Mathematical Finance Seminar

April 24, 2003 , 5:30 PM to 7:00 PM

Robert Jarrow, Cornell University

Liquidity Risk and Arbitrage Pricing Theory

Classical theories of financial markets assume an infinitely liquid market and that all traders are price-takers. This theory is a good approximation for highly liquid stocks, athough even there it does not apply well for large traders or for modelling transaction costs. We propose a new model that takes into account illiquidities, while extending the classical model. Alternatively, or even simultaneously, one can use our model for transaction costs. In essence, we relax the standard assumption of a competitive market, where each trader can either buy or sell unlimited quantities of stock at the market price. Our apporach hypothesizes a stochastic supply curve for a security's price as a function of trade size. This leads to some interesting mathematical issues as well as natural restrictions on hedging strategies.