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35
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 97 (2 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.
Of Smiles and Smirks: A TermStructure Perspective
 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
, 1998
"... An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts i ..."
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Cited by 79 (3 self)
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An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anamolies have largely focussed on two extensions of the BlackScholes model: introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonlyused versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We find that each model exhibits some "termstructure" patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.
Derivative asset analysis in models with leveldependent and stochastic volatility
 CWI QUARTERLY
, 1996
"... In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope wit ..."
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Cited by 38 (1 self)
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In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical BlackScholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical BlackScholes model. After a review of the known empirical contradictions to the classical BlackScholes model we consider models with leveldependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.
The Econometrics of Option Pricing
"... The growth of the option pricing literature parallels the spectacular developments of derivative securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will ..."
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Cited by 12 (1 self)
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The growth of the option pricing literature parallels the spectacular developments of derivative securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will put emphasis on the more recent contributions since there are
Testing the Volatility Term Structure Using Option Hedging Criteria
, 1998
"... The volatility term structure (VTS) reflects market expectations of asset volatility over different horizons. These expectations change over time, giving dynamic structure to the VTS. This paper evaluates volatility models on the basis of their performance in hedging option price changes due to shif ..."
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Cited by 11 (1 self)
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The volatility term structure (VTS) reflects market expectations of asset volatility over different horizons. These expectations change over time, giving dynamic structure to the VTS. This paper evaluates volatility models on the basis of their performance in hedging option price changes due to shifts in the VTS. An innovative feature of the hedging approach is its increased sensitivity to several important forms of model misspecification relative to previous testing methods. Volatility hedge parameters are derived for several volatility models incorporating different predicted VTS dynamics and information variables. Hedging tests using S&P500 index options indicate that the GARCH components with leverage VTS estimate is most accurate. Evidence is obtained for meanreversion in volatility and correlation between VTS shifts and S&P500 returns. While a convexity hedge dominates the volatility hedges for the observed sample, this result appears to be due to sample selection bias. _________...
Option Pricing for a StochasticVolatility JumpDiffusion Model with LogUniform JumpAmplitudes
, 2006
"... An alternative option pricing model is proposed, in which the stock prices follow a diffusion model with square root stochastic volatility and a jump model with loguniformly distributed jump amplitudes in the stock price process. The stochasticvolatility follows a squareroot and meanreverting d ..."
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Cited by 7 (2 self)
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An alternative option pricing model is proposed, in which the stock prices follow a diffusion model with square root stochastic volatility and a jump model with loguniformly distributed jump amplitudes in the stock price process. The stochasticvolatility follows a squareroot and meanreverting diffusion process. Fourier transforms are applied to solve the problem for riskneutral European option pricing under this compound stochasticvolatility jumpdiffusion (SVJD) process. Characteristic formulas and their inverses simplified by integration along better equivalent contours are given. The numerical implementation of pricing formulas is accomplished by both fast Fourier transforms (FFTs) and more highly accurate discrete Fourier transforms (DFTs) for verifying results and for different output.
BAYESIAN OPTION PRICING USING MIXED NORMAL HETEROSKEDASTICITY MODELS
, 2009
"... While stochastic volatility models improve on the option pricing error when compared to the BlackScholesMerton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order moment ..."
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Cited by 6 (2 self)
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While stochastic volatility models improve on the option pricing error when compared to the BlackScholesMerton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order moments of the risk neutral distribution. Parameter inference using Gibbs sampling is explained and we detail how to compute risk neutral predictive densities taking into account parameter uncertainty. When forecasting outofsample options on the S&P 500 index, substantial improvements are found compared to a benchmark model in terms of dollar losses and the ability to explain the smirk in implied volatilities.
Security Tokens and Their Derivatives
 In 7th International Conference of the Society for Computational Economics (SCE'01
, 2001
"... The primary purpose of this paper is to model uncertain digital objects in view of financial risk management in an open network. We have made an abstraction of the objects and defined the security token, which is abbreviated into a word coinage setok. Each setok has its price, values, and timestamp ..."
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Cited by 4 (1 self)
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The primary purpose of this paper is to model uncertain digital objects in view of financial risk management in an open network. We have made an abstraction of the objects and defined the security token, which is abbreviated into a word coinage setok. Each setok has its price, values, and timestamp on it as well as the main contents. Not only the price but also the values can be uncertain and may cause risks. A number of properties of the setok are defined. They include value response to compromise, price response to compromise, refundability, tradability, online divisibility, and offline divisibility. Then, in search of riskhedging tools, a derivative written not on the price but on the value is introduced. The derivative investigated is a simple Europeantype call option. With the help of stochastic theory, we have derived several optionpricing formulae. These formulae do not require any divisibility of the underlying setok. With respect to applications, an inverse estimation of compromise probability is studied. The stochastic approach is extended to deal with a jump caused by the compromise and the resultant revocation. This extension gives a partial differential equation (PDE) to price the call option; given a set of parameters including the compromise probability, the PDE can tell us the option price. By making an inverse use of this, we can estimate the risk of compromise. Key words: network security, digital object, setok, risk hedge, derivative, option pricing. Contents 1
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
, 2000
"... : This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate t ..."
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Cited by 3 (0 self)
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: This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or "leverage effect" does help to explain the skewness of the volatility "smile", allowing for stochastic interest rates has minimal impact on o...