Robust One-Period Option Hedging

The paper considers robust optimization to cope with uncertainty about the stock return process in one period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second order cone program that can be solved efficiently. We apply the approach to find an optimal portfolio to hedge an index option. Portfolio selection concerns the allocation of wealth to assets such that return is maximized and risk is minimized. The best known mathematical model for portfolio selection is the Markowitz (1952) model. The Markowitz model measures return by the expected value of the random portfolio return and risk by the variance of the portfolio return. The mathematical model is a quadratic programming model. A good reference on portfolio optimization is Zenios (1993). Critics have...

• Type: Journal
• Year: 2006
• Where: IOR
• Authors: Frank Lutgens, Jos F. Sturm, Antoon Kolen
• Keywords: IOR 2006, Model, Parameter, Portfolio Optimization