Hedging At-the-money Digital Options Near Maturity

Augusto Blanc-Blocquel, Luis Ortiz-Gracia () and Rodolfo Oviedo
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Augusto Blanc-Blocquel: Universitat Politècnica de Catalunya
Luis Ortiz-Gracia: University of Barcelona
Rodolfo Oviedo: Independent Financial Advisor

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-18

Abstract: 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.

Keywords: Digital option; Short maturity; At-the-money; Hedging; Bull call spread; Black-Scholes; Heston model; CGMY model (search for similar items in EconPapers)
JEL-codes: C61 C63 G13 G32 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10013-6

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