Hedging an option portfolio with minimum transaction lots: A fuzzy goal programming problem

Chang Chun Lin*, Yi Ting Liu, An-Pin Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Options are designed to hedge against risks to their underlying assets such as stocks. One method of forming option-hedging portfolios is using stochastic programming models. Stochastic programming models depend heavily on scenario generation, a challenging task. Another method is neutralizing the Greek risks derived from the Black-Scholes formula for pricing options. The formula 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 human intervention for generating scenarios. Linear programming models have been proposed for constructing option portfolios with neutralized risks and maximized investment profit. However, problems with these models exist. First, feasible solutions that can perfectly neutralize the Greek risks might not exist. Second, models that involve multiple assets and their derivatives were incorrectly formulated. Finally, these models lack practicability because they consider no minimum transaction lots. Considering minimum transaction lots can exacerbate the infeasibility problem. These problems must be resolved before option hedging models can be applied further. This study presents a revised linear programming model for option portfolios with multiple underlying assets, and extends the model by incorporating it with a fuzzy goal programming method for considering minimum transaction lots. Numerical examples show that current models failed to obtain feasible solutions when minimum transaction lots were considered. By contrast, while the proposed model solved the problems efficiently.

Original languageEnglish
Pages (from-to)295-303
Number of pages9
JournalApplied Soft Computing Journal
StatePublished - 1 Oct 2016


  • Fuzzy goal programming
  • Greek risks
  • Hedging
  • Minimum transaction lots
  • Option portfolio

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