Arbitrage-Free Pricing Before and Beyond Probabilities
Abstract"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We give examples of such cases. We also show that arbitrage freedom is equivalent to the continuity of the pricing linear form in the relevant topology. Finally we analyze the possible loss of martingality of asset prices with lognormal stochastic volatility. For positive correlation martingality is lost when the financial process is modelled through standard probability theory. We show how to recover martingality using the appropriate mathematical tools.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1310.1102.
Date of creation: Oct 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-10-11 (All new papers)
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