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26
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.
Dynamic Derivative Strategies
, 2003
"... We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to ..."
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Cited by 33 (5 self)
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We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to volatility risk, derivatives enable nonmyopic investors to exploit the timevarying opportunity set; and as a means of exposure to jump risk, they enable investors to disentangle the simultaneous exposure to diffusive and jump risks in the stock market. Calibrating to the S&P 500 index and options markets, we find sizable portfolio improvement from derivatives investing.
Likelihood based inference for diffusion driven models, working paper
 In submission
, 2004
"... This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be nonstationary. Although our method ..."
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Cited by 21 (1 self)
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This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be nonstationary. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample the posterior distribution of the relevant unknowns, our general strategies and details are different from previous work along these lines. The methods we develop are simple to implement and simulation efficient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data.
Impact of Jumps on Returns and Realised Variances: Econometric analysis of timedeformed Lévy processes
 Journal of Econometrics
, 2004
"... In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of real ..."
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Cited by 13 (11 self)
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In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the timechange in the nonBrownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.
Stochastic Volatility
, 2005
"... Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and ..."
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Cited by 12 (0 self)
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote “... there is evidence of nonstationarity in the variance. More work must be done to predict variances using the information available. ” Heterogeneity has deep implications for the theory and practice of financial economics and econometrics. In particular, asset pricing theory is dominated by the idea that higher rewards may be expected when we face higher risks, but these risks change through time in complicated ways. Some of the changes in the level of risk can be modelled stochastically, where the level of volatility and degree of codependence between assets is allowed to change over time. Such models allow us to explain, for example, empirically observed departures from BlackScholesMerton prices for options and understand why we should expect to see occasional dramatic moves in financial markets. The outline of this article is as follows. In section 2 I will trace the origins of SV and provide links with the basic models used today in the literature. In section 3 I will briefly discuss some of the innovations in the second generation of SV models. In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. In section 6 I will consider the connection of SV with realised volatility. A extensive reviews of this literature is given in Shephard (2005). 2 The origin of SV models The origins of SV are messy, I will give five accounts, which attribute the subject to different sets of people.
Bayesian Inference for Derivative Prices
, 2003
"... This paper develops a methodology for parameter and state variable inference using both asset and derivative price information. We combine theoretical pricing models and asset dynamics to generate a joint posterior for parameters and state variables and provide an MCMC simulation strategy for infere ..."
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Cited by 8 (4 self)
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This paper develops a methodology for parameter and state variable inference using both asset and derivative price information. We combine theoretical pricing models and asset dynamics to generate a joint posterior for parameters and state variables and provide an MCMC simulation strategy for inference. There are several advantages of our inferential approach. First, more precise parameter estimates are obtained when both asset and derivative price information are used. Secondly, we provide a diagnostic tool for model misspecification based on agreement of the state and parameter estimates with and without derivative price information. Furthermore, the time series properties of the state variables can also be used to evaluate model fit. We illustrate our methodology using daily equity index options on the Standard and Poor's (S&P 500) index from 19982002.
Stochastic volatility: origins and overview
 Handbook of Financial Time Series
, 2008
"... Stochastic volatility (SV) models are used heavily within the fields of financial economics and mathematical finance to capture the impact of timevarying volatility on financial markets and decision making. The development of the subject has been highly multidisciplinary, with results drawn from fi ..."
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Cited by 7 (0 self)
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Stochastic volatility (SV) models are used heavily within the fields of financial economics and mathematical finance to capture the impact of timevarying volatility on financial markets and decision making. The development of the subject has been highly multidisciplinary, with results drawn from financial economics, probability theory and econometrics blending to produce methods that
MEANVARIANCE HEDGING WHEN THERE ARE JUMPS
, 2005
"... In this paper, we consider the problem of meanvariance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem, and closed form e ..."
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Cited by 3 (0 self)
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In this paper, we consider the problem of meanvariance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem, and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and the theory of backward stochastic differential equations. The results we have obtained show how backward stochastic differential equations can be used to obtain solutions to optimal investment and hedging problems when discontinuities in the underlying price processes are modeled by the arrivals of Poisson processes with stochastic intensities. Applications to the problem of hedging default risk are also discussed.
Volatility models: from garch to multihorizon cascades
 Financial Markets and the Global Recession. Nova Science Publishers Inc, NY (forthcoming
, 2010
"... We overview different methods of modeling stock prices and exchange rates volatility, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of volatility change across the time scales of observations. Adequacy of volatility models for descri ..."
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Cited by 3 (2 self)
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We overview different methods of modeling stock prices and exchange rates volatility, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of volatility change across the time scales of observations. Adequacy of volatility models for describe price dynamics at several time horizons simultaneously Special attention is a central topic of this study. We propose a detailed survey of recent volatility models, accounting for multiple horizons. These models are based on different and sometimes competing theoretical concepts, belonging either to GARCH or stochastic family of models and often borrowing methodological tools from statistical physics. We compare their properties and comment on their practical usefulness and perspectives.
On Bayesian analysis of nonlinear continuoustime autoregression models
, 2004
"... This paper introduces a method for performing fully Bayesian inference for nonlinear conditional autoregressive continuoustime models, based on a finite skeleton of observations. Our approach uses MCMC and involves imputing data from times at which observations are not made. It uses a reparameteri ..."
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Cited by 3 (0 self)
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This paper introduces a method for performing fully Bayesian inference for nonlinear conditional autoregressive continuoustime models, based on a finite skeleton of observations. Our approach uses MCMC and involves imputing data from times at which observations are not made. It uses a reparameterisation technique for the missing data, and due to the nonMarkovian nature of the models, it is necessary to adopt an overlapping blocks scheme for sequentially updating segments of missing data. We illustrate the methodology using both simulated data and a data set from the S & P 500 index. 1