A Comparison of Margin Calculation Methods for Exchange Traded Contracts

Abstract

The main objective of this thesis is to analyse methods used by clearing organizations for calculating margin requirements on contract portfolios. Margin requirements are calculated to protect the clearinghouse in case of an unfavourable market outcome. Methods analysed include SPAN, TIMS and OMS II, these are compared both theoretically, and with the help of simulations. The simulations are performed with futures and options taken from the Sydney Futures Exchange. The comparisons are not made to rank the methods, but rather to highlight differences between them. As will be seen in the simulations TIMS can differ from SPAN and OMS with as much as a factor three in the margin requirement. Theoretically, we show that the scanning risk parts of TIMS, OMS II are coherent measures, as has previously been shown for the scanning risk part of SPAN. We further show that the full SPAN, including inter-month risks and inter-commodity credits, satisfies the axioms of translational invariance (T), subadditivity (S) and positive homogeneity (PH) of coherent risk measure theory. We have been unable to show if SPAN, including inter-month risks and inter-commodity credits, satisfies the monotonicity (M) axiom of coherent risk measure theory.