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 …

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 …

volatility models. We provide a succinct error analysis to demonstrate that we can achieve an exponential convergence rate in the …

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 … the parameter estimation process, the inclusion of long-memory dynamics in volatility is beneficial for improving the out …

In this paper we propose a stochastic volatility model for crude oil markets that has the particularity to feature a … OVX volatility data. The model characterizes two states: a normal state with low volatility and negative variance premium … and acrisis state with high volatility and positive variance risk premium. The estimated states are consistent with GDP …

underlying stock (asset) is subject to discontinuous market regime type of shifts in its mean or volatility whose risk can be …

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 …