Time-Discrete Hedging of Down-and-Out Puts with Overnight Trading Gaps

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier hit that would render claim worthless afterwards, challenging. All hedging methods potentially lead to large errors when underlying already close and hedge portfolio can only be adjusted in discrete time intervals. In this paper, we analyze situation, especially case of overnight trading gaps. We show how position short-term vanilla call option used for efficient hedging. Using mean-variance approach, calculate optimal ratios both options as instruments. derive semi-analytical formulas Black–Scholes setting continuous (as benchmark) For more complex models, numerical study sufficient approximation, even stochastic volatility jumps are present.