Modeling Feedback Effects Using Stochastic Liquidity

Abstract

This chapter deals with the modeling of asset liquidity. One aspect of liquidity includes the price impact involved in acquiring or liquidating a position. Our objective is to study the interaction between the trading strategy of a large investor, the asset price process, and liquidity in one single setup. There is a growing number of theoretical papers investigating the interaction of liquidity and trading strategies of large investors. Part of this literature considers optimal liquidation strategies for large portfolios, for instance Dubil [17], and Almgren and Chriss [1]. Recently, research has focused more and more on the modeling and hedging aspects that are introduced by liquidity and the presence of large traders. Cvitanić and Ma [14], Frey [22], Frey and Patie [23], and Liu and Yong [31] consider liquidity as an exogenously given source of risk. Frey and Stremme [25], Kampovsky and Trautmann [29], Papanicolaou and Sircar [34], and Schönbucher and Wilmott [38] serve as prominent examples taking into account equilibrium setups.