We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options etc.) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of the time-to-maturity; these series are obtained via a factorized integral representation in the Mellin space evaluated by means of residues in \(\mathbb {C}\) or \(\mathbb {C}^2\). Comparisons with numerical methods and efficiency tests are also discussed.

中文翻译：

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谱负 Lévy 过程下与功率相关的期权的价值

我们在由单边稳定或缓和稳定过程驱动的指数 Lévy 模型框架内，提供具有奇异特征（上限或对数收益、缺口期权等）的定价权期权分析工具。定价公式采用对数远期货币性和到期时间的幂系列快速收敛的形式；这些序列是通过 Mellin 空间中的因式分解积分表示获得的，该表示通过\(\mathbb {C}\)或\(\mathbb {C}^2\)中的留数求值。还讨论了与数值方法和效率测试的比较。