Model-Free Representation of Pricing Rules as Conditional Expectations

16 Pages Posted: 30 Mar 2009

See all articles by Sara Biagini

Sara Biagini

LUISS University

Rama Cont

University of Oxford

Date Written: December 18, 2006

Abstract

We introduce a distinction between model-based and model-free arbitrage and formulate an operational definition for absence of model-free arbitrage in a financial market, in terms of a set of minimal requirements for the pricing rule prevailing in the market. We show that any pricing rule verifying these properties can be represented as a conditional expectation operator with respect to a probability measure under which prices of traded assets follow martingales. Our result can be viewed as a model-free version of the fundamental theorem of asset pricing, which does not require any notion of "reference" probability measure.

Keywords: arbitrage, pricing rule, martingale, fundamental theorem of asset pricing

JEL Classification: G13

Suggested Citation

Biagini, Sara and Cont, Rama, Model-Free Representation of Pricing Rules as Conditional Expectations (December 18, 2006). Available at SSRN: https://ssrn.com/abstract=1370563 or http://dx.doi.org/10.2139/ssrn.1370563

Sara Biagini

LUISS University ( email )

Viale Romania 32
Rome, 00197
Italy

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

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