A parsimonious parametric model for generating margin requirements for futures

Abstract

Major exchanges employ the Standard Portfolio Analysis of Risk (SPAN) software to measure maintenance margins. However, its methodology has become cumbersome and opaque, having evolved over several decades and by now it requires that several hundred parameter values are re-set every day. We present a new, parsimonious parametric model for calculating margin requirements for futures which has a rigorous econometric foundation, being derived entirely from the median tail loss (MTL) of the returns distribution. This facilitates maximum likelihood volatility model calibration and state-of-the-art backtests. Then the parameters of the margin scheme which overlays the MTL may be calibrated using a variety of objectives. We examine three such objectives, including two which are designed to generate margins which mimic SPAN.