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Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility models

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  • Elisa Al`os
  • `Oscar Bur'es

Abstract

In this paper, we present a numerical method for option pricing and the computation of Greeks under stochastic volatility Bachelier-type models, based on elementary linear algebra. The method allows option prices and Greeks to be computed for infinitely many strikes (within a range of convergence) by evaluating only a finite number of expectations, independent of the number of strikes. For the SABR model, we derive an explicit range of convergence. Numerical examples are provided for both the SABR and the rough Bergomi models.

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  • Elisa Al`os & `Oscar Bur'es, 2026. "Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility models," Papers 2606.26024, arXiv.org.
    • Handle: RePEc:arx:papers:2606.26024
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    References listed on IDEAS

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    1. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    2. Pirjol, Dan, 2026. "Conditional distribution of the time-average of a geometric Brownian motion and option pricing in the SABR model," Applied Mathematics and Computation, Elsevier, vol. 529(C).
    3. Elisa Al`os & `Oscar Bur'es, 2026. "Analytic approximation for Bachelier option prices and applications," Papers 2605.02040, arXiv.org, revised May 2026.
    4. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April.
    5. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    6. Alan L. Lewis & Dan Pirjol, 2022. "Proof of non-convergence of the short-maturity expansion for the SABR model," Quantitative Finance, Taylor & Francis Journals, vol. 22(9), pages 1747-1757, September.
    7. Ning Cai & Yingda Song & Nan Chen, 2017. "Exact Simulation of the SABR Model," Operations Research, INFORMS, vol. 65(4), pages 931-951, August.
    8. Elisa Alòs & Jim Gatheral & Radoš Radoičić, 2020. "Exponentiation of conditional expectations under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 20(1), pages 13-27, January.
    9. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
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