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Yongjun Kim (2002)
Option Pricing under Stochastic Interest Rates: An Empirical InvestigationAsia-Pacific Financial Markets, 9
Philip Dybvig, J. Ingersoll, S. Ross (1996)
Long Forward and Zero-Coupon Rates Can Never FallThe Journal of Business, 69
M. Bernaschi, L. Torosantucci, Adamo Uboldi (2007)
Empirical evaluation of the market price of risk using the CIR modelPhysica A-statistical Mechanics and Its Applications, 376
S. Heston (1993)
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency OptionsReview of Financial Studies, 6
J. Cox, J. Ingersoll, S. Ross (1985)
A theory of the term structure of interest rates'', Econometrica 53, 385-407
C. Moreno (2020)
Análisis comparativo de rentabilidades de un portafolio de inversión valorado con diferentes metodologías
M. Lavielle (2005)
Using penalized contrasts for the change-point problemSignal Process., 85
Memoirs of the American Mathematical Society
M. Tehranchi (2010)
Implied Volatility: Long Maturity Behavior
H. Soner, S. Shreve, Jakša Cvitanić (1995)
There is no nontrivial hedging portfolio for option pricing with transaction costsAnnals of Applied Probability, 5
Oldrich Vasicek (1977)
An equilibrium characterization of the term structureJournal of Financial Economics, 5
Stephen Figlewski (1989)
Options Arbitrage in Imperfect MarketsJournal of Finance, 44
F. Black, Myron Scholes (1973)
The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 81
I. Karatzas, S. Shreve (2019)
Stochastic Differential EquationsHow to Measure the Infinite
J. Hull, Alan White (1993)
One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative SecuritiesJournal of Financial and Quantitative Analysis, 28
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.
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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