We consider the saddlepoint approximation methods for pricing derivatives whose payoffs depend on the discrete realized variance of the underlying price process of a risky asset. Most of the earlier pricing models of variance products and volatility derivatives use the quadratic variation approximation as the continuous limit of the discrete realized variance. However, the corresponding discret...

We implement an estimator of the model-free implied volatility derived by Britten-Jones and Neuberger (2000) and investigate its information content in the S&P 500 index options. In contrast to the commonly used Black-Scholes implied volatility, the model-free implied volatility is not based on any specific option pricing model and thus provides a direct test of the informational efficiency of ...

Volatility is an integral and inescapable variable of financial engineering, modeling, and finance theory itself Classical financial economics proxies volatility for risk itself, as it becomes difficult to predict future price realizations of a given asset when that asset exhibits significant price volatility over a given time. However, the nature of volatility as it is explained by classical f...

We introduce a new framework, Realized GARCH, for the joint modeling of returns and realized measures of volatility. A key feature is a measurement equation that relates the realized measure to the conditional variance of returns. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility. Realized GARCH models with a linear or log-linear spec...

We propose a new family of easy-to-implement realized volatility based forecasting models. The models exploit the asymptotic theory for high-frequency realized volatility estimation to improve the accuracy of the forecasts. By allowing the parameters of the models to vary explicitly with the (estimated) degree of measurement error, the models exhibit stronger persistence, and in turn generate m...

We design adaptive realized kernels to estimate the integrated volatility in a framework that combines a stochastic volatility model with leverage effect for the effi cient price and a semiparametric microstructure noise model specified at the highest frequency. Some time dependence parameters of the noise model must be estimated before adaptive realized kernels can be implemented. We study the...