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, although even there it does not apply well for large traders, or for modeling transaction costs. We propose a new model that takes into account illiquidities, while extending the classical model. In essence, we relax the standard assumption of a competitive market, where each trader can either buy or sell unlimited quantities of a stock at the market price. Our approach 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.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).