Optimal Timing of Mark-to-Market for Contingent Credit Risk Control

Collateral is one of the most important and widespread credit risk mitigation techniques used by practitioners. This paper studies the effect of mark-to-market (MTM) timing in collateral agreements on the contingent credit risk exposure. We measure contingent credit risk exposure using Potential Future Exposure (PFE), the maximum amount of exposure expected to occur at a specified confidence during the remaining duration of the underlying contract. The parameters of a collateral agreement that can affect the contingent credit risk exposure include the frequency and timing of marking-to-market, trigger level for margin calls and the level of collateralization. However, these decisions are often made in an ad-hoc manner, without reference to an analytical framework. While the frequency of mark-to-market and collateral level has been studied, very little academic research has addressed the quantitative analysis of mark-to-market timing. The goal of this research is to fill this theoretical gap and propose a framework for optimizing the timing of mark-to-market in collateral agreements to minimize potential future exposure. Our framework computes the probability of maximum risk exposure of the underlying contract above a specified level during its remaining time until maturity using one or two MTMs whose timing is decided simultaneously at the contract initiation, or in a sequential manner. This probability is expressed as a function of the parameters of the underlying contract which is assumed to follow a Brownian motion and the decision variables in collateralization, including initial margin, trigger level and variation margin. Numerical examples are investigated with different values of volatility and duration of the underlying contract. Sensitivity analysis and numerical results reveal the optimal timing of MTM that minimizes PFE. Simulations are used to test preliminary conclusions from numerical analysis