Model-independent pricing with insider information: A Skorokhod embedding approach

Beatrice Acciaio, Alexander M. G. Cox, Martin Huesmann

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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.

Original languageEnglish
Pages (from-to)30-56
Number of pages27
JournalAdvances in Applied Probability
Volume53
Issue number1
Early online date17 Mar 2021
DOIs
Publication statusPublished - 31 Mar 2021

Keywords

  • Inside information
  • Skorokhod embedding problem
  • model-independent pricing and hedging
  • monotonicity principle

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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