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

Rainer Baule and Philip Rosenthal
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Rainer Baule: Chair of Banking and Finance, University of Hagen, Universitätsstraße 41, 58084 Hagen, Germany
Philip Rosenthal: Chair of Banking and Finance, University of Hagen, Universitätsstraße 41, 58084 Hagen, Germany

JRFM, 2022, vol. 15, issue 1, 1-20

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

Keywords: exotic option; down-and-out put; time-discrete hedging; mean-variance hedging; Black–Scholes model; jump diffusion (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2022
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