Review of Derivatives Research

, Volume 22, Issue 1, pp 77–167 | Cite as

Pricing and risk of swing contracts in natural gas markets

  • Hendrik Kohrs
  • Hermann Mühlichen
  • Benjamin R. AuerEmail author
  • Frank Schuhmacher


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.


Natural gas Forward curve dynamics Swing options Delta Gamma Simulation 

JEL Classification

G12 G13 C63 C65 



We thank the Verbundnetz Gas AG for supporting our research by supplying forward price data and by contributing important ideas for the design of the estimation methods developed in our article. We are also indebted to Max von Renesse, Ralf Wunderlich, Xaver Muschik, the editor, and an anonymous reviewer for valuable comments and suggestions. Generous financial support was provided by the Wissenschaftsförderung der Sparkassen-Finanzgruppe e.V.

Supplementary material


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Hendrik Kohrs
    • 1
  • Hermann Mühlichen
    • 2
  • Benjamin R. Auer
    • 1
    • 3
    Email author
  • Frank Schuhmacher
    • 1
  1. 1.Department of FinanceUniversity of LeipzigLeipzigGermany
  2. 2.Risk Management/Quantitative AnalysisVNG Handel & Vertrieb GmbHLeipzigGermany
  3. 3.Research Network Area Macro, Money and International FinanceCESifo MunichMunichGermany

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