Multiobjective Decision-Making Model for Optimal Option Hedging Strategy

Derivatives provide hedging approaches for businesses and individuals to help them avoid down-side risks while retaining a certain level of reward. Investors control risks within an acceptable range through forming portfolios of options and corresponding target assets. Studies that construct option portfolios based on the Greek risks of Black-Scholes pricing model simulate the price paths of options and their target assets using financial quantitative methodologies. These studies construct portfolios that consider only a few risk factors for increased risk factors complicate the simulation and make the computation time-consuming. Option hedging portfolios require multiple risk factors because they literally affect option prices and thus cannot be disregarded. Recently, Papahristodoulou (2004), Horasanh (2008) and Gao (2009) respectively proposed their linear programming models for option hedging portfolio selection. However, these models have their respective flaws, including potential insolvability, unconsidered investor risk preferences, or disregarded incommensurability between risk metrics. Option hedging portfolio selection is intrinsically a multiobjective decision-making problem where investors do have their preferences regarding risk factors. Also, trading of options and stocks is literally constrained by minimum transaction lots and budge limits, which therefore should be considered in constructing portfolios to achieve portfolio implementability. This study proposed an integer programming model for option hedging portfolio selection to obtain portfolios that is practicable and acceptable to the investor. The model is based on a multiobjective decision-making method, and considers budge limits and the minimum transaction lots of options and target assets. Besides, the study employs a genetic algorithm to increase solving efficiency when the integer programming model becomes inefficient for increased asset number. Meanwhile, the effectiveness and efficiencies of both approaches will be discussed.

Project ID:PF9806-1159
External Project ID:NSC98-2410-H182-005