Linear and Non-Linear Illiquidity Models in Finance and Insurance

Abstract

Not being able to price the illiquidity costs of a portfolio can often be an expensive gambit for investors. Yet, mathematical models of illiquidity are rare in the literature. The object of this thesis is to explore the discrete-time illiquidity framework of both Christodoulou and Schweizer et al. to understand the impact of illiquidity under various market regimes. Secondly, we will add the illiquidity framework to unit-linked insurance, and finally, we will explore if the conclusions of Schweizer et al. hold under a non-linear supply curve. We found that the illiquidity cost in the model of Christodoulou was influenced by the length to maturity of the derivative, the size of the illiquidity parameter, and the amount of stock purchased. Additionally, we found that the illiquidity cost was subject to a desaturation point and we succeeded in expanding the model of Schweizer et al. to a non-linear supply curve. The results of this thesis apply to a broad class of trading strategies and our findings can be used to find the behavior and bounds of an illiquid trading strategy.