We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive relationships between the different concepts. The relationships are of an exact analytical type if this is possible, else we use expansions to obtain approximate expressions. We close...

We study measures of foreign exchange rate volatility based on high-frequency (5-minute) $/DM exchange rate returns using recent nonparametric statistical techniques to compute realized return volatility and its separate continuous sample path and jump components, and measures based on prices of...

Recent developments allow a nonparametric separation of the continuous sample path component and the jump component of realized volatility. The jump component has very different time series properties than the continuous component, and accounting for this allows improved forecasting of future...

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on...

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency...

This paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy-tailed student-t distributions (with unknown degrees of freedom) and covariate effects in the observation and volatility equations and a jump component in the observation...

The advent of close to zero or even negative rates in major currencies has made the traditional lognormal Black-Scholes-Merton volatility as a representation of option prices in the interest rate market obsolete. Recently more and more cap/floor and even swaption prices in major currencies are...

Following recent advances in the non-parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyze the distributional...

Contemporaneous inference from economic data releases for policy and business decisions has become increasingly relevant in the high pace of the information age. The released data are typically filtered to eliminate seasonal patterns to reveal underlying trends and cycles. The nature of economic...