Motivated by the growing importance of swing contracts in natural gas markets, this article extends the literature on commodity price modelling as well as valuation methods and sensitivity analysis for swing options. While most previous studies focused on simple price models, we face the challenge of deriving option properties under more realistic commodity price dynamics. We begin by formulating a multi-factor price forward curve model with parametric volatility functions, which can capture uncertainty in both yearly seasonality and time-to-maturity effects, and propose a two-step calibration procedure to fit such models to empirical data. We then show how results from the literature can be combined to obtain swing option values and sensitivities in such a general framework. In this context, we also provide new theoretical results and a first numerical approach to efficiently estimate swing options’ gammas. For options’ deltas, we expand upon existing studies by including a larger variety of contract specifications and by focusing on a multidimensional variant of the Longstaff–Schwartz algorithm as an alternative option valuation method. With these contributions, we supply important tools for swing option sellers and buyers relying on accurate option value and risk estimates to maintain their business models, hedge option-related risks and adequately represent swing options in financial reporting.

中文翻译：

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天然气市场中摇摆合同的定价和风险

由于摇摆合同在天然气市场中的重要性日益提高，本文扩展了有关商品价格建模以及摇摆期权的估值方法和敏感性分析的文献。尽管以前的大多数研究都集中在简单的价格模型上，但我们面临着在更现实的商品价格动态下推导出期权属性的挑战。我们首先建立具有参数波动率函数的多因素价格远期曲线模型，该模型可以捕获年度季节性和到期时间的不确定性，并提出两步校准程序以使此类模型适合经验数据。然后，我们展示了如何将文献中的结果组合起来，以在这种通用框架中获得秋千期权的价值和敏感性。在这种情况下，我们还提供了新的理论结果和第一个数值方法来有效地估计挥杆期权的伽玛。对于期权的差额，我们通过包括更多种类的合同规格以及着眼于Longstaff-Schwartz算法的多维变体作为替代期权评估方法来扩展现有研究。有了这些贡献，我们为摇摆期权买卖双方提供了重要的工具，他们依靠准确的期权价值和风险估计来维持其业务模型，与套期期权相关的风险并在财务报告中充分体现摇摆期权。我们通过包括更多种类的合同规格以及着眼于Longstaff–Schwartz算法的多维变体作为替代的期权评估方法，扩展了现有的研究。有了这些贡献，我们为摇摆期权买卖双方提供了重要的工具，他们依靠准确的期权价值和风险估计来维持其业务模型，与套期期权相关的风险并在财务报告中充分体现摇摆期权。我们通过包括更多种类的合同规格以及着眼于Longstaff–Schwartz算法的多维变体作为替代的期权评估方法，扩展了现有的研究。有了这些贡献，我们为摇摆期权买卖双方提供了重要的工具，他们依靠准确的期权价值和风险估计来维持其业务模型，与套期期权相关的风险并在财务报告中充分体现摇摆期权。