Mathematical Issues regarding Counterparty Risk

Abstract

Counterparty risk refers to the possibility that a counterparty in an over-the-counter financial derivatives contract may default before the contract matures, resulting in a loss without the exposure being paid according to the contract. The 2008 financial crisis brought counterparty risk into the spotlight. Specifically, research on computation methods for credit valuation adjustment (CVA), regarded as the “market price of counterparty risk,” flourished in the first half of the 2010s. In recent years, the exchange of margin has been employed as a standard measure in practice for counterparty risk management due to international regulations — specifically, the importance of initial margin (IM) to cover the risk of fluctuations in the contract value between the counterparty’s default and final settlement has been recognized. This study considers CVA and IM as fundamental tools in counterparty risk management from a mathematical perspective.