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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频谱负Lévy过程下与功率相关的期权的价值

我们提供分析工具，用于在由单边稳定或回火稳定过程驱动的指数Lévy模型的框架中对具有异国情调的功能（上限或对数收益，缺口选项等）进行定价。定价公式采用对数货币性和到期时间的一系列快速收敛的幂的形式。这些序列是通过在Mellin空间中通过\（\ mathbb {C} \）或\（\ mathbb {C} ^ 2 \）中的残差评估的因式积分表示获得的。还讨论了与数值方法和效率测试的比较。