A Risk-Sharing Framework of Bilateral Contracts

We propose a risk-sharing framework for bilateral contracts to find the optimal pair, initial price and amount of collateral, with presence of default risks, collateral, and funding spreads. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. For inter-dealers contracts, which are governed by regulations, the optimal collateral can interpret circumstances where the margin requirement is indeed optimal. We will see later that absence of market frictions is an inherent assumption for the margin requirement in Basel III. In addition, as we consider entity-specific information in bilateral pricing, law of one price does not hold. Moreover, inclusion of funding spreads causes asymmetry in individual pricing. Thus, the two parties should enter derivative contracts with a negotiated price, which is the other part of the solution of the risk-sharing framework. The risk-sharing framework defines the negotiation as a problem that maximizes the sum of utilities of the two parties. The optimal price from the risk-sharing framework does not have asymmetry due to different funding spreads of each party.