Optimal option portfolios in markets with position limits and margin requirements

Mordecai Avriel, Haim Reisman

Abstract

ABSTRACT

This paper derives an optimal option trading strategy for a trader who pays no transaction costs and who is subject to margin requirements and position limits. This trading strategy is derived under the assumption that option prices follow an implied binomial tree, while the true volatility is different from the one implied by the tree. The trader's objective is to maximize the rate of riskless profit she can extract, given her margin requirements and position limits. The strategy proposed is analyzed via numerical examples under the assumption that margin requirements and position limits are as in the standard portfolio analysis of risk, or SPAN, method.