate about choices of the most suitable model amongst avariety of model specifications and parameterizations. The first dissertation essay investigateswhether asymmetric leptokurtic return distributions such as Hansen’s (1994) skewed tdistributioncombined with GARCH specifications can outperform mixed GARCH-jump modelssuch as Maheu and McCurdy’s (2004) GARJI model incorporating the autoregressiveconditional jump intensity parameterization in the discrete-time framework. I find that the moreparsimonious GJR-HT model is superior to mixed GARCH-jump models. Likelihood-ratio (LR)tests, information criteria such as AIC, SC, and HQ and Value-at-Risk (VaR) analysis confirmthat GJR-HT is one of the most suitable model specifications which gives us both better fit to thedata and parsimony of parameterization. The benefits of estimating GARCH models usingasymmetric leptokurtic distributions are more substantial for highly volatile series such asemerging stock markets, which have a higher degree of non-normality. Furthermore, Hansen’sskewed t-distribution also provides us with an excellent risk management tool evidenced by VaRanalysis.The second dissertation essay provides a variety of empirical evidences to supportredundancy of stochastic volatility for SP500 index returns when stochastic volatility is takeninto account with infinite activity pure Lévy jumps models and the importance of stochasticvolatility to reduce pricing errors for SP500 index options without regard to jumps specifications.This finding is important because recent studies have shown that stochastic volatility in acontinuous-time framework provides an excellent fit for financial asset returns when combinedwith finite-activity Merton's type compound Poisson jump-diffusion models. The second essay also shows that stochastic volatility with jumps (SVJ) and extended variance-gamma withstochastic volatility (EVGSV) models perform almost equally well for option pricing, whichstrongly imply that the type of Lévy jumps specifications is not important factors to enhancemodel performances once stochastic volatility is incorporated. In the second essay, I computeoption prices via improved Fast Fourier Transform (FFT) algorithm using characteristicfunctions to match arbitrary log-strike grids with equal intervals with each moneyness andmaturity of actual market option prices.