Essays on financial derivatives and credit risks

Abstract

Credit derivatives and non-standard derivatives have become very popular. They are recognized as useful hedging tools for certain kinds of market risk and credit risk. Reflecting this practical interest, modeling credit derivatives and pricing non-standard derivatives has been paid much attention in academic literature. This thesis also explores the issues in modeling and pricing these derivatives, and extends the existing literature. This thesis consists of four essays. The first three essays study the issues in modeling credit risk. The last essay studies a non-standard derivative, that is, an American barrier option. The first essay studies a Markov chain model that, unlike the existing models, has a stochastic default rate model so as to reflect real world phenomena. We extend the existing Markov chain models as follows: First, our model includes both the economy-wide and the rating-specific factors, which affect credit ratings. Secondly, our model allows both continuous and discrete movements in credit spreads, even when there exist no changes in credit ratings. Under these assumptions, we provide a valuation formula for a credit spread option, and examine its effects. Based on these empirical results, a parsimonious model is suggested in this chapter. As in Wei (2002), we find that rating-specific factors are important in pricing credit spread options. Also, discrete movements seem to play a large role depending on the firm``s credit rating. Finally, we show that a model, like the Kodera model, that uses only a common factor without allowing for discrete movements may overprice credit spread put options. The second essay studies credit spreads when the default intensity is affected by jump risks. A simple pricing model of risky bonds is derived using a reduced-form approach when there are jump risks of the factors of the default intensity, as supported by empirical evidence. Numerical analyses show that the additional credit spreads caused by jumps can be...