Margin Calculation of Multi-Leg Option Strategies

Abstract

Since options in a portfolio can offset one another partially in terms of the market risk, the margin calculation for option portfolios is complicated due to its combinatorial nature. We consider in this technical note margining balanced option portfolios, in which the number of long positions equals to that of short positions, respectively, in calls and puts. We first introduce a new concept of base offsets and propose an integer programming model for margin calculation based on the strategy-based approach. We then prove that our integer programming model is tractable due to its equivalence to a linear programming formulation. While the strategy-based approach is likely to overestimate the market risk in general, we identify certain situations in which our model yields exact estimation of market risk. Finally we prove that our model with up to six legs is guaranteed to yield exact margin requirement.