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Closed-form Arrow-Debreu pricing for the Hull-White short rate model

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  • C. Turfus

Abstract

We consider the Hull-White short rate model and provide a systematic derivation of an Arrow-Debreu pricing formula for European-style options in closed form, applying it to cap/floor pricing and CMS (constant maturity swap) index calculation. We present in the process a useful exponential expansion formula which facilitates the analytic solution of pricing equations. We propose that the methodology here described is of interest insofar as it is applicable to a wider range of short rate modelling problems potentially involving lognormal rates/credit volatility, local-stochastic volatility and/or multiple stochastic factors or underlyings.

Suggested Citation

  • C. Turfus, 2019. "Closed-form Arrow-Debreu pricing for the Hull-White short rate model," Quantitative Finance, Taylor & Francis Journals, vol. 19(12), pages 2087-2094, December.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:12:p:2087-2094
    DOI: 10.1080/14697688.2019.1636125
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    Cited by:

    1. Colin Turfus & Aurelio Romero-Berm'udez, 2023. "Analytic RFR Option Pricing with Smile and Skew," Papers 2301.01260, arXiv.org.
    2. Yongwoong Lee & Kisung Yang, 2020. "Finite Difference Method for the Hull–White Partial Differential Equations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    3. Anna Knezevic, 2024. "Enhancing path-integral approximation for non-linear diffusion with neural network," Papers 2404.08903, arXiv.org.

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