Studies On The Pricing Of Corporation Bonds And Credit Derivatives With Counterparty Risk

The topics in this paper are the pricing of credit bonds and credit derivatives with counterparty risk. The main results in this thesis are:Firstly, a geometrical attenuation function is introduced to reflect the correlated default intensities of competitors or copartners. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, so can we derive the pricing formula for corporation bonds.Secondly, we obtain the valuation formulas for credit default swap and credit option with counterparty risk in the geometrical attenuation model. On condition that default is independent of the default-free term structure and that protection buyer is assumed to be default-free, we obtain the fair swap premium of a CDS. Next, we generalize the results. The valuation of vulnerable options is discussed in the next section. Suppose the dynamics of the market value of the asset underlying the option are assumed to be jump-diffusion process, we obtain the pricing formulas for vulnerable option and generalize Merton's formula[46]. Moreover, we prove that counterparty risks of vulnerable option have an effect on its price. Finally, we provide a formula for credit option with counterparty risk. Thirdly, we study the structures and the pricing mechanisms of credit derivatives. We presents a simple framework for valuing single-name credit derivatives such as CDS, CLN and TRS in jump-diffusion models. The Gaver-Stehfest algorithm is used to calculate the CDS spread when the dynamics of the reference entity is assumed to the double exponential jump diffusion process. We model directly the credit spread using a geometric Ornstein-Uhlenbeck process with a jump and derive the pricing formula for credit spread option. Furthmore, we achieve correlation between defaults of firms in two ways: through correlation between innovations to the asset value and through mutual jumps. Using the Gaver-Stehfest algorithm, we can calculate single firm default probabilities for any point in time. We derive the prices of CDO tranches via a recursion technique developed by Andersen et al.[48].Finally, we discuss the generalized quantum entropy and the quantum binomial model of financial markets. The generalized quantum entropies are introduced and some important properties are proved. In the sequence, we obtain the pricing formula for credit bonds in the quantum binomial model.In brief, this thesis concentrates on the derivative pricing in the counterparty-risk model. We introduce a more realistic model in which there is attenuation effect of one firm's default on the other firms' default intensities, thereby obtaining the analytic solutions of the price of the risky bonds and the fair swap of CDS. On the other hand, the dynamics of the asset valuation process is being modeled through jump-diffusion process. In this model, we can get the price of a CDS adopting the structural approach and then use the Gaver-Stehfest algorithm to get the numerical solution which can be implemented in the derivative trading. At last, we analyze quantitatively the risk hedging and the pricing framework of derivative instruments using the quantum information theory and offer theoretical background and empirical evidence for financial innovation as well.