Légion d'Honneur

I had a rare glimpse of the French establishment today when I attended the ceremony in which Monique Jeanblanc became a Chevalier de l'Ordre National de la Légion d'Honneur.

Being a member of the Order is the highest decoration in France, fully deserved by Monique. The nice touch is that, although new members are appointed directly by the President of the Republic, the formal induction can be performed by a current member with some personal connections with the inductee, in this case Nicole El Karoui, herself a Chevalier and a lifelong friend and colleague of Monique's.

When computer nerds try to communicate

A propos of nothing, except for the fact that I'm under a couple of deadlines and having to type a lot in Latex and transfer many Unix files, it never ceases to amuse me how computer experts really don't have any language skills.

My all times favorite irritant from Latex is:

"Missing $ inserted."

by which the lovely folks who created Latex simply mean that the compiler found an unmatched dollar sign, as opposed to the existential puzzle it evokes.

Then of course there is Unix saying that something or other cannot be "canonicalized", which even this blog editor knows is not a word. Memo to Unix creators: the noun is canon, the adjective is canonical and the verb is canonize.

End of bubbles course

I gave the 4th and final lecture for my Cours Bachelier on bubbles last Friday, following the lecture that I reviewed here (where you can find links to the first two).

The central topic for this lecture was the local martingale approach of Jarrow, Protter and Shimbo (and previous references therein), where bubbles are characterized under the NFLVR (no free lunch with vanishing risk) condition. This is the current accepted way to express no arbitrage in modern mathematical finance language and is significantly weaker than an equilibrium condition, since it does not require any notion of optimality of market clearing. As such, the results for bubbles in this setting generalize those related to rational bubbles, which are typically done in equilibrium. On the other hand, it would be nice to use a similar mathematical framework (i.e semimartingales) to address the models for irrational bubbles that were discussed in the previous lectures. In my view, there are still many low hanging fruits for mathematicians to pick in this field.

The last part of the lecture (and the course) was dedicated to a brief review of the statistical tests proposed to detect bubbles in real data. Since I'm not a statistician, I mostly followed the this review, with a special emphasis on the work on volatility bounds.

I then concluded with a breakneck-speed tour of famous bubbles throughout history, including the tulipmania, which may of may not have been a bubble, the Mississippi and South Sea bubbles, which might have been just a huge (yet failed) macroeconomic experiment, and the crash of 1929, which almost certainly was a bubble, even under the most optimistic definitions of fundamental values.

All references (and possibly slides and lecture notes in the near future) can be found here.

Bubbles course - part III

I gave the third lecture of my Cours Bachelier at IHP yesterday, which followed the lectures that I described here and here.

I first reviewed the work of Frank Allen and Douglas Gale on the role that financial intermediation has in creating bubbles and crises. The idea is that when investors buy assets with borrowed money, the possibility of defaulting on the original loans makes the equilibrium price higher than it would be if they had to buy with their own money. Essentially, the loan plays the role of a "call option" whose convex payoff drives the asset price up. The key insight is that this type of bubble can be created by uncertainty in the amount of credit itself, rather than in the real economy. They show that in some cases a crises can occur even when credit is expanding, essentially because it didn't expand as much as necessary to keep fueling the overinflated asset price. In my view this is a neat toy model for the Minsky story about financial instability.

For the second part of the lecture, I focused bubbles caused by heterogeneous beliefs. The essential idea is simple: when short sales are possible, the views of optimists are balances by those of pessimists and asset prices reflect fundamental value, whereas if there are short sale constraints, pessimists sit on the side lines, prices reflect the views of optimists and a bubble ensues. This mechanism was described for discrete-time models by Harrison and Kreps in a paper on speculative behavior.

One possible source for heterogeneous beliefs is overconfidence, as proposed in a continuous-time model by Scheinkman and Xiong, which I reviewed towards the end of the lecture.

All references for the course can be found here.

Monique Jeanblanc's influence in architecture

The mathematical finance group at Evry is so influential that they convince the local architects to build a cadlag elevator:

Grasselli x Grasselli

People at the Groupe parisien Bachelier must have a sense of humor, as they schedule both Martino Grasselli and myself to speak on the same morning this week :)

This should give irrefutable evidence that we are not the same person, or are we ?

Bubbles course - part II

Following up on this post, I gave the second lecture of my graduate course on asset price bubbles on October 22nd.

I started by discussing how rumors (say mean--reverting shocks not related to fundamentals) can be incorporated into an asset price in a way that is compatible with the fact that observed prices are not very forecastable, as explained by Robert Shiller in a paper on social dynamics. I then further explained the idea that prices can deviate from fundamentals because of irrational traders using a famous paper by Brad DeLong, Andrei Shleifer, Larry Summers and Robert Waldmann on noise trader risk. I concluded with a discussion of the equally famous paper by Andrei Shleifer and Robert Vishny on limits of arbitrage when investors use other people's money and are subject to performance reviews.

The point is that these "market inefficiencies" can lead to asset prices which deviate a lot from their fundamental values in a way that is different from the rational bubbles discussed in the first lecture. In particular, these inefficiency bubbles are not necessarily "growing bubbles", and therefore not subject to the type of transversality conditions that are typically used to rule out rational bubbles.

Specific mechanisms for the formation of these inefficiency bubbles will be discussed in the next lecture.

All references for the course can be found here.