Closed-form option formulas for Kou-like models

Matteo Gardini and Piergiacomo Sabino

Quantitative Finance, 2025, vol. 25, issue 10, 1517-1534

Abstract: The aim of this study is to expand the Kou model to emulate the Samuelson effect, a characteristic attribute observed in commodity options. This study explores both the NOA additive jump diffusive model for future contracts and an exponential jump diffusion dynamics. We derive closed-formulas for call and put options with different types of jump distributions all related to the exponential law. As a side product, we can derive the densities of the convolution between several Erlang-like laws and the Gaussian distribution in addition to simplifications of the original Kou model formulas, rendering them more accessible involving simple functions only. Finally, we present extensive numerical applications within energy markets and conduct comparative analyses against other well-established models.

Date: 2025
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DOI: 10.1080/14697688.2025.2546000

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