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SSRN Electronic Journal, 2004
Hallerbach (2004) derives an approximation formula to compute a Black-Scholes implied volatility. This formula is equivalent to equation (7) in Corrado and Miller (1996a), with the substitution of a geometric average of stock and strike prices in place of an arithmetic average. Ceteris paribus the same numerical values are obtained.
Charles J. Corrado, Thomas W. Miller
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Hallerbach (2004) derives an approximation formula to compute a Black-Scholes implied volatility. This formula is equivalent to equation (7) in Corrado and Miller (1996a), with the substitution of a geometric average of stock and strike prices in place of an arithmetic average. Ceteris paribus the same numerical values are obtained.
Charles J. Corrado, Thomas W. Miller
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Stock Splits, Volatility Increases, and Implied Volatilities
The Journal of Finance, 1989ABSTRACTA test of the efficiency of the Chicago Board Options Exchange, relative to post‐split increases in the volatility of common stocks, is presented. The Black‐Scholes and Roll option pricing formulas are used to examine the behavior of implied standard deviations (ISDs) around split announcement and ex‐dates.
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2015
For path-dependent and forward starting options, it is important to assess Vega, the sensitivity of the option’s value to changes in volatility, and in particular to assess these sensitivities for forward buckets. A first step in this process is to determine how forward volatilities for these forward buckets are calculated from the spot volatilities ...
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For path-dependent and forward starting options, it is important to assess Vega, the sensitivity of the option’s value to changes in volatility, and in particular to assess these sensitivities for forward buckets. A first step in this process is to determine how forward volatilities for these forward buckets are calculated from the spot volatilities ...
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Implied volatility indices – A review
The Quarterly Review of Economics and Finance, 2009An implied volatility index reflects the market expectations for the future volatility of the underlying equity index. This study tests and documents the information content, regarding both the realized volatility and the returns of the underlying equity index, of all publicly available implied volatility indices across the world.
Costas Siriopoulos, Athanasios Fassas
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TIGHTER BOUNDS FOR IMPLIED VOLATILITY
International Journal of Theoretical and Applied Finance, 2017We establish bounds on Black–Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of ...
Gatheral, Jim +3 more
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Management Science
We propose a methodology for estimating option-implied, forward-looking variances and covariances of assets and portfolios, which may not possess actively traded options. Our approach relies on the observation that, if asset returns follow a factor structure, then the variances and covariances of the factors span the systematic variances and ...
Ohad Kadan, Fang Liu, Xiaoxiao Tang
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We propose a methodology for estimating option-implied, forward-looking variances and covariances of assets and portfolios, which may not possess actively traded options. Our approach relies on the observation that, if asset returns follow a factor structure, then the variances and covariances of the factors span the systematic variances and ...
Ohad Kadan, Fang Liu, Xiaoxiao Tang
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FORWARD AND FUTURE IMPLIED VOLATILITY
International Journal of Theoretical and Applied Finance, 2011We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities.
PAUL GLASSERMAN, QI WU
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ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS
Mathematical Finance, 2010Using an expansion of the transition density function of a one‐dimensional time inhomogeneous diffusion, we obtain the first‐ and second‐order terms in the short time asymptotics of European call option prices. The method described can be generalized to any order.
J. Gatheral +4 more
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IMPLIED AND LOCAL VOLATILITIES UNDER STOCHASTIC VOLATILITY
International Journal of Theoretical and Applied Finance, 2001For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process.
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2016
There is a natural order of market data speed, with spot levels changing faster than at-the-money volatility, at-the-money volatility changing more rapidly than volatility skew and volatilities being more volatile than dividend forecasts. Hedging performance can be improved by assuming a link between different market parameters, see Andreasen and Huge (
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There is a natural order of market data speed, with spot levels changing faster than at-the-money volatility, at-the-money volatility changing more rapidly than volatility skew and volatilities being more volatile than dividend forecasts. Hedging performance can be improved by assuming a link between different market parameters, see Andreasen and Huge (
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