Darrell Duffie, the Dark Lord

And by that I don't mean that Darrell replaced Lord Voldemort as the most powerful dark wizard of all times. What I do mean is that he is the person who knows the most about Dark Markets, as he demonstrated during the Distinguished Lecture Series at Fields last week.

In the first lecture Darrell described how over-the-counter markets differ from centralized ones, in particular with respect to the transfer of capital, which tend to be slow in the former, resulting in asset prices which can show a persistent deviation from "fundamentals". He also remarked prices for the same asset at the same time can show a large dispersion, since agents trade bilaterally, with no access to information that can reveal a unique "fair" price at the time of trade. By way of examples, he showed intriguing evidence from the time signature of prices for treasury bonds (that is, how they vary in time near the moment of issuance), as well as cross sectional dispersion in prices. Towards the end of the lecture, he commented on the benefits of clearing houses for derivative contracts.

Having laid the intuition for OTC markets, Darrell used his second lecture to explain an idealized mathematical model for a continuum of agents meeting for bilateral trades at random times according to a given intensity. Through a heavy use of infinite population, the law of large numbers, and independence, he was able to derive an evolution equation (a version of the Boltzman equation) for the "types" of agents in the population. Since at equilibrium bids and types are in a one-to-one correspondence, this evolution equation describes how information "percolates" in the population through an infinite series of double auctions.

In the third and final lecture, which took place during the Financial Econometric workshop, Darrell focused on the interbank market for Fed Funds and used a logit model to describe the probability of a transaction occurring between two banks and fitted the model to a data set comprising of 225 million observations for 8000 banks in 2005.