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41
The Dynamics of Stochastic Volatility: Evidence from Underlying and Option Markets
, 2000
"... This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultane ..."
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Cited by 72 (1 self)
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This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. The parameters of the model under both the objective and riskneutral measures are estimated simultaneously. I conclude that the square root stochastic variance model of Heston (1993) and others is incapable of generating realistic returns behavior and find that the data are more accurately represented by a stochastic variance model in the CEV class or a model that allows the price and variance processes to have a timevarying correlation. Specifically, I find that as the level of market variance increases, the volatility of market variance increases rapidly and the correlation between the price and variance processes becomes substantially more negative. The heightened heteroskedasticity in market variance that results generates realistic crash probabilities and dynamics and causes returns to display values of skewness and kurtosis much more consistent with their sample values. While the model dramatically improves the fit of options prices relative to the square root process, it falls short of explaining the implied volatility smile for shortdated options.
Towards a Theory of Volatility Trading
 Reprinted in Option Pricing, Interest Rates, and Risk Management, Musiella, Jouini, Cvitanic
, 1998
"... Introduction ffl Three methods have evolved for trading vol: 1. static positions in options eg. straddles 2. deltahedged option positions 3. volatility swaps ffl The purpose of this talk is to explore the advantages and disadvantages of each approach. ffl I'll show how the first two methods can ..."
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Cited by 60 (12 self)
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Introduction ffl Three methods have evolved for trading vol: 1. static positions in options eg. straddles 2. deltahedged option positions 3. volatility swaps ffl The purpose of this talk is to explore the advantages and disadvantages of each approach. ffl I'll show how the first two methods can be combined to create the third. ffl I'll also show the link between some "exotic" volatility swaps and some recent work by Dupire[3] and Derman, Kani, and Kamal[2]. Part I Static Positions in Options Trading Vol via Static Positions in Options ffl The classic position for trading vol is an atthemoney straddle. ffl Unfortunately, the position loses sensitivity to vol as the underlying moves away from the strike. ffl Is there a static options position which maintains its sensitivity to vol as the underlying moves? ffl To answer this q
A Market Model For Stochastic Implied Volatility
, 1998
"... In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied BlackScholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. T ..."
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Cited by 27 (1 self)
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In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied BlackScholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. The conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and its numerical implementation is discussed.
Deviance Information Criterion for Comparing Stochastic Volatility Models
 Journal of Business and Economic Statistics
, 2002
"... Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed d ..."
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Cited by 26 (7 self)
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Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this paper is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measureoffit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the S&P100 index.
The price of a smile. Hedging and spanning in option markets
 Review of Financial Studies
, 2001
"... i Abstract: The volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed in order to accommodate that change. Deterministic volatility models allow for more °exible volatility surfaces but refrain from introducing additional riskfactors. Thus, o ..."
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Cited by 19 (1 self)
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i Abstract: The volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed in order to accommodate that change. Deterministic volatility models allow for more °exible volatility surfaces but refrain from introducing additional riskfactors. Thus, options are still redundant securities. Alternatively, stochastic models introduce additional riskfactors and options are then needed for spanning of the pricing kernel. We develop a statistical test based on this di®erence in spanning. Using daily S&P500 index options data from 19861995, our tests suggest that both in and outofthemoney options are needed for spanning. The ¯ndings are inconsistent with deterministic volatility models but are consistent with stochastic models which incorporate additional priced riskfactors such as stochastic volatility, interest rates, or jumps. What is a good model to price equity derivatives and to manage risk? Starting from Black and Scholes (1973), a common approach in the derivative pricing literature has been to model the underlying asset as a geometric Brownian motion with constant volatility. Early tests of options on stocks such as Rubinstein (1985) more or less supported the empirical implications of a geometric
The Forecast Quality of CBOE Implied Volatility Indexes. Working
, 2003
"... (CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor’s 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide ..."
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Cited by 10 (1 self)
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(CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor’s 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide even higher quality forecasts of future volatility. We further find that attenuation biases induced by the econometric problem of errors in variables appear to have largely disappeared from CBOE
Volatility Puzzles: A Unified Framework for Gauging ReturnVolatility Regressions
 Finance and Economics Discussion Series 200340, Board of Governors of the Federal Reserve System
, 2003
"... This paper provides a simple unified framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depe ..."
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Cited by 9 (0 self)
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This paper provides a simple unified framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the lagged returnvolatility asymmetry, or the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the aggregate S&P market index. JEL Classification: G12, C51, C22.
Forecasting the variability of stock index returns with stochastic volatility models and implied volatility
, 2002
"... We compare the predictive ability of Stochastic Volatility (SV) models to that of volatility forecasts implied by option prices. An SV model is proposed with implied volatility as an explanatory variable in the variance equation which allows the use of statistical testing; we refer to this model as ..."
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Cited by 3 (0 self)
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We compare the predictive ability of Stochastic Volatility (SV) models to that of volatility forecasts implied by option prices. An SV model is proposed with implied volatility as an explanatory variable in the variance equation which allows the use of statistical testing; we refer to this model as the SVX model. Next we obtain a Stochastic Implied Volatility (SIV) model by restricting the volatility persistence parameter in the SVX model to equal zero. All SV models are estimated by exact maximum likelihood using Monte Carlo importance sampling methods. The performance of the models is evaluated both withinsample and outofsample for daily returns on the Standard & Poor’s 100 index. Our insample results confirm the information content of implied volatility measures as the SVX and SIV models produce more effective estimates of the underlying volatility process than the standard SV model based solely on historical returns. The outofsample volatility forecasts are evaluated against daily squared returns and intraday volatility measures for forecasting horizons ranging from 1 to 20 days. For both the squared daily returns and the cumulative intraday squared 10minute returns we find that the SIV model outperforms both the SV and the SVX model on several evaluation criteria but that the SV model produces volatility forecasts with the smallest bias. All models underestimate the volatility process on average which in our opinion is closely related to the fact that the average level of volatility in the estimation samples is lower than in the evaluation sample.
A Simple Expected Volatility (SEV) Index: Application to SET50 Index Options
, 2010
"... Abstract: In 2003, the Chicago Board Options Exchange (CBOE) made two key enhancements to the volatility index (VIX) methodology based on S&P options. The new VIX methodology seems to be based on a complicated formula to calculate expected volatility. In this paper, with the use of Thailand’s SET50 ..."
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Cited by 2 (2 self)
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Abstract: In 2003, the Chicago Board Options Exchange (CBOE) made two key enhancements to the volatility index (VIX) methodology based on S&P options. The new VIX methodology seems to be based on a complicated formula to calculate expected volatility. In this paper, with the use of Thailand’s SET50 Index Options data, we modify the VIX formula to a very simple relationship, which has a higher negative correlation between the VIX for Thailand (TVIX) and SET50 Index Options. We show that TVIX provides more accurate forecasts of option prices than the simple expected volatility (SEV) index, but the SEV index outperforms TVIX in forecasting expected volatility. Therefore, the SEV index would seem to be a superior tool as a hedging diversification tool because of the high negative correlation with the volatility index.