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Consistent Upper Price Bounds For Exotic Options

Author

Listed:
  • NICOLE BÄUERLE

    (Department of Mathematics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, Karlsruhe 76131, Germany)

  • DANIEL SCHMITHALS

    (Department of Mathematics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, Karlsruhe 76131, Germany)

Abstract

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

Suggested Citation

  • Nicole Bäuerle & Daniel Schmithals, 2021. "Consistent Upper Price Bounds For Exotic Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-29, March.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:02:n:s0219024921500114
    DOI: 10.1142/S0219024921500114
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    Citations

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    Cited by:

    1. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    2. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.

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