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Hedging At-the-money Digital Options Near Maturity

Author

Listed:
  • Augusto Blanc-Blocquel

    (Universitat Politècnica de Catalunya)

  • Luis Ortiz-Gracia

    (University of Barcelona)

  • Rodolfo Oviedo

    (Independent Financial Advisor)

Abstract

Hedging at-the-money digital options near maturity, remains a challenge in quantitative finance. In the present work, we carry out a hedging strategy by means of a bull spread. We study the probability of super- and sub-hedge the digital option and minimize the probability of a sub-hedge considering the cost of hedging and illiquidity issues. We perform a wide variety of numerical experiments under different models for the underlying asset dynamics. A calibration to market data is provided and used to get the optimal composition of the bull spread satisfying the cost of hedging restriction.

Suggested Citation

  • Augusto Blanc-Blocquel & Luis Ortiz-Gracia & Rodolfo Oviedo, 2023. "Hedging At-the-money Digital Options Near Maturity," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10013-6
    DOI: 10.1007/s11009-023-10013-6
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    References listed on IDEAS

    as
    1. Valeri Zakamouline, 2009. "The Best Hedging Strategy In The Presence Of Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 833-860.
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    3. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221, World Scientific Publishing Co. Pte. Ltd..
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Digital option; Short maturity; At-the-money; Hedging; Bull call spread; Black-Scholes; Heston model; CGMY model;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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