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Model-independent pricing with insider information: a skorokhod embedding approach

Part of: Mathematical finance Stochastic processes

Published online by Cambridge University Press:  17 March 2021

Beatrice Acciaio ,
Alexander M. G. Cox Open the ORCID record for Alexander M. G. Cox [Opens in a new window]  and
Martin Huesmann
Beatrice Acciaio*
Affiliation:
ETH Zurich
Alexander M. G. Cox*
Affiliation:
University of Bath
Martin Huesmann*
Affiliation:
Universität Münster
*
*Postal address: Department of Mathematics, ETH Zurich, Switzerland.
**Postal address: Department of Mathematical Sciences, University of Bath, UK. Email address: a.m.g.cox@bath.ac.uk
***Postal address: Institute of Mathematical Stochastics, Universität Münster, Germany.
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Abstract

In this paper we consider the pricing and hedging of financial derivatives in a model-independent setting, for a trader with additional information, or beliefs, on the evolution of asset prices. In particular, we suppose that the trader wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the payoff of the derivative, and the insider’s information or beliefs, which take the form of a set of impossible paths, are time-invariant. In this way we accommodate drawdown constraints, as well as information/beliefs on quadratic variation or on the levels hit by asset prices. Our setup allows us to adapt recent work of [12] to prove duality results and a monotonicity principle. This enables us to determine geometric properties of the optimal models. Moreover, for specific types of information, we provide simple conditions for the existence of consistent models for the informed agent. Finally, we provide an example where our framework allows us to compute the impact of the information on the agent’s pricing bounds.

Keywords

Inside informationmodel-independent pricing and hedgingSkorokhod embedding problemmonotonicity principle

MSC classification

Primary: 91G20: Derivative securities
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 1 , March 2021 , pp. 30 - 56
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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