Robust Pricing and Hedging of American Options in Continuous Time
Researchers have solved a long-standing challenge in pricing and hedging American options in continuous time, even when the underlying financial model is uncertain. By linking American options to European options on an expanded space and introducing concepts like randomised stopping times and Azéma supermartingales, they prove that the superhedging price equals the highest expected payoff over all risk-neutral measures and stopping times. The work is mathematically advanced but may be difficult for non-specialists and lacks practical numerical methods.
What it examines
This paper studies how to price and hedge American options in continuous time when there is uncertainty about the model, especially about volatility. The authors use advanced mathematical tools, including optimal transport and randomised stopping times, to prove a robust pricing-hedging duality under general volatility constraints and market information.
What it concludes
The results show that robust pricing-hedging duality holds for American options even with model uncertainty and volatility constraints. This work helps financial institutions manage risk more reliably. Applications include pricing and hedging options in uncertain markets. Future research may extend these methods to more complex financial products or market settings.
Evidence objects
Researchers achieve a breakthrough in robust pricing and hedging of American options in continuous time, proving a duality even under model uncertainty and general volatility constraintsa challenge that has long stumped experts.
key_findings bullet 1 · key_findings · validation V0
A novel approach identifies American options with European options on an enlarged space, restoring duality even when European options are traded dynamicallyovercoming limitations of previous methods and expanding practical applicability.
key_findings bullet 2 · key_findings · validation V0
The paper introduces advanced tools like randomised stopping times, Azma supermartingales, and pathwise stochastic integration, showing the superhedging price equals the supremum of expected payoffs over all risk-neutral measures and stopping times.
key_findings bullet 3 · key_findings · validation V0
This paper uniquely resolves a major open problem in robust pricing and hedging of American options in continuous time, extending duality results from discrete to continuous settings. By introducing novel probabilistic techniques and leveraging optimal transport duality, it offers original theoretical advancements with significant implications for both quantitative finance research and practical applications.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
Abstract: We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex constraints on the volatility. We prove the robust pricing-hedging duality. When European options with given prices are available for static trading, we show that dualit… ▽ More We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex constraints on the volatility. We prove the robust pricing-hedging duality. When European options with given prices are available for static trading, we show that duality holds against richer models where these options are traded dynamically. Our proofs rely on probabilistic treatment of randomised stopping times and suitable measure decoupling, and on optimal transport duality. In addition, similarly to the approach of Aksamit et al. (2019) in discrete time, we identify American options with European options on an enlarged space. △ Less
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