Results 1  10
of
561
Bayesian Analysis of Stochastic Volatility Models
, 1994
"... this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH ..."
Abstract

Cited by 601 (26 self)
 Add to MetaCart
this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and logvolatility equations have separate error terms. The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility found in many economic time series has fostered an explosion in the use of ARCH models. On the other hand, the likelihood function for stochastic volatility models is difficult to evaluate, and hence these models have had limited empirical application
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
Abstract

Cited by 549 (50 self)
 Add to MetaCart
this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionallyintegrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated highfrequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormalnormal mixture forecast distribution provides conditionally wellcalibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitragefree multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from highfrequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
The Variance Gamma Process and Option Pricing.
 European Finance Review
, 1998
"... : A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional par ..."
Abstract

Cited by 365 (34 self)
 Add to MetaCart
: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model d...
Econometric analysis of realized volatility and its use in estimating stochastic volatility models
, 2002
"... ..."
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
Abstract

Cited by 347 (4 self)
 Add to MetaCart
(Show Context)
We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
The distribution of realized exchange rate volatility,
 Journal of the American Statistical Association
, 2001
"... Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximatel ..."
Abstract

Cited by 333 (29 self)
 Add to MetaCart
(Show Context)
Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.
The distribution of realized stock return volatility
, 2001
"... We examine "realized" daily equity return volatilities and correlations obtained from highfrequency intraday transaction prices on individual stocks in the Dow Jones ..."
Abstract

Cited by 243 (22 self)
 Add to MetaCart
We examine "realized" daily equity return volatilities and correlations obtained from highfrequency intraday transaction prices on individual stocks in the Dow Jones
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 ..."
Abstract

Cited by 237 (9 self)
 Add to MetaCart
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.