Structural Approach of Credit Risk with Jump Diffusion Process

“Structural Approach of Credit Risk with Jump Diffusion Process” proposes three essays in the modelling of the firm’s asset value as a jump diffusion process within the structural approach of credit risk. The first essay deals with the modelling of a perpetual coupon debt structure using two different jump diffusion processes: double exponential and uniform. The second models a debt structure of roll-over perpetual, where the firm’s asset value follows a double exponential jump diffusion process. The third develops a model with zero coupon debt structure, and takes into account a stopping time marked by an important negative jump. In our essays, we obtain almost closed form formulae for the debt, equity and firm values, as well as the endogenous default barrier and credit spreads. Levels of credit spreads obtained are closer to the market data and confirm the existence of an optimal capital structure, which takes into account the risk free rate, pay-out ratio, firm risk, tax rate, default costs, and jump intensity & sizes.These essays are designed to provide academic and practitioners with useful and insightful knowledge of credit risk, default event as well as credit spreada.