Robust One Period Option Modelling

This paper considers robust optimization to cope with uncertainty about the stock return process in one period portfolio selection problems involving options. The robust approach relates portfolio choice to uncertainty, making more cautious portfolios when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlyings and show that for this set the robust problem is a second order cone program that can be solved efficiently. We illustrate the approach for a benchmark tracking problem and discuss the added value of adopting the robust approach in a stochastic programming framework.