A study of the Basel III CVA formula

Abstract

In this thesis we compare the official Basel III method for computing credit value adjustment (CVA) against a model that assumes piecewise constant default intensities for a number of both market and fictive scenarios. CVA is defined as the price deducted from the risk-free value of a bilateral derivative to adjust for the counterparty credit risk. Default intensity is defined as the rate of a probability of default, conditional on no earlier default. In the piecewise constant model, the default intensity is calibrated against observed market quotes of credit default swaps using the bootstrapping method. We compute CVA for an interest rate swap in a Cox-Ingersoll-Ross framework, where we calculate the expected exposure using the internal model method and assume that no wrong-way risk exists.

Our main finding is that the models generate different values of CVA. The magnitude of the difference appears to depend on the size of the change in the spreads between credit default swap maturities. The bigger the change from one maturity to another is, the bigger the difference between the models will be.