In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semistatic portfolios should more properly be thought of as separate classes of derivatives, with nontrivial, model‐dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr–Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizably larger than the errors of variance‐minimizing portfolios. We explain why the exact semistatic hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance‐minimizing semistatic portfolios. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener–Hopf factors and Laplace–Fourier inversion.

中文翻译：

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静态和半静态对冲作为逆势或顺应性押注

在本文中，我们认为，一旦适当考虑了对冲投资组合的维护成本，就应该更恰当地将半静态投资组合视为衍生品的独立类别，并且具有非平凡的，与模型相关的收益结构。我们从香草收益方面衍生出新的欧洲异国期权收益积分表示法，与Carr-Madan表示法不同，并建议使用市场上可用的香草来近似理想的静态对冲/复制投资组合。我们研究了套期保值误差对定价模型的依赖性，结果表明，静态套期保值投资组合的套期误差的方差可以比最小化投资方差的误差大得多。我们解释了为什么对于具有跳跃的过程无法进行障碍期权的精确半静态对冲，并推导了用于最小化半静态投资组合的一般公式。我们显示，使用香草套期保值比使用香草和首次触摸数字套期保值只会导致更大的错误。在所有情况下，