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arXiv · 2011.00557

A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'

Jaehyuk Choi·Lixin Wu
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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.

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Jaehyuk Choi, Lixin Wu. 2020-11-01. A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'. https://doi.org/10.1080/14697688.2021.1876908

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