CDAM: Computational, Discrete and Applicable
Mathematics@LSE


CDAM Research Report, LSECDAM200728October 2007 
Robust Replication Under Model Uncertainty
Pavel V. Gapeev, Tommi Sottinen, and Esko Valkeila
We consider the robust hedging problem in which an investor wants to superhedge an option in the framework of uncertainty in a model of a stock price process. More specifically, the investor knows that the stock price process is Hselfsimilar with H∈(1/2,1), and that the logreturns are Gaussian. This leads to two natural but mutually exclusive hypotheses both being selfcontained to fix the probabilistic model for the stock price. Namely, the investor may assume that either the market is efficient, i.e. the stock price process is a semimartingale, or that the centred logreturns are stationary. We show that to be able to superhedge a convex European vanillatype option robustly the investor must assume that the markets are efficient. If it turns out that if the other hypothesis of stationarity of the logreturns is true, then the investor can actually superhedge the option as well as receive a net hedging profit.A PDF file (194 kB) with the full contents of this report can be downloaded by clicking here.
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