A general approximate computational framework for basket spread options pricing with and without default risk

Qifeng Zhong; Zheng Liu; Jing Yao; Xingye Yue; Qifeng Zhong; Zheng Liu; Jing Yao; Xingye Yue

doi:10.3934/jimo.2026060

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 4: 1629-1649. doi: 10.3934/jimo.2026060

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A general approximate computational framework for basket spread options pricing with and without default risk

Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou, 215006, China

Received: 16 December 2025 Revised: 05 February 2026 Accepted: 11 February 2026 Published: 09 March 2026
60G51, 62P20, 91B70, 91G20

In this paper, we propose a synthetic computation framework for basket spread options pricing with and without default risk. Our approach is applicable whenever the underlying assets' joint moment-generating function is known, enabling both model-free pricing based solely on data and accurate closed-form pricing formulas under specified models that are up to a user's calibration. Specifically, we utilize a so-called Lau-Bjerksund-Stensland approach to handle the payoffs of basket spread options with and without default risk. By combining it with the Fourier-sinc method, we first derive a closed-form pricing formula for the non-defaultable basket spread options, which is more efficient than the existing ones in the literature. Furthermore, by measure-change techniques, we extend our model-free pricing framework to basket spread options with default risk. To the best of our knowledge, this is the first model-free pricing for such options, whereas previous research is based on specific models. Numerical examples demonstrate that our pricing formula exhibits high accuracy and robust performance across varying parameters. In particular, our model-free pricing formula still performs well even with limited data.
- basket spread option,
- default risk,
- closed-form pricing,
- Fourier-sinc method,
- approximation
Citation: Qifeng Zhong, Zheng Liu, Jing Yao, Xingye Yue. A general approximate computational framework for basket spread options pricing with and without default risk[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 1629-1649. doi: 10.3934/jimo.2026060

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Abstract

In this paper, we propose a synthetic computation framework for basket spread options pricing with and without default risk. Our approach is applicable whenever the underlying assets' joint moment-generating function is known, enabling both model-free pricing based solely on data and accurate closed-form pricing formulas under specified models that are up to a user's calibration. Specifically, we utilize a so-called Lau-Bjerksund-Stensland approach to handle the payoffs of basket spread options with and without default risk. By combining it with the Fourier-sinc method, we first derive a closed-form pricing formula for the non-defaultable basket spread options, which is more efficient than the existing ones in the literature. Furthermore, by measure-change techniques, we extend our model-free pricing framework to basket spread options with default risk. To the best of our knowledge, this is the first model-free pricing for such options, whereas previous research is based on specific models. Numerical examples demonstrate that our pricing formula exhibits high accuracy and robust performance across varying parameters. In particular, our model-free pricing formula still performs well even with limited data.

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