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Arbitrage-Free Pricing Before and Beyond Probabilities

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  • Louis Paulot

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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  • Louis Paulot, 2013. "Arbitrage-Free Pricing Before and Beyond Probabilities," Papers 1310.1102, arXiv.org.
  • Handle: RePEc:arx:papers:1310.1102
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    File URL: http://arxiv.org/pdf/1310.1102
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    Cited by:

    1. Travis Fisher & Sergio Pulido & Johannes Ruf, 2017. "Financial Models with Defaultable Numéraires," Working Papers hal-01240736, HAL.
    2. Travis Fisher & Sergio Pulido & Johannes Ruf, 2015. "Financial Models with Defaultable Num\'eraires," Papers 1511.04314, arXiv.org, revised Oct 2017.

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