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Robust replication under model uncertainty

Gapeev, Pavel V, Sottinen, T and Valkeila, E (2007) Robust replication under model uncertainty. LSE-CDAM-2007-28, London School of Economics and Political Science, London, UK.

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Abstract

We consider the robust hedging problem in which an investor wants to super-hedge 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 H-self-similar with H∈(1/2,1), and that the log-returns are Gaussian. This leads to two natural but mutually exclusive hypotheses both being self-contained 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 log-returns are stationary. We show that to be able to super-hedge a convex European vanilla-type option robustly the investor must assume that the markets are efficient. If it turns out that if the other hypothesis of stationarity of the log-returns is true, then the investor can actually super-hedge the option as well as receive a net hedging profit.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/Files/cdam-2007-...
Additional Information: © 2007 The Authors
Library of Congress subject classification: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Jul 2008 08:23
URL: http://eprints.lse.ac.uk/6735/

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