An Equilibrium Model for an Otc Derivative Market Under a Counterparty Risk Constraint

Abstract

In this study, we develop an equilibrium pricing model for an option contract with a counterparty risk, a collateral agreement, a counterparty risk constraint, and a threshold. Since we consider the option market to be an example of the derivatives market, we suppose that the buyer of an option has only countertparty risk of a seller defaulting. In addition, we consider a model where the buyer is allowed to enter into an option contract within an allocated amount of risk capital for counterparty risk, and requires (cash) collateral to the seller if the exposure exceeds the threshold. The counterparty risk is measured as a credit valuation adjustment. We provide an equilibrium pricing rule and an equilibrium volume formula by solving participants’ static utility-maximization problems. Based on numerical simulations, we verify the mechanisms through which collateralization, risk capital, and the threshold affect the size of the over-the-counter (OTC) option market. Finally, we analyze the influence of the buyer’s risk-aversion on the market, without collateralization. The results imply that the risk constraint might be a proxy for an investor’s attitude towards risk.