A guaranteed deterministic approach to margining on exchange-traded derivatives market

Abstract

The article discusses a modern approach to risk management of the central counterparty, primarily the issue of the sufficiency of its financial resources, including the provision of clearing members, the capital of the central counterparty and the mutual liability fund. The main subject is the margining system, responsible for an adequate level of collateral for clearing members, that plays an important role in risk management. The regulation that is currently accepted in international practice is critically analyzed. A system of margining a portfolio of options and futures in the derivatives market is described, with default management based on the methodology proposed by a number of inventors, registered in 2004. For this system, a mathematical model of margining (i.e. determining the required level of the collateral) is built. The main idea is that the measurement of portfolio risk for margining purposes should take into account the default management method, and instead of the simple procedure of liquidating the defaulted positions, the central counterparty should use the default portfolio management. The novelty of this article is in the use of the ideology of a guaranteed deterministic approach to superhedging, proposed by one author in a number of publications and based on a game-theoretic interpretation. The Bellman–Isaacs equations for the required margin level are directly derived from the economic meaning of the problem. The properties of these equations are studied, in particular, the property of subadditivity of the portfolio margin is proved, which is an important requirement for the margin system from an economic point of view. The equations are reduced to a form convenient for calculations, allowing to carry out numerical experiments; the results of analysis of the margin system’s performance will be presented in a subsequent publication.