Hedging At-the-money Digital Options Near Maturity

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.