Hedging European Options Against Risks Experienced In The Derivatives Market

Abstract

Options are a popular type of investment in the nancial derivatives market. The intention of buying or selling options is to make pro ts. However, investors might end up making losses if the market goes against their anticipation. The Greeks describe di erent dimensions of risk involved when taking an option’s position. The Greeks are Delta, Gamma, Rho, Kappa and Theta. The main aim of this study is achieved by creating a linear program that maximizes a calculated theoretical pro t. The pro t is calculated by subtracting the real market price of Net ix options from prices calculated using the Black-Scholes formula. We observe that the theoretical prices are higher than the market price. The constraints in our linear program are Greek neutralities. The neutrality of each Greek is achieved by equating the sum of the positional Greeks to zero. The results of the discussion show that Linear Programming can be applied to options to hedge against a combination of all risks that are experienced in the nancial derivatives market. The case study reviewed how the pro t related to options changes when we include all Greeks and when we reduce the number of Greeks. It was observed that pro t is lowest when we include all Greeks and is highest when we use one Greek. The number of shares to buy and sell in order to achieve an optimal strategy for our portfolio are also derived. The e ect of shadow price on the risks experienced in the market were also observed