A Study On The Pricing Of Credit Derivatives With Counterparty Risk

In the 2008 international financial crisis,American International Group(AIG)got into trouble,and the US government invested 180 billion US dollars to rescue AIG from bankruptcy.The AIG event makes it possible to consider the impact of counterparty risk in the pricing model of credit derivatives.At present,there are two main types of pricing models of credit derivatives:structural form model and reduced form model.Based on the existing research results,this dissertation mainly studies the pricing of convertible bonds,ordinary bonds,credit default swaps,catastrophe put options in the reduced form model and the pricing of catastrophe put options in the structural form model with regime switching,respectively.The main results of this dissertation are as follows:Firstly,we study the pricing of convertible bonds with counterparty risk in the reduced form model.We assume that the default intensity process of the convert-ible bond issuer and the interest rate process satisfy the Vasicek model.By using martingale theory and the method of measure transformation,we derive the pricing expressions for convertible bonds with counterparty risk in the model.In addition,we show the influence of the model's parameter change on the convertible bond price through numerical analysis.Secondly,we study the pricing of corporate bonds and credit default swaps with counterparty risk in the reduced form model.Under the Primary-Secondary framework in the reduced form model,we introduce a contagion model of correlated defaults.The model assumes that the default intensity process of the primary firm depends on the interest rate process,and the default intensity process of the secondary firm depends on the interest rate process and the counterparty's default process.By using martingale theory and the properties of stochastic exponentials,we derive the pricing expressions for corporate bonds and credit default swaps with counterparty risk and make some numerical analysis on the explicit formulae.Finally,we study the pricing of catastrophe put options with counterparty risk in the reduced form model and the structured form model with regime switching,respectively.In the reduced form model,we assume that the default intensity process of the catastrophe put options issuer and the interest rate process satisfy the the Vasicek model.In the structured form model,we introduce the regime switching model.We assume that the economic state of the market is described by a continuous time Markov chain with a finite state space,and the default intensity process of the catastrophe put option issuer and the interest rate depend on the Markov chain.By using martingale theory and the method of measure transformation,we derive the pricing expressions for the catastrophe put option with counterparty risk in the reduced model and the structured form model with regime switching,respectively.In addition,we make some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.