This thesis is written based on our studies of credit risk in the field of financial engineering.

The first part proposes a continuous time Markov chain approximation approach to price both European-style and path-dependent, equity and credit derivatives in a unified hybrid model. We provide theoretical justifications of these approximations’ convergence and numerical demonstrations of our method’s high efficiency and accuracy. Additionally, we examine the model implied credit spreads and implied volatilities, which indicates that our model can successfully capture market phenomenons such as nonzero asymptotic credit spread and real volatility smiles.

The second part develops a structural model with endogenous liquidity risk and credit risk and considers the interactions in between. B...[ Read more ]

This thesis is written based on our studies of credit risk in the field of financial engineering.

The first part proposes a continuous time Markov chain approximation approach to price both European-style and path-dependent, equity and credit derivatives in a unified hybrid model. We provide theoretical justifications of these approximations’ convergence and numerical demonstrations of our method’s high efficiency and accuracy. Additionally, we examine the model implied credit spreads and implied volatilities, which indicates that our model can successfully capture market phenomenons such as nonzero asymptotic credit spread and real volatility smiles.

The second part develops a structural model with endogenous liquidity risk and credit risk and considers the interactions in between. Both liquidity shock intensity and trading cost in our model are endogenously determined by the firm’s distance to default. Theoretical and numerical results in our model indicate that the existence of liquidity amplifies the credit risk. We solve the model explicitly and derive analytical expressions for debt value, equity value, and firm value. Calibrating to market observed credit spreads demonstrates that our model captures the empirical patterns pretty well, which provides a stand support for our model.