An introduction to CVA, Capital Requirements and KVA

Specialeforsvar ved Anna Emilie Granau

Titel: An introduction to CVA, Capital Requirements and KVA

Abstract: In this thesis, credit valuation adjustment, CVA, is introduced to adjust the value of an interest rate swap for the associated counterparty credit risk. A standard CVA model with stochastic hazard rate and stochastic short rate are implemented by using Monte Carlo. Afterwards the capital require-ments capitalising the potential losses from jump to default risk and the price fluctuations due to changes in credit worthiness introduced by adjusting the derivative value for CVA, are presented. The two capital requirements associated with CVA and counterparty credit risk applied in this thesis are based on the Basel Accords. The first being the default risk capital charge which covers the risk of actual default of the counterparty. The second being the CVA risk capital charge that capitalises the risk of migrating credit rating. The default risk charge is in this thesis implemented by applying both an internal model method and a standard approach. The CVA risk capital charge is calculated only by the use of the standard method. The impact of these capital requirements on the fair value of the interest rate swap is examined through the estimation of the lifetime cost of capital, which is equal to the capital valuation adjustment, KVA. In this thesis, the Green and Kenyon [2014] model is used to analyse and quantify KVA.
This thesis considers a single OTC traded interest rate swap to which no risk mitigation techniques have been applied for the quantification of CVA, capital requirements and KVA. The interest rate swap is assumed to be traded with an AAA rated financial institution with investment graded bonds. CVA is estimated both under stressed market conditions and under normal market conditions. Afterwards, the total capital requirement by the use of an internal model method for the default risk capital charge and by applying the standard method for the default risk capital charge is computed. Lastly, KVA is quantified if an internal model method is used to calculate the capital requirement and if the standard approach is used to calculate the capital requirement. The quantification of KVA leads to the conclusion that the lifetime cost of capital would have a larger impact on the fair value than counterparty credit risk.

Vejleder:  Rolf Poulsen
Censor:    Elisa Nicolato, Aarhus Universitet