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Behavioral analysis of long-term implied volatilities

Behavioral analysis of long-term implied volatilities The purpose of this paper is to analyze different behaviors between long-term options’ implied volatilities and realized volatilities.Design/methodology/approachThis paper uses a widely adopted short interest rate model that describes a stochastic process of the short interest rate to capture interest rate risk. Price a long-term option by a system of two stochastic processes to capture both underlying asset and interest rate volatilities. Model capital charges according to the Basel III regulatory specified approach. S&P 500 index and relevant data are used to illustrate how the proposed model works. Coup with the low interest rate scenario by first choosing an optimal time segment obtained by a multiple change-point detection method, and then using the data from the chosen time segment to estimate the CIR model parameters, and finally obtaining the final option price by incorporating the capital charge costs.FindingsMonotonic increase in long-term option implied volatility can be explained mainly by interest rate risk, and the level of implied volatility can be explained by various valuation adjustments, particularly risk capital costs, which differ from existing published literatures that typically explained the differences in behaviors of long-term implied volatilities by the volatility of volatility or risk premium. The empirical results well explain long-term volatility behaviors.Research limitations/implicationsThe authors only consider the market risk capital in this paper for demonstration purpose. Dealers may price the long-term options with the credit risk. It appears that other than the market risks such as underlying asset volatility and interest rate volatility, the market risk capital is a main nonmarket risk factor that significantly affects the long-term option prices.Practical implicationsAnalysis helps readers and/or users of long-term options to understand why long-term option implied equity volatilities are much higher than observed. The framework offered in the paper provides some guidance if one would like to check if a long-term option is priced reasonable.Originality/valueIt is the first time to analyze mathematically long-term options’ volatility behavior in comparison with historically observed volatility. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Economics and Finance Emerald Publishing

Behavioral analysis of long-term implied volatilities

Xu, Min; Xie, Hong; Wu, Yuehua
Studies in Economics and Finance , Volume 38 (3): 18 – Jul 27, 2021
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References (15)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1086-7376
eISSN
1086-7376
DOI
10.1108/sef-06-2018-0170
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to analyze different behaviors between long-term options’ implied volatilities and realized volatilities.Design/methodology/approachThis paper uses a widely adopted short interest rate model that describes a stochastic process of the short interest rate to capture interest rate risk. Price a long-term option by a system of two stochastic processes to capture both underlying asset and interest rate volatilities. Model capital charges according to the Basel III regulatory specified approach. S&P 500 index and relevant data are used to illustrate how the proposed model works. Coup with the low interest rate scenario by first choosing an optimal time segment obtained by a multiple change-point detection method, and then using the data from the chosen time segment to estimate the CIR model parameters, and finally obtaining the final option price by incorporating the capital charge costs.FindingsMonotonic increase in long-term option implied volatility can be explained mainly by interest rate risk, and the level of implied volatility can be explained by various valuation adjustments, particularly risk capital costs, which differ from existing published literatures that typically explained the differences in behaviors of long-term implied volatilities by the volatility of volatility or risk premium. The empirical results well explain long-term volatility behaviors.Research limitations/implicationsThe authors only consider the market risk capital in this paper for demonstration purpose. Dealers may price the long-term options with the credit risk. It appears that other than the market risks such as underlying asset volatility and interest rate volatility, the market risk capital is a main nonmarket risk factor that significantly affects the long-term option prices.Practical implicationsAnalysis helps readers and/or users of long-term options to understand why long-term option implied equity volatilities are much higher than observed. The framework offered in the paper provides some guidance if one would like to check if a long-term option is priced reasonable.Originality/valueIt is the first time to analyze mathematically long-term options’ volatility behavior in comparison with historically observed volatility.

Journal

Studies in Economics and Finance – Emerald Publishing

Published: Jul 27, 2021

Keywords: CIR model; Interest rate risk; Black–Scholes model; Historical volatility; Implied volatility; Risk capital cost

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