Hedging strategy for a portfolio of options and stocks with linear programming

This paper extends the model proposed by Papahristodoulou [C. Papahristodoulou, Option strategies with linear programming, European Journal of Operational Research 157 (2004) 246–256] to a multi-asset setting to deal with a portfolio of options and underlying assets. General linear programming model is given and it is applied to Novartis, Sanofi and AstraZeneca’s call and put options. A portfolio of options and their underlying assets is constructed under a hedging strategy that considers all the Greek letters such as delta, gamma, theta, rho and vega. The impact of each Greek constraint on the portfolio’s return is investigated considering the shadow prices.