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

by Jaehyuk Choi*, Lixin Wu

ARTICLE | Quantitative Finance | Online Published in March 2021

Abstract

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide short term 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 Gauss-Hermite quadrature. We further obtain the option price by similarly integrating the constant elasticity of variance (CEV) option prices 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.

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