Gapeev, Pavel V 
ORCID: 0000-0002-1346-2074, Sottinen, T and Valkeila, E
(2007)
Robust replication under model uncertainty.
LSE-CDAM-2007-28.
London School of Economics and Political Science, London, UK.
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 |
| Divisions: | Mathematics |
| Subjects: | H Social Sciences > H Social Sciences (General) |
| Date Deposited: | 09 Jul 2008 08:23 |
| Last Modified: | 01 Nov 2024 05:04 |
| URI: | http://eprints.lse.ac.uk/id/eprint/6735 |
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