A Note on the Option Price and 'Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics'

Quantitative Finance, 21(7):1083-1086, 2021

6 Pages Posted: 29 Dec 2020 Last revised: 8 Jun 2021

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University HSBC Business School

Lixin Wu

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: October 27, 2020

Abstract

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss--Hermite quadrature. We further obtain the option price by integrating the constant elasticity of variance (CEV) option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709-737]. For the uncorrelated SABR model, the new option pricing method is accurate and arbitrage-free across all strike prices.

Keywords: Stochastic Volatility, SABR Model, CEV Model, Gauss-Hermite Quadrature

JEL Classification: C15, C52, G13

Suggested Citation

Choi, Jaehyuk and Wu, Lixin, A Note on the Option Price and 'Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics' (October 27, 2020). Quantitative Finance, 21(7):1083-1086, 2021, Available at SSRN: https://ssrn.com/abstract=3709778 or http://dx.doi.org/10.2139/ssrn.3709778

Jaehyuk Choi (Contact Author)

Peking University HSBC Business School ( email )

Shenzhen

HOME PAGE: http://jaehyukchoi.net/phbs_en

Lixin Wu

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong
2358-7435 (Phone)
2358-1643 (Fax)

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