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When terminal facelift enforces Delta constraints

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  • Jean-Franc{c}ois Chassagneux
  • Romuald Elie
  • Idris Kharroubi

Abstract

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of interest, is the so-called facelift transform of the claim. We investigate under which conditions the super-replication price and strategy of a large class of claims coincide with the exact replication price and strategy of the facelift transform of this claim. In one dimension, we observe that this property is satisfied for any local volatility model. In any dimension, we exhibit an analytical necessary and sufficient condition for this property, which combines the dynamics of the stock together with the characteristics of the closed convex set of constraints. To obtain this condition, we introduce the notion of first order viability property for linear parabolic PDEs. We investigate in details several practical cases of interest: multidimensional Black Scholes model, non-tradable assets or short selling restrictions.

Suggested Citation

  • Jean-Franc{c}ois Chassagneux & Romuald Elie & Idris Kharroubi, 2013. "When terminal facelift enforces Delta constraints," Papers 1307.6020, arXiv.org.
    • Handle: RePEc:arx:papers:1307.6020
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    References listed on IDEAS

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    1. Emmanuel Gobet, 2004. "Revisiting the Greeks for European and American Options," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 3, pages 53-71, World Scientific Publishing Co. Pte. Ltd..
    2. repec:dau:papers:123456789/11551 is not listed on IDEAS
    3. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
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