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Option pricing under the normal SABR model with Gaussian quadratures

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  • Jaehyuk Choi
  • Byoung Ki Seo

Abstract

The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal ($\beta=0$) SABR model is a popular model choice for interest rates because it allows negative asset values. The option price and delta under the SABR model are typically obtained via asymptotic implied volatility approximation, but these are often inaccurate and arbitrageable. Using a recently discovered price transition law, we propose a Gaussian quadrature integration scheme for price options under the normal SABR model. The compound Gaussian quadrature sum over only 49 points can calculate a very accurate price and delta that are arbitrage-free.

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  • Jaehyuk Choi & Byoung Ki Seo, 2023. "Option pricing under the normal SABR model with Gaussian quadratures," Papers 2301.02797, arXiv.org.
    • Handle: RePEc:arx:papers:2301.02797
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    References listed on IDEAS

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    1. Bin Chen & Cornelis W. Oosterlee & Hans Van Der Weide, 2012. "A Low-Bias Simulation Scheme For The Sabr Stochastic Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-37.
    2. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    3. Jaehyuk Choi & Chenru Liu & Byoung Ki Seo, 2019. "Hyperbolic normal stochastic volatility model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 186-204, February.
    4. Nan Chen & Nian Yang, 2019. "The principle of not feeling the boundary for the SABR model," Quantitative Finance, Taylor & Francis Journals, vol. 19(3), pages 427-436, March.
    5. Jaehyuk Choi & Lixin Wu, 2021. "A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics’," Quantitative Finance, Taylor & Francis Journals, vol. 21(7), pages 1083-1086, July.
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    8. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    9. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
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