Counterparty Risk Valuation On Credit Derivatives

In this thesis,we study the valuation of credit risk.We mainly conduct the thorough research from three aspects: the value process obtained by the pricing model,explicit formulas of pricing by using partial differential equation method and the numerical analysis.To deal with the Credit-linked notes(CLN)with counterparty risk,We consider the pricing and risk measurement from the following two aspects:(a)Without default contagion among credit entities.The traditional reduced-form model assumes that the credit entities are conditional independent,namely,given reference information,credit entities can not default simultaneously.As the extension application in reduced-form model,markov chain model subject that it can occur with simultaneous default but without default contagion among credit entities.Based on this assumption,we first price the CLN with counterparty risk by using Markov copula model.With the condition of Markov copula,we can calculate the margin default probability distribution and the joint distribution.By Feynman-Kac formulation,we turn the pricing problem to the terminal problem of PDEs.To solve this problem,we find there's fundamental solution for the parabolic equation problem.Based on this,by using the Green formula,explicit formulas of CLN with counterparty risk can be obtained.By investigating the results,we find the result obtained by the traditional reduced-form model coincides with that by Markov copula model while we assume the intensity of simultaneous default equals 0.In addition,counterparty risk(CVA)is also measured,and the corresponding explicit formula is obtained.Then,we study CLN valuation with several credit entities by using common shock model.In this model,we regard the default of credit entities is driven by the ”trigger events” and the default time is determined by the time of first events occurance.By constructing the ”trigger events” time,we get the default probability distribution of credit entities.With the cash flow process and PDE method,we also get the explicit formulas as that in chapter 3.Meanwhile,we find the common shock model is equivalent to the markov copula model,which also can be found in [23].(b)with default contagion among credit entities.While investigating the CLN pricing model with default contagion,we first consider the case that one entity's default may impact the other credit entity but inverse not.By constructing default times,we also calculate the conditional default probabilities.Based on this,we use PDE method to get the solution of CLN with counterparty risk.In addition,we promote the model of Leung et.al mentioned in [35] and get the infinite generator matrix of multiple markov chain.Finally,by complex calculation,we get marginal default probability distributions of credit entities and the corresponding joint distribution.