IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1307.6020.html
   My bibliography  Save this paper

When terminal facelift enforces Delta constraints

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1307.6020
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-François Chassagneux & Romuald Elie & Idris Kharroubi, 2015. "When terminal facelift enforces delta constraints," Finance and Stochastics, Springer, vol. 19(2), pages 329-362, April.
    2. Kasper Larsen & H. Mete Soner & Gordan Zitkovic, 2014. "Facelifting in Utility Maximization," Papers 1404.2227, arXiv.org.
    3. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    4. Peter Bank & Selim Gokay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
    5. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    6. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
    7. Ramachandran, Lakshmi Shankar & Tayal, Jitendra, 2021. "Mispricing, short-sale constraints, and the cross-section of option returns," Journal of Financial Economics, Elsevier, vol. 141(1), pages 297-321.
    8. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    9. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    10. Bentahar, Imen & Bouchard, Bruno, 2006. "Barrier option hedging under constraints: A viscosity approach," SFB 649 Discussion Papers 2006-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    12. Aliprantis, C. D. & Brown, D. J. & Werner, J., 2000. "Minimum-cost portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1703-1719, October.
    13. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    14. Huang, Kevin X. D., 2002. "On infinite-horizon minimum-cost hedging under cone constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 283-301, December.
    15. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    16. Kharroubi Idris & Lim Thomas & Warin Xavier, 2021. "Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 27-55, March.
    17. René Doff & Jan Bilderbeek & Bert Bruggink & Pieter Emmen, 2009. "Performance Management in Insurance Firms by Using Transfer Pricing," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 12(2), pages 213-226, September.
    18. Erdnç Akyildirim & Albert Altarovici, 2016. "Partial hedging and cash requirements in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 929-945, June.
    19. Atmaz, Adem & Basak, Suleyman, 2019. "Option prices and costly short-selling," Journal of Financial Economics, Elsevier, vol. 134(1), pages 1-28.
    20. Nakatsu, Tomonori, 2023. "On density functions related to discrete time maximum of some one-dimensional diffusion processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1307.6020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.