# 2005 Economics Nobel by Mitra L. '07

MIT's intellectual monopoly over game theory knowledge continues. (~9 pictures)

Nobel week is always an exciting time around MIT. Bryan and Matt have done a great job documenting Professor Schrock‘s Nobel prize.

On Monday, the 2005 Nobels in Economics were announced.

Congrats to the two 2005 Nobel Laureates in Economics! —

and — Robert J. Aumann and Thomas C. Schelling. The Nobel website has a nice summary of their work on “conflict and cooperation through the lens of game theory.”

Aumann actually is an MIT alum — he received his Masters and PhD from MIT in Course 18: Mathematics. (Here’s some more info from the MIT News Office)

Here’s my Nobel-worthy rendering of the E52-383 office cluster. In the first office is Professor Haluk Ergin, my advisor, who studies game theory. In the second and third spaces are Professors Emeriti (and, incidentally, Nobel Laureates) Solow and Samuelson.

A third longtime faculty member, the late Professor Emeritus Modigliani, earned a Nobel “for his pioneering analyses of saving and of financial markets.”

Joseph Stiglitz (PhD ’66) and John Nash (faculty ’51-’59 — you may have heard of him) are other MIT-affiliated economists who have won Nobel Prizes for breakthroughs in game theory. Obviously, it’s only a matter of time before my advisor wins his Nobel.

Here’s the Alfred P. Sloan Building (E52), home of the department of cconomics. (This is where all the magic happens.)

Huge kudos again to Professor Aumann for his great achievement!

hmmmm… wow, just wow

Poor Professor Solow… he wins a Nobel Prize and he’s still stuck with the same size office as Professor Ergin. Who, in turn, has to come in and see two Nobel Prizes every morning. In conculsion: rocks to be Samuelson.

I forgot to blog about Solow and Samuelson’s National Medals of Science… which are both up on the wall.

So, do you still have the “Master Model Builder” bio on Paul Samuelson (Larry Summers’ uncle) in your binder? (And, I was wondering: did I show “Trillion Dollar Bet” with Samuelson in it — it was all about the LTCM debacle — the Scholes-Black formula)?

That was the video where Paul Samuelson expressed the hope that the mathematical theory of probability in statistics could be a skeleton key to help investers understand the nature of chance, perhaps to predict it better, or even perhaps to control it?

NARRATOR: Unknown to the economists of the 1930s, a French graduate student at the turn of the century, Louis Bachelier, had already exploited the structure of randomness in his doctoral thesis titled, “The Theory of Speculation.” He compared the behavior of buyers and sellers to the random movements of particles suspended in fluid, anticipating key insights later developed by Einstein and the mathematics of probability. But Bachelier’s accomplishments would go unnoticed for decades.

PAUL SAMUELSON: In the early 1950s I was able to locate by chance this unknown book, rotting in the library of the University of Paris, and when I opened it up it was as if a whole new world was laid out before me. In fact as I was reading it, I arranged to get a translation in English, because I really wanted every precious pearl to be understood.

NARRATOR: Using a series of equations, Bachelier created the first complete mathematical model of stock market fluctuations. He too believed stock prices moved at random and that it was impossible to make exact predictions about them. But then Bachelier said he had found a way to control risk, through an obscure financial contract called an option. He realized options could protect investors from market fluctuations and made the first attempt to figure out how to price them. But his superiors were unimpressed. His academic career faltered.

A stock option is a contract that gives you the right — but not the obligation — to buy or sell a stock at a pre-specified price (the exercise price) for a pre-specified time, that is, until the option “expires.” If the option gives you the right to buy shares of a stock, it is a call option. If the option gives you the right to sell shares of a stock, it is a put option. Exactly how much you should pay for these contracts is determined using the Black-Scholes Formula.

Options are usually sold in sets of 100 (which would allow you to buy or sell 100 shares of the underlying stock at a certain price for the duration of the option).

There are two kinds of stock options: American-type and European-type. American-type stock options allow you to buy or sell the shares of the underlying stock at the exercise price (“exercise” the option) any time until the option expires. European-type stock options allow you to exercise the option only at its expiration date. The formula we provide here applies to a European-type call option. You can buy and sell options just like stocks; their value is determined by the likelihood that they will be “exercised” for a payoff (“in the money”). You can calculate the exact value of the call option using the Black-Scholes Formula (if you know what you’re doing, of course).

The Black-Scholes equation:

C = SN(d1) – Le-rTN(d1 –