OPTIMIZATION PROBLEM IN OPTION PRICING ANDPORTFOLIO SELECTION - Febrianti, Werry
finance. Not many studies have modeled options and portfolios as optimization problems. This dissertation focuses on examining options and portfolios which are modeled as optimization problems. There are three research topics studied in this dissertation. The first topic, namely option prices, is modeled as a multiobjective optimization problem which is solved using the adaptive weighted sum method and metaheuristic optimization. The metaheuristic optimization used in this study is the differential evolution algorithm. This differential evolution algorithm is also applied to determine the option price using the Black-Scholes partial differential equation which is the second topic of the research. In addition to option pricing, the third topic that is the focus of this research is the calculation of the proportion of assets in the mean-variance portfolio with buy-in threshold constraints and cardinality constraints which is done by modeling the portfolio as a mixed integer nonlinear programming problem and solved using a spiral optimization algorithm Determining the option price by approaching the solution of the Black-Scholes partial differential equation is done by changing the option pricing problem into an optimization problem using the weighted residual method. This weighted residual method is solved using a differential evolution algorithm and its approximation function is built based on the concept of a neural network. The results show that the developed differential evolution algorithm can approach the solution of the Black- Scholes partial differential equation for determining European and barrier option prices. The next option price determination is done by modeling the option price as a multiobjective optimization problem. Then, the option price that has been modeled as a multiobjective optimization problem is changed into a single-objective optimization problem using the adaptive weighted sum method and solved using a differential evolution algorithm. The results show that the differential evolution algorithm is able to produce an optimal Pareto solution to approximate Vanilla option prices before and after COVID-19. Calculation of the proportion of assets in the mean-variance portfolio with buyin threshold constraints and cardinality constraints is performed by modeling the portfolio as a mixed integer nonlinear programming problem and solved using a spiral optimization algorithm. This study uses data from Bartholomew-Biggs and Kane. The optimal portfolio results obtained from the results of the spiral optimization algorithm are compared with the results from Bartholomew-Biggs and Kane which are solved using Quasi-Newton and DIRECT. The spiral optimization algorithm produces less risk than the Quasi-Newton results and is similar to the results from DIRECT.