Option-Hedging Portfolios with Minimum Transaction Lots

• Main Authors: Liu, Yi-Ting, 劉依婷
• Other Authors: Chen, An-Pin
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/rrpqx8

博士 === 國立交通大學 === 資訊管理研究所 === 104 === Options are designed to hedge against risks to their underlying assets. One method of forming option-hedging portfolios is using stochastic programming models that depend heavily on scenario generation, a challenging task. Another method is neutralizing the Greek risks derived from the Black–Scholes formula, which expresses the option price as a function of the stock price, strike price, volatility, risk-free interest rate, and time to maturity. Greek risks are the derivatives of the option price with respect to these variables. Hedging Greek risks requires no scenario generation. Linear programming models were proposed for constructing option portfolios with neutralized risks and maximized profit. However, problems with these models exist. First, feasible solutions might not exist to neutralize Greek risks perfectly. Second, models that involve multiple assets and their derivatives were incorrectly formulated. Third, these models lack practicability because they consider no minimum transaction lots. Minimum transaction lots can exacerbate the infeasibility problem. These problems must be resolved before option-hedging models can be further applied. Furthermore, current models for option portfolio selection are mainly for arbitrage; models for hedging are scarce. Hedging differs from arbitrage in that arbitrage requires zero-risk, whereas hedging aims to reduce risks as much as possible. Therefore, zero-risk is not mandatory to hedging. The only model for hedging stems from an arbitrage model. The difference lies in that each Greek risk can have an upper and a lower limit, but this is exactly where its shortcomings. Because options have multiple risk factors covering different value ranges, how to set the respective upper and lower limits without having certain risks dominating the portfolio selection process has become a thorny issue. This study proposed a revised model for option portfolios with multiple underlying assets, and then extended the model by incorporating it with a fuzzy goal programming approach to consider the requirement of minimum transaction lots. Numerical examples show that current models failed to obtain feasible solutions when minimum transaction lots were considered. By contrast, the proposed models solved the problems efficiently. Afterwards, this study proposed a new model for the option-hedging portfolio selection problem. This model minimizes the sum of normalized absolute risks with respect to a desirable profit. Empirical results show that this model can be applied directly to problems with minimum transaction lots. Moreover, it was found that option portfolios have efficient frontiers similar to those of stock portfolios, except that some segments of the efficient frontier appeared to be lines than curves. In addition to having resolved the risk aggregation problem existing in current option portfolio optimization models, this study has proposed a new option portfolio selection model that can be used for hedging as well as arbitrage. Minimum transaction lots can be easily took into consideration in this model. In addition to having applicability, hopefully the results of this study can lay the foundation for future studies on option portfolios.