MODEL-INDEPENDENT NO-ARBITRAGE CONDITIONS ON AMERICAN PUT OPTIONS

DOI10.1111/MAFI.12058zbMath1380.91128arXiv1301.5467OpenAlexW2152787912MaRDI QIDQ2800003

Christoph Hoeggerl, Alexander Matthew Gordon Cox

Publication date: 14 April 2016

Published in: Mathematical Finance (Search for Journal in Brave)

Abstract: We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American Put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process.

Full work available at URL: https://arxiv.org/abs/1301.5467

zbMATH Keywords

American optionSkorokhod embeddingmodel-independent arbitrageLegendre-Fenchel transformationconvex conjugate

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20)

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Related Items (4)

Perturbation analysis of sub/super hedging problems ⋮ Robust bounds for the American put ⋮ Model uncertainty and the pricing of American options ⋮ No-Arbitrage and Hedging with Liquid American Options

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