An equilibrium model for the OTC derivative with the counterparty risk via the credit charge

Abstract

In this article, we propose an equilibrium model for the OTC derivative market with the counterparty risk. We consider an incomplete market model and apply the utility-based pricing. These lead to the demand function and supply function for the claim, and enables us to gain the equilibrium volume/price for it. We set up two approaches to incorporate the counterparty risk into the pricing formula. The one is the pricing model with the credit charge and the other is with the credit risk model. The latter especially corresponds to a traditional pricing method for the defaultable claim. We then demonstrate the influence of the counterparty risk on the equilibrium price, volume, and the market size for both approaches. Our results verify the role of the credit charge in the OTC derivatives market, that is, the credit charge has a possibility to recover the liquidity and the market size.