# Credit Default Swap: Værdiansættelse af justeringen for bilateral modpartsrisiko

Lauge Otto Kjær Jacobsen

Student thesis: Master thesis

## Abstract

The objective of this thesis is to derive and implement a model for bilateral counterparty risk valuation with application to credit default swaps (CDS). The model will take it to account the possibility of wrong-way risk through correlation. The derivation of the model consists mainly of the derivation of the formulas for the bilateral risk credit value adjustment, and the value of a CDS. Both formulas are derived as the risk neutral valuation of an expected cash ow. The two formulas are combined to give the formula the bilateral risk credit value adjustment with application to CDS (BR-CVA-CDS). A default model is also needed. The defaults are modeled with a Cox process for each of the parties in the CDS. The correlation in default between the parties of the CDS is made through the exponential trigger variables of the Cox process. The implementation of the model is done with Monte Carlo simulation. First the defaults are simulated for the three parties. If the investor or the counterpart is the rst to default, valuation of the CDS is done, given the default. Calculating the value of the CDS, requires derived copula functions and Fourier inversion. In the end the the average, of a su ciently large simulation, will approximately give the bilateral credit value adjustment. For the implementation of the model to be possible, approximation of the model has to be made, in order to get the computational time down to a su cient level. But even though the time to calculate a 1000 simulations, varies from three to nineteen hours. This means, even with a faster computer and better programming, that the model will not be able to price in real time. Because of the computational di culties, the signi cance of the error, made by the approximations, is not fully investigated in this thesis. The e ect correlation of the parties in the model, on the BR-CVA-CDS di ers from nothing to a lot, depending on the value of the correlation, and who is correlated. The correlation can be both a positive and a negative to the BR-CVA-CDS, meaning that there is both wrong- and right-way risk. The e ect that the investor goes from being considered risk free to risky, has generally a lowering e ect on the investors BR-CVA-CDS. The e ect can become so great, that the BR-CVA-CDS becomes negative for the investor.