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Testing the Closed-Form Spread Option Pricing Formula Based on Gauss-Hermite Quadrature for a Jump-Diffusion Model

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Abstract

In this paper we develop a closed-form spread option pricing formula based on Gauss-Hermite quadrature (GHQ) and show that the proposed method is a competitive method for the Black-Scholes model and is best-suited for the jump-diffusion model. The GHQ method turns the integral of spread option pricing formula into a summation of call option pricing formulas with adjusted parameters, and therefore the final formula remains in closed-form which ensures its computational advantage. Under the basic Black-Scholes model, the proposed GHQ formula provides equally nice accuracy compared to the best-performing LDZ formula in the literature. But for the extended jump-diffusion model, the LDZ formula sees a significant loss of accuracy due to the multi-layered summation, whereas the GHQ formula is still able to achieve very high accuracy at only slightly increased computing costs. Various closed-form formulas are tested in our numerical analysis which demonstrates that the proposed GHQ formula is the most recommended for pricing spread options under the jump-diffusion model.

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Acknowledgements

The authors acknowledge the supports from the Ministry of Science and Technology of Taiwan under the Grant Number MOST-108-2410-H-011-027.

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Authors and Affiliations

  1. Accounting Information, Aletheia University, New Taipei City, Taiwan

    Xenos Chang-Shuo Lin

  2. Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei City, Taiwan

    Daniel Wei-Chung Miao

  3. Financial Products Department, Yuanta Commercial Bank, Taipei City, Taiwan

    Emma En-Tze Chang

Authors
  1. Xenos Chang-Shuo Lin
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  2. Daniel Wei-Chung Miao
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  3. Emma En-Tze Chang
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Correspondence to Daniel Wei-Chung Miao.

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Lin, X.CS., Miao, D.WC. & Chang, E.ET. Testing the Closed-Form Spread Option Pricing Formula Based on Gauss-Hermite Quadrature for a Jump-Diffusion Model. Comput Econ (2024). https://doi.org/10.1007/s10614-023-10468-2

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  • DOI: https://doi.org/10.1007/s10614-023-10468-2

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