market, volatility and jump risks, and observation error of time changes. To operationalize the models, we use volume …

Brownian motion. -- asymptotic uniformity ; local limit theorem ; volatility …

We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is … empirical Laplace transform of the unobservable volatility. The estimation then is done by matching moments of the integrated …-day data into the Realized Laplace Transform of volatility, which is a model-free and jump-robust estimate of daily integrated …

This paper studies the information content of the S&P 500 and VIX markets on the volatility of the S&P 500 returns. We … risk-neutral distributions as well as the term structure of volatility smiles and of variance risk premia. We find that the …

the parameter estimation process, the inclusion of long-memory dynamics in volatility is beneficial for improving the out …This article studies the impact of long memory on volatility modelling and option pricing. We propose a general … discrete-time pricing framework based on affine multi-component volatility models that admit ARCH(ccc) representations. This …

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits … asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between … the risk-neutral and objective expectations of the volatility, is distinctly less persistent and appears short …

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits … asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between … the risk-neutral and objective expectations of the volatility, is distinctly less persistent and appears short …

volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM), and can be tracked using … density on volatility. Our analysis relies on a specification of the martingale change of measure, which we will refer to as … separability. This specification has a multiplicative component that behaves like a risk premium on volatility-uncertainty in the …