In this dissertation, we first generalize Leland (1994b)’s structural model from constant volatility to the state-dependent volatility with constant elasticity (CEV) and obtain the analytical solution for most variables of interest, including first-passage default probability, corporate debt and equity value. After incorporating jumps into asset dynamics, we develop an efficient algorithm to calculate the first passage default probability by adopting a restricted structure of default times and derive numerical solutions for the variables of interest. We find that the extra parameter in the CEV structural model has a significant impact on the optimal capital structure, the debt capacity, the term structure of credit spreads, the duration and convexity of risky debt, the equity volatility, the asset substitution impacts and the cumulative default probabilities.
Further, we incorporate the liquidity risk of the secondary bond market into the structural model with a constant elasticity of variance through the rollover channel and derive the analytical expressions for the variables of interest with an innovative method in Chapter 2. We find that state dependent volatility has noticeable impacts for all the interesting results, including the endogenous default boundary, the optimal leverage and the credit spreads, which depend on the value of the state dependence parameter. 
In Chapter III, we compare the empirical performance of the two alternative volatility assumptions that we used in our study within the context of the Leland (1994b) model. Using time series data from both firm and risk level, We document that CEV structural model with the elasticity parameter around -0.67 on average exhibits a superior fitting in the CDS spreads across all the maturities. The relationship between the sign and value of and the firm specific measures of default risk, such as leverage ratios, CDS spreads and current ratios indicates that there is a tendency for   to increase as the risk of the firm decreases, but that the tendency is weak and fluctuates. We also note that the CDPs generated by the CEV structural model can fit the Moody’s observed data much better compared to these with constant asset volatility. 
In the last Chapter, we study the market efficiency between the CDS and Loan CDS (LCDS) markets by constructing a CDS and LCDS parity relation under the no arbitrage assumption. We document persistent and significant violations of this relation with the cross sectional data from both markets. We identify time-varying and significant positive arbitrage profits from an artificial default risk-free portfolio that trades in both markets and simultaneously longs an undervalued contract and shorts the corresponding overvalued contract for exactly the same underlying firm, maturity, currency and restructure clauses. We show that the profits cannot be accounted for by trading costs or imperfect data about loan recovery rates in the event of default. Using panel regressions with macroeconomic and firm-level variables, we find that firm-level informational asymmetry and difficulty of loan recovery in case of default are much more important than macroeconomic factors in accounting for the arbitrage profits.