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

6 Pages Posted: 29 Dec 2020

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University - HSBC School of Business

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 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 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 method of option pricing 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). Available at SSRN: https://ssrn.com/abstract=3709778 or http://dx.doi.org/10.2139/ssrn.3709778

Jaehyuk Choi (Contact Author)

Peking University - HSBC School of Business ( email )

University Town
Nanshan District
Shenzhen, Guang Dong 518055
China

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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