Dissecting initial margin forecasts: models, limitations and backtesting

Vladimir Chorniy and Sergii Arkhypov

Abstract

Initial margin (IM) has a significant impact on counterparty exposure, pricing, capital and limits. This makes the modeling of future IM a critical element of counterparty risk management and pricing. All the current approaches, which we review in this paper, consider IM as value-at-risk (VaR) and therefore develop methods for forecasting forward VaR, and some approaches have then further proposed backtesting of VaR forecasts for model verification. We show that such approaches are limited and have also biased the industry regarding the use of backtesting and model verification. This paper attempts to correct this bias. First, we highlight that IM is not VaR but merely its approximation. Then we show that even with an “IM is VaR” assumption, the forecast of IM is a forecast of a forecast, which is principally different from “just” forward VaR forecasting. We demonstrate the fundamental limitations that follow from this assumption, and after reviewing the literature on IM forecasting, we propose a generic backtesting and verification framework that accommodates both forecasting limitations and existing models. For model verification we consider two approaches: direct backtesting/monitoring and an “elicitability”-related approach. Our analysis also includes the special case of a bank’s model of IM/VaR being a near perfect replica of an exchange’s IM.