The probability and severity of a future default event can be evaluated through either P-measure or Q-measure probabilities. The P-measure probabilities are usually based on historical data while Q-measure probabilities are based on market information regarding future credit risk. Practitioners often use credit ratings to estimate P-measure default probabilities. This method is not able to capture the economic fluctuation and individual company information. In this thesis I propose a P-measure intensity-based model that can capture the economic fluctuations to overcome one of the shortcomings. Furthermore, I suggest a Poisson-Gamma distribution to model the default probabilities that capture the economic background instead of using a fixed rate of default for all companies in the same rating class.; In the Q-measure world, the default possibility and severity obtained reflect the future anticipation of credit risk. Individual information and economic factors are included and are reflected in market prices. We can view credit risk from either the cause or the effect of possible future default. From the view of point of the cause, a default event is triggered by a firm's capital structure when the value of the firm falls below its financial obligation. From the view of point of the effect, the corporate bond price is lower than the government bond price by a spread which is a function of default probability and mean recovery rate. Specifically for a reduced-form model, I find a forward-spread formula for a recovery of treasury value scheme that converges to the Duffie and Singleton (1995) formula. In general, the key problem in credit risk is that we know the product of the default probability and mean recovery rate but we are not able to identify these two from a credit spread.; In this thesis, I am able to unify structural models with reduced-form models. I show that the Merton (1974) credit spread model formula can be written as the credit spread formula for a reduced-form model.; When the value of a firm process follows a jump-diffusion process, there have not yet been developed closed-form solutions of the default probability and the mean recovery rate if the time of default can be any time before the bond's maturity. In this thesis, I point out that the jump component should follow an exponential distribution instead of a lognormal jump proposed by Zhou (1997) in order to make the recovery rate independent of the time of maturity. (Abstract shortened by UMI.)
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