||Chapter 1 Volatility Factors in the Cross-sectional Option Prices The stochastic volatility plays a very important role for option pricing, but there is no consensus on how to model volatility for option pricing purpose. In this paper, using nonparametric methods, we explore the features of volatility factors in the cross-sectional option prices, and address the question of what features that a stochastic volatility model should have to price the cross-sectional options well. In other words, the features regarding to the volatility process are extracted from option price data without imposing any functional restrictions. Specifically, we test how many volatility factors are embedded in the cross-sectional option prices, and examine the drift and the variance function of the volatility process. We construct model free volatility indices from option prices for various maturities to proxy the unobserved volatility factors. Using a bootstrap test, we identify that a short term and a long term volatility indices are sufficient to capture the dynamics of volatility factors in the cross-sectional option prices. Principal components analysis of the implied volatility surface shows that the first principal component is the level, and the slopes of the implied volatility across moneyness and across maturity are related, which constitute the second principal component. Two-factor volatility processes are able to capture such variation in the implied volatility surface and the cross-sectional option prices. The estimated drift function of the squared volatility indices is nonlinear, and the estimated variance function is inconsistent with the square root process. The dynamics of the short term and the long term volatility indices are jointly determined by each other. The conclusion of the paper is that option pricing models with the volatility process of two-factor, nonlinear drift, and disproportionally large variance at high level of volatility should be developed to price options better. Chapter 2 Overpricing and Liquidity of Derivative Warrants in Hong Kong It is observed that the derivative warrants written on the Hang Seng Index in the Hong Kong securities market are traded at higher prices and have shorter holding periods than the options with identical cash flows. In this paper, we reconcile the observed facts by showing the evidence of difference in the bid-ask spread and holding period returns between the derivative warrants market and the options market. We show that the bid-ask spread of the derivative warrants is lower than that of the options, and the short term holding period returns of the derivative warrants are in fact higher than those of the options. The short term investors, who seek the investment opportunities that provide higher short term returns, trade in the derivative warrants market. Comparing with the options, the low bid-ask spread of the derivative warrants reduces the cost of frequent trading substantially. The relatively longer term investors invest in the options market for lower prices and higher long term holding period returns. The results are consistent with the ”clientele effect” in Amihud and Mendelson (1986) that the assets with higher bid-ask spread are allocated to the investors with longer expected holding periods.