Combinatorial and price efficient optimization of the underlying assets in basket options

Abstract: The purpose of this thesis is to develop an optimization model that chooses the optimal and price efficient combination of underlying assets for a equally weighted basket option. To obtain a price efficient combination of underlying assets a function that calculates the basket option price is needed, for further use in an optimization model. The closed-form basket option pricing is a great challenge, due to the lack of a distribution describing the augmented stochastic price process. Many types of approaches to price an basket option has been made. In this thesis, an analytical approximation of the basket option price has been used, where the analytical approximation aims to develop a method to describe the augmented price process. The approximation is done by moment matching, i.e. matching the first two moments of the real distribution of the basket option with an lognormal distribution. The obtained price function is adjusted and used as the objective function in the optimization model. Furthermore, since the goal is to obtain en equally weighted basket option, the appropriate class of optimization models to use are binary optimization problems. This kind of optimization model is in general hard to solve - especially for increasing dimensions. Three different continuous relaxations of the binary problem has been applied in order to obtain continuous problems, that are easier to solve. The results shows that the purpose of this thesis is fulfilled when formulating and solving the optimization problem - both as an binary and continuous nonlinear optimization model. Moreover, the results from a Monte Carlo simulation for correlated stochastic processes shows that the moment matching technique with a lognormal distribution is a good approximation for pricing a basket option.