| The dissertation consists of three essays on dynamic models of finance, each being one chapter of this dissertation.; In the first chapter, we develop the theoretical and numerical tools necessary to perform conditional estimation of diffusion processes within a generalized method of moments framework because there are circumstances in finance in which it is useful to estimate diffusion processes conditional on some event. We illustrate our method by estimating a univariate diffusion process for a standard time-series of interest rate data conditioned to remain between lower and upper boundaries. A test statistic fails to reject by a wide margin the linearity of the conditionally estimated drift coefficient.; The second chapter looks at option price deviations from Black-Scholes formula. For the S&P 500 index options, we find that these deviations from the Black-Scholes formula follow a simple pattern. Loosely, the slope and curvature of the price deviations are described by a simple function of at-the-money-forward total volatility. Similarly, the slope and curvature of the volatility skew are described by a simple function of at-the-money-forward total volatility. This implies that the term structure of at-the-money-forward volatilities is sufficient to determine the entire volatility surface. Finally, we find that the implied risk-neutral probability density is bimodal. This finding has interesting implications for models of stochastic volatility.; The third chapter is on a damped diffusion framework in financial modelling. With the popular CEV process for the underlying stock or stochastic volatility, the martingale option pricing approach can fail. I propose a flexible damped diffusion framework to overcome these drawbacks. This framework is useful in many areas of financial modeling. To perform MLE, I express the small-time expansion developed by Ait-Sahalia in the untransformed variable and obtain explicitly the second-order coefficient. This result makes it easier to approximate the transition densities of diffusion processes. |
