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Model-Free Exotic Option Bounds with Dynamic Option Trading

Article arXiv papers · Author: Ariel Neufeld et al.
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Summary

This paper studies model-independent super-replication prices for exotic derivatives when a trader can use both discrete-time semi-static strategies and dynamic trading in a finite set of options. Super-replication bounds describe the cost of strategies designed to cover a derivative's payoff across possible outcomes, without committing to a single pricing model.

The analysis develops duality results and characterizes which pricing rules for the dynamically traded options improve those bounds relative to conventional martingale optimal transport bounds. The document outlines theoretical results, but supplies no specific derivative examples, numerical comparisons, or empirical tests. Its practical implications therefore depend on the options available for dynamic trading and on whether the stated pricing conditions hold in a given market.

Key ideas

  • The framework allows dynamic trading in a finite number of options alongside discrete-time semi-static strategies.
  • It studies model-independent super-replication prices for exotic derivatives.
  • Duality results connect the pricing problem to its corresponding optimization formulation.
  • Certain pricing rules for dynamically traded options can tighten bounds relative to conventional martingale optimal transport results.

Tags

OptionsDerivatives pricingArbitrageRisk management
Full text
# Model-free price bounds under dynamic option trading


# Model-free price bounds under dynamic option trading









In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives. These include duality results as well as a precise characterization of pricing rules for the dynamically tradable options triggering an improvement of the price bounds for exotic derivatives in comparison with the conventional price bounds obtained through the martingale optimal transport approach.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.