We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps and generally has good finite sample properties. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility,...

In this paper we present parametric estimation of models for stock returns by describing price dynamic as the sum of two independent Levy components. The increments (moves) are viewed as discrete-time log price changes that follow an infinitely divisible distribution, i.e. stationary and...

We develop a nonparametric estimator of the stochastic volatility density of a discretely-observed Ito semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two steps. The first is aggregating the high-frequency increments into the realized...

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods to...

This paper derives the asymptotic behavior of realized power variation of pure-jump It^o semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a...

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage e®ects relative to returns. At the same time, the volatility risk premium, de¯ned by the di®erence between the risk-neutral and objective expectations of the...

We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform of the latent stochastic volatility process over a given interval of time....

We develop a discrete-time real endowment economy featuring recursive preferences and a L´evy time-change subordinator, which represents a clock that connects business time to calendar time. This setup provides a convenient equilibrium framework for pricing non-Gaussian risks, with closed-form...

A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the Black-Scholes price with the forward integrated variance replacing the...

We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for...