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Model-independent bounds for Asian options: a dynamic programming approach

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  • Alexander M. G. Cox
  • Sigrid Kallblad

Abstract

We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we consider the problem as a dynamic programming problem, where the controlled process is the conditional distribution of the asset at the maturity date. By formulating the problem in this manner, we are able to determine the model-independent price through a PDE formulation. Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to generalise to many related problems.

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  • Alexander M. G. Cox & Sigrid Kallblad, 2015. "Model-independent bounds for Asian options: a dynamic programming approach," Papers 1507.02651, arXiv.org, revised Jul 2016.
    • Handle: RePEc:arx:papers:1507.02651
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    References listed on IDEAS

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    1. Martin Forde & Antoine Jacquier, 2010. "Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 241-259.
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    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    5. Yan Dolinsky & Halil Mete Soner, 2013. "Martingale Optimal Transport and Robust Hedging in Continuous Time," Swiss Finance Institute Research Paper Series 13-13, Swiss Finance Institute.
    6. Florian Stebegg, 2014. "Model-Independent Pricing of Asian Options via Optimal Martingale Transport," Papers 1412.1429, arXiv.org.
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