The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

Choi, Jaehyuk; Wu, Lixin

doi:10.1016/j.jedc.2021.104143

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…It has been a standard practice for practitioners to obtain the option price and delta from the asymptotic approximation of implied volatility (Hagan et al, 2002), but the approximation loses accuracy and allows arbitrage as the variance of volatility becomes large. Despite numerous attempts to improve implied volatility approximation (Ob lój, 2007;Paulot, 2015;Lorig et al, 2017;Yang et al, 2017;Choi and Wu, 2021a), it does not seem possible to obtain an approximation accurate for all parameter ranges. To date, there are several full-scale methods for pricing the SABR model: Monte-Carlo simulations (Chen et al, 2012;Leitao et al, 2017a,b;Cai et al, 2017;Choi et al, 2019;Cui et al, 2021), finite difference methods (Park, 2014;von Sydow et al, 2019), and continuous-time Markov chains (Cui et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Option pricing under the normal SABR model with Gaussian quadratures

Choi¹,

Seo²

2023

Preprint

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The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal (β = 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 arbitrage-able. 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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Section: Introductionmentioning

confidence: 99%

Option pricing under the normal SABR model with Gaussian quadratures

Choi¹,

Seo²

2023

Preprint

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“…Emanuel and MacBeth [14] utilized the CEV model in the context of European options and derived several analytical solutions. Choi and Wu [10] studied the SABR model under CEV and derived some new analytic approximations. Araneda and Bertschinger study the sub-fractional CEV model [1] and Rezaei et al [37].…”

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confidence: 99%

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Javaid,

Aziz,

Aziz

2024

DCDS-S

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This study aims to use the classical Lie symmetry algorithm to solve a mathematical model that represents the American put option. The model is based on a constant elasticity of variance (CEV) framework and includes factors like dividend yield. An infinitesimal transformation and symmetry generators are obtained for the governing parabolic (1+1) PDE which is also known as a price equation. Classical symmetries for the Black Scholes, Cox-Ingersoll-Ross, and general CEV models with dividend yield help us understand the mathematical structure of these models and their relationships, enabling us to develop more accurate pricing models and better understand investment risks. Group invariant solutions of governing PDE are obtained by using similarity variables which are evaluated by solving the characteristic equation of the symmetry operator. A graphical representation of solutions with different dividend yields is presented and discussed to identify the new attribute. The results indicate that rising interest rates, volatility, dividends, and expiration time conform to the established trends. The effects of the dividends yield in all three cases show a high premium value.

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A Black–Scholes user's guide to the Bachelier model

Choi

Kwak

Tee

et al. 2022

Journal of Futures Markets

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To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges temporarily switched the option model from Black-Scholes to Bachelier in 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical results on volatility conversion, risk management, stochastic volatility, and barrier options pricing to facilitate the model transition. In particular, using the displaced Black-Scholes model as a model family with the Black-Scholes and Bachelier models as special cases, we not only connect the two models but also present a continuous spectrum of model choices.

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The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

Cited by 5 publications

References 29 publications

Option pricing under the normal SABR model with Gaussian quadratures

Option pricing under the normal SABR model with Gaussian quadratures

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

A Black–Scholes user's guide to the Bachelier model

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