This talk is long but very good. If you are impatient you can skip to the last 3 minutes where Merton answers a question about the CDS market that has been widely discussed. He points out the value for real world companies of being able to transfer credit risk as opposed to the narrower application of insuring a bond that they actually own.
The central point of the first part of the talk  the embedded put option in a plain vanilla loan, and associated nonlinearities  is nice but I don't think it is as essential to the current crisis as he suggests. (It's obviously in his interests to downplay the complexity of new financial instruments relative to traditional ones. The difference, of course, is that we've had much more time to get used to the traditional ones and build the proper safeguards and regulatory systems.) Merton is refreshingly modest about his understanding of the complex causes of the crisis. At one point he notes that the post mortem investigation into the crisis is unlikely to produce a Feynman moment, in which someone holds up an Oring that caused the disaster!
Here is another link in case the player below doesn't work for you.
I sat in on Merton's graduate class on options pricing theory at Harvard in the early 1990s. I still have the lecture notes and a black paperback copy of Continuous Time Finance. He seemed much more confident at the time, but of course that was before LTCM :)
I was one of the first people to recast options pricing theory into the language of Feynman path integrals. (You don't need the power of quantum field theory for this; the log of the price of the underlying security is just the position of a particle in simple 1D quantum mechanics in imaginary time  i.e., it's just Brownian motion.) A friend of mine had been assigned a thesis project by Andy Lo at MIT, to price a certain type of exotic, path dependent option sold by Citibank. Lo didn't know the option could be priced in closed form (neither did Citi, it turns out); he asked my friend to do it numerically by brute force Monte Carlo. Using path integrals I found an exact expression for my friend, which agreed perfectly with his simulations.
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12 comments:
"I was one of the first people to recast options pricing theory into the language of Feynman path integrals."
Are you running a fund Steve? Why not? Your children and your wife would love you for it.
Merton is a gentile, right?
Of course he isn't a gentile.
Yes, you mentioned this work of yours a few years ago on this blog, saying that it can still be found lurking on some (MITrelated?) site somewhere. I'm very interested in this topic and have searched and searched, but come up emptyhanded... can you give a fat hint?
Steve, I recommend this article from the News Hour on PBS. I think it belies some perceptions regarding how popular these investments were and also the impact of the rating agencies on the sales appeal of them.
http://www.pbs.org/newshour/bb/business/janjune09/houseofcards_0320.html
I'd like to get your thoughts.
Fred
Anon: Do I have a fund? No, I wish I did. But then again I am not so overconfident (unlike Scholes, Merton and LTCM company ;) to be sure that I have any magic alpha touch...
Grim: This thesis was done before there was electronic preprint distribution for finance / econ. At the time, only theoretical physics had it :)
So, you can't find it except perhaps in hard copy at the MIT / Sloan library.
If you have specific technical questions feel free to email me about it. Basically, you can obtain a closed form solution for any path dependent exotic option using this method. You need the free particle propagator (Green's function) for nonrelativistic QM and a bunch of delta function potentials. You are basically just computing the expected return and the delta functions are there to put in the path weighting. You'll find it trivial once you understand it :)
I wish I could say that listening to Merton restored my confidence in financial "science" and the ability of its practitioners, but it didn't. When you sat in on his class you must have been slumming! Sorry, and maybe I am wrong.
P.S. Samuelson's selfregard is just plain embarassing. He's the Barbara Streisand of the profession. I wager his reputation will go to zero soon after he kicks the bucket, just like that king of sociology at Harvard a generation back, what was his name? O, yea, Parsons.
Actually, Merton is clearly quite sharp in person (certainly at the time) and fairly strong mathematically. There were stronger people auditing his class, but his mastery of the material  much of which he invented  was clear.
What impressed me about this talk is his humility and understanding of the limitations of the theory. More often you get famous economists who overrate the effectiveness of their models (particularly Chicago types).
Fred: I think Cohan is on the money re: incentives, agency risk. The overnight financing factor is true but it's not that central; the overall leverage is the issue.
I just read Bookstaber's "Demon of our own design". Basically what he says is that however good your model, when an Fscale liquidity crisis strikes, and you are highly leveraged on the wrong side of the trade, it is game over.
If there is a closed form solution of the path integral then there should also be one using Ito calculus right? It will end up as solving a PDE with jump discontinuities?
Carson: yes.
This shows up in the procedure of rating AIG as AAA, which did not take into account the nonlinear risk of their switch portfolio.
Vanessa
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