Mathematical Finance Seminar

February 9, 2006 5:30 PM to 7:00 PM

Philip Protter, Cornell

Recent Results in Liquidity Risk

Classical theories of financial markets assume an infinitely liquid market and that all traders act as 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 modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. This turns out to be important for hedging options and for calculating the consequent liquidity, in the course of following a hedging strategy to replicate an option (approximately). Our approach hypothesizes a stochastic supply curve for a security's price as a function of trade size. This leads to a new definition of a self-financing trading strategy, and additional restrictions on hedging strategies. Book data provided by Morgan Stanley is used to test the model, and to describe the supply curves of highly liquid, somewhat liquid, and relatively illiquid stocks.