Option Pricing in an Imperfect World

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation from which it is possible, as in the original work of Breeden and Litzenberger, to extract the implied probability. Eventually we test this conclusion empirically via a new non parametric approach.Comment: The paper has been withdrawn because in the newer version it was split into two different papers, each of which have been uploaded into Arxi

Non Parametric Estimates of Option Prices Using Superhedging

We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we first test the methodology on a simulated sample of option prices and then on the S\&P 500 index options.Comment: arXiv admin note: text overlap with arXiv:1406.041

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob-Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measur

Yan Theorem in L ∞ with Applications to Asset Pricing

Abstract : We prove an L ∞ version of the Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets, in which asset prices are a continuous ℝ d valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measure