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SUMMARY:Adversarial Option Pricing: How Robust is Black-Scholes? - Rafael 
 M. Frongillo (Berkeley)
DTSTART:20121029T150000Z
DTEND:20121029T160000Z
UID:TALK41239@talks.cam.ac.uk
CONTACT:Felix Fischer
DESCRIPTION:Option contracts are a type of financial derivative that allo
 w investors to hedge risk and speculate on an asset’s future market pric
 e.  In 1973\, Black and Scholes proposed a valuation model for options tha
 t essentially estimates the tail risk of the asset under the assumption th
 at the price will fluctuate according to geometric Brownian motion.  More
  recently\, DeMarzo et al. proposed a more robust valuation scheme which h
 as much weaker assumptions on the price path\; indeed\, in their model the
  asset’s price can even be chosen adversarially.  This framework can be 
 considered as a sequential two-player zero-sum regret game between the inv
 estor and Nature.  We analyze the value of this game in the limit\, where 
 the investor can trade at smaller and smaller time intervals.  Under weak 
 assumptions on the actions of Nature (the adversary)\, we show that the mi
 nimax option price asymptotically approaches exactly the Black-Scholes val
 uation.  The key piece of our analysis is showing that Nature’s minimax 
 optimal dual strategy converges to geometric Brownian motion in the limit.
   Joint work with Jake Abernethy and Andre Wibisono.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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