A Risk-Sharing Framework of Bilateral Contracts

Abstract

We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same pricing methodology and parameters. Thus, the two parties should enter the derivative contracts with a negotiated price, and we call the negotiation a risk-sharing problem. This framework defines the negotiation as a problem that maximizes the sum of utilities of the two parties. By the derived optimal price, we provide a theoretical analysis on how the price is determined between the two parties. As well as the price, the risk-sharing framework produces an optimal amount of collateral. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. However, inter-dealers markets are governed by regulations. As recommended in Basel III, it is a convention in inter-dealer contracts to pledge the full amount of a close-out price as collateral. In this case, using the optimal collateral, we interpret conditions for the full margin requirement to be indeed optimal.

American options in nonlinear markets

“…The inequalities satisfied by unilateral prices and the range fair bilateral prices were studied in papers by Nie and Rutkowski [60,61] for models with either an exogenous or endogenous collateralization, respectively. More recently, Bichuch et al [7,8] (see also Lee et al [52] and Lee and Zhou [53] for related studies) explicitly addressed the issue of hedging the counterparty credit risk and analyze the CVA for European claims in the Black-Scholes model complemented by EJP 26 (2021), paper 90. defaultable bonds issued by the counterparties and they also examined bounds for fair bilateral prices. We stress that the above-mentioned papers are mainly concerned with prices of contingent claims of a European style and thus it is natural to ask analogous questions regarding American contingent claims in a nonlinear market model with idiosyncratic funding costs, counterparty credit risk and other market frictions affecting the trading mechanism.…”