Market Liquidity and Adverse Permanent Effects in Hedging Equity & Interest Rates Derivatives

Abstract

This work presents a review of modeling techniques for pricing in incomplete markets and managing liquidity costs. We go through a variety of financial models and mathematical aspects related to market liquidity. We present in Chapter 1 the temporary liquidity modeling proposed by Cetin, Jarrow and Protter (2004). We extend this framework to limit order books with liquidity supply and consumption streams. In Chapter 2, we present our main contribution that consists in generalizing Almgren et al. (2011)’s liquidity adverse impacts modeling and hedging strategies from standards of short-term high-frequency trading to the general economy of financial markets. This allows us to introduce, in Chapter 3, a new paradigm to model both temporary and permanent liquidity costs for the Fixed-Income market. Numerical aspects about stochastic control and Backward Stochastic Differential Equations (BSDE) are discussed in Chapter 4. Conclusions are addressed afterward.This work is elaborated in partial fulfillment of the requirements for the degree of Master of Science (DEA) in Quantitative Finance and Mathematical Engineering of the Ecole Nationale des Ponts et Chaussees (Paris, France).