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Derivative Pricing and Hedging Under Local Viability Constraints

Article arXiv papers · Author: Huy N. Chau et al.
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Summary

The paper presents a general method for pricing and hedging derivatives in frictionless markets. Its approach is designed to apply even when an equivalent local martingale measure does not exist, a condition that can limit standard pricing methods. The central result is a superhedging duality for American options, including settings where wealth processes may become negative and trading strategies face cone constraints.

The work therefore extends a duality framework to markets with these features and addresses a question previously raised by other researchers. The short description states the scope and main theoretical result but gives no proof details, worked examples, or empirical evaluation. It does not describe a trading strategy or indicate how the framework performs in any particular market, so its practical application depends on assumptions and results beyond those summarized here.

Key ideas

  • The proposed framework addresses derivative pricing and hedging in general frictionless markets.
  • It remains applicable when an equivalent local martingale measure is unavailable.
  • The paper establishes a superhedging duality for American options.
  • The result allows negative wealth processes and cone-constrained trading strategies.
  • The brief description gives theoretical scope but no empirical evidence or market-specific implementation.

Tags

OptionsDerivatives pricingRisk managementStatistics
Full text
# A general framework for pricing and hedging under local viability


# A general framework for pricing and hedging under local viability









In this paper, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to exist. Our main results include a new superhedging duality for American options when wealth processes can be negative and trading strategies are subject to a cone constraint. This answers one of the questions raised by Fernholz, Karatzas and Kardaras.

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.