Portfolio optimization in the illiquid market using the empirical distribution

Abstract

This paper focuses on the portfolio optimization problem in the presence of the European options in the illiquid market. To do this, we extract the features of the market data using the statistical test to design a general financial model. After that, applying the dynamic replicating portfolio strategy, we derive a comprehensive partial integral differential equation for European option pricing in the illiquid market where the jump part of the model follows the empirical distribution. Since the structure of the equation is complex, we use the finite difference method to solve it. Furthermore, we apply the MCVaR portfolio optimization model with the short selling constraint to obtain the optimal portfolio strategy according to the risk tolerance amounts of the investors. Finally, we find the optimal portfolio under different amounts of the model’s parameters based on the S&P market data.