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19
The JumpRisk Premia Implicit in Options: Evidence from an Integrated TimeSeries Study
 Journal of Financial Economics
"... Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more p ..."
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Cited by 285 (2 self)
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Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more prominent during volatile markets. This form of jumprisk premia is important not only in reconciling the dynamics implied by the joint data, but also in explaining the volatility “smirks” of crosssectional options data.
A JumpDiffusion Model for Option Pricing
 Management Science
, 2002
"... Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (as ..."
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Cited by 149 (5 self)
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Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called “volatility smile ” in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jumpdiffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of optionpricing problems, including call and put options, interest rate derivatives, and pathdependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.
Do stock prices and volatility jump? Reconciling evidence from spot and option prices
, 2001
"... This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation ..."
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Cited by 144 (4 self)
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This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation period. This contrasts previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts outofsample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.
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 103 (3 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.
JumpDi®usion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
 Review of Derivatives Research
, 2000
"... Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Parti ..."
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Cited by 76 (2 self)
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Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Partial IntegroDifferential Equation) and demonstrates how this equation can be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples from the S&P500 market.
An Econometric Model of the Yield Curve with Macroeconomic Jump Effects
, 2000
"... This paper develops an arbitragefree timeseries model of yields in continuous time that incorporates central bank policy. Policyrelated events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linearquadratic jump ..."
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Cited by 43 (2 self)
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This paper develops an arbitragefree timeseries model of yields in continuous time that incorporates central bank policy. Policyrelated events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linearquadratic jumpdiffusions as state variables, which allows for a wide variety of jump types but still leads to tractable solutions for bond prices. I estimate a version of this model with U.S. interest rates, the Federal Reserve’s target rate, and key macroeconomic aggregates. The estimated model improves bond pricing, especially at short maturities. The “snakeshape ” of the volatility curve is linked to monetary policy inertia. A new monetary policy shock series is obtained by assuming that the Fed reacts to information available right before the FOMC meeting. According to the estimated policy rule, the Fed is mainly reacting to information contained in the yieldcurve. Surprises in analyst forecasts turn out to be merely temporary components of macro variables, so that the “humpshaped” yield response to these surprises is not consistent with a Taylortype policy rule.
The Term Structure of Simple Forward Rates with Jump Risk
 Jump Risk.” Mathematical Finance
, 2002
"... This paper characterizes the arbitragefree dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instan ..."
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Cited by 33 (5 self)
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This paper characterizes the arbitragefree dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates.
Convergence Of Numerical Schemes For Viscosity Solutions To IntegroDifferential Degenerate Parabolic Problems Arising In Financial Theory
 NUMER. MATH
, 2001
"... We study the numerical approximation of viscosity solutions for integrodifferential, possibly degenerate, parabolic problems. Similar models arise in option pricing, to generalize the celebrated BlackScholes equation, when the processes which generate the underlying stock returns may contain both ..."
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Cited by 19 (4 self)
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We study the numerical approximation of viscosity solutions for integrodifferential, possibly degenerate, parabolic problems. Similar models arise in option pricing, to generalize the celebrated BlackScholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Convergence is proven for monotone schemes and numerical tests are presented and discussed.
Estimation of Continuous  Time Processes via the Empirical Characteristic Function
 Journal of Business & Economic Statistics
, 2002
"... This paper examines a particular class of continuoustime stochastic processes commonly known as afne diffusions (AD) and afne jumpdiffusions (AJD). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an efcient estimation technique ba ..."
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Cited by 9 (0 self)
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This paper examines a particular class of continuoustime stochastic processes commonly known as afne diffusions (AD) and afne jumpdiffusions (AJD). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an efcient estimation technique based on empirical characteristic functions (ECF) and a GMM estimation procedure based on exact moment conditions. The estimators developed in this paper require neither discretization nor simulation. We demonstrate that our methods are in particular useful for the AD and AJD models with latent variables. We illustrate our approach with a detailed examination of the continuoustime squareroot stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.
Essays in Financial Econometrics
, 2000
"... We examine methods to extract various types of information from derivative prices by means of continuous time models and modern estimation and filtering methods. The first essay introduces the approach allowing the joint estimation of the objective and riskneutral measures based on the time series ..."
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Cited by 2 (0 self)
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We examine methods to extract various types of information from derivative prices by means of continuous time models and modern estimation and filtering methods. The first essay introduces the approach allowing the joint estimation of the objective and riskneutral measures based on the time series of assets returns and options prices in the stochastic volatility model framework. The second essay develops a model, which allows for simultaneous consideration of multiple assets and their derivatives. This model, when combined with the filtering techniques, allows for unbiased estimation of the stochastic discount factor without any initial assumptions about the utility function. The third essay extends the approach by suggesting a new class of jump diffusion models, which allows for analytical option pricing. The various estimation strategies are discussed.