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Change of numeraire in the two-marginals martingale transport problem

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  • Luciano Campi
  • Ismail Laachir
  • Claude Martini

Abstract

In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studied in \cite{BrenierMartingale}. We show that, in the case of positive martingales, a suitable change of numeraire applied to \cite{HobsonKlimmek2013} exchanges forward start straddles of type I and type II, so that the optimal transport plan in the subhedging problems is the same for both types of options. Moreover, for \cite{BrenierMartingale}'s construction, the right monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire. An application to stochastic volatility models is also provided.

Suggested Citation

  • Luciano Campi & Ismail Laachir & Claude Martini, 2014. "Change of numeraire in the two-marginals martingale transport problem," Papers 1406.6951, arXiv.org, revised Mar 2016.
    • Handle: RePEc:arx:papers:1406.6951
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    References listed on IDEAS

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    1. Tehranchi, Michael R., 2009. "Symmetric martingales and symmetric smiles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3785-3797, October.
    2. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    3. David Hobson & Martin Klimmek, 2013. "Robust price bounds for the forward starting straddle," Papers 1304.2141, arXiv.org.
    4. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    5. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
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    Cited by:

    1. Huesmann, Martin & Stebegg, Florian, 2018. "Monotonicity preserving transformations of MOT and SEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1114-1134.

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