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Error bound for the asymptotic expansion of the Hartman-Watson integral

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  • Dan Pirjol

Abstract

This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $\theta(r,t)$ in the regime $rt=\rho$ constant. The leading order term has the form $\theta(\rho/t,t)=\frac{1}{2\pi t}e^{-\frac{1}{t} (F(\rho)-\pi^2/2)} G(\rho) (1 + \vartheta(t,\rho))$, where the error term is bounded uniformly over $\rho$ as $|\vartheta(t,\rho)|\leq \frac{1}{70}t$.

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  • Dan Pirjol, 2025. "Error bound for the asymptotic expansion of the Hartman-Watson integral," Papers 2504.04992, arXiv.org.
    • Handle: RePEc:arx:papers:2504.04992
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    References listed on IDEAS

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    1. Bruno Buonaguidi, 2023. "Finite Horizon Sequential Detection with Exponential Penalty for the Delay," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 224-238, July.
    2. Stefan Gerhold, 2010. "The Hartman-Watson Distribution revisited: Asymptotics for Pricing Asian Options," Papers 1011.4830, arXiv.org, revised May 2011.
    3. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    4. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    5. Dan Pirjol, 2023. "Subleading Correction To The Asian Options Volatility In The Black–Scholes Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 26(02n03), pages 1-19, May.
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