Minimax Option Pricing Meets Black-Scholes in the Limit
Speaker: Jake Abernethy , U Penn
Date: May 1 2012
Time: 4:15PM to 5:15PM
Location: 32-155
Host: Costis Daskalakis, CSAIL, MIT
Contact: Be Blackburn, 3-6098, imbe@mit.edu
Relevant URL: Option contracts are a type of financial derivative that allow
investors to hedge risk and speculate on the volatility of an asset's
future market price. In short, an option has a particular payout that
is based on the market price for an asset on a given date in the
future. In 1973, Black and Scholes proposed a valuation model that
gives a "fair price" for an option under the assumption that the price
fluctuates according to geometric Brownian motion (GBM). Black and
Scholes provided a continuous-time trading strategy for an investor,
known as a "replication strategy" or "hedging strategy", which allows
the investor to buy and sell the asset in order to "replicate" the
option's payoff.
In this talk we'll consider the the design of replication strategies,
and hence a pricing mechanism, for options and other derivatives that
does not rely on the GBM assumption. Indeed, we shall address the
following question: what can an investor achieve when the asset's
price path is chosen by... an adversary? What we show is that, even
under these worst-case conditions, we ultimately recover the Black
Scholes pricing model but without the GBM assumption.
This talk will dive into topics like finance and repeated game
playing, but will be relatively accessible to anyone with an interest
in game theory, learning theory, or online algorithms.
Joint work with Rafael Frongillo and Andre Wibisono.
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