It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges this estimation approach, as evidenced by recent empirical studies finance. The present work attempts lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an approach takes advantage rich sources tick-by-tick data while preserving assumption on underlying Under our framework, it...

In theory, the sum of squares log returns sampled at high frequency estimates their variance. When market microstructure noise is present but unaccounted for, however, we show that optimal sampling finite and derives its closed-form expression. But even with sampling, using say 5-min when transactions are recorded every second, a vast amount data discarded, in contradiction to basic statistical principles. We demonstrate modeling all better solution, if one misspecifies distribution. So...

Journal Article Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics Get access Suzanne S. Lee, Lee Search for other works by this author on: Oxford Academic Google Scholar Per A. Mykland The Review of Studies, Volume 21, Issue 6, November 2008, Pages 2535–2563, https://doi.org/10.1093/rfs/hhm056 Published: 09 December 2007

Abstract Markov chain sampling has recently received considerable attention, in particular the context of Bayesian computation and maximum likelihood estimation. This article discusses use splitting, originally developed for theoretical analysis general state-space chains, to introduce regeneration into samplers. allows regenerative methods analyzing output these samplers can provide a useful diagnostic sampler performance. The approach is applied several samplers, including certain...

The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy volatility and related quantities. We here study this local-constancy approximation as a general approach to estimation in such data. show that the technique yields asymptotic properties (consistency, normality) correct subject an ex post adjustment involving likelihood ratios. These adjustments documented. Several examples provided: powers volatility, leverage...

High–frequency financial data are not only discretely sampled in time but the separating successive observations is often random. We analyze consequences of this dual feature when estimating a continuous–time model. In particular, we measure additional effects randomness sampling intervals over and beyond those due to discreteness data. also examine effect simply ignoring randomness. find that many situations has larger impact than

Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with nonparametric regression relationship between two such We interested in quadratic variation (integrated volatility) residual this regression, over a unit time (such as day). A main conceptual finding that can be estimated almost if process were observed, difference being there also bias which same asymptotic order mixed normal error term. The proposed...

AbstractThe leverage effect has become an extensively studied phenomenon that describes the (usually) negative relation between stock returns and their volatility. Although this characteristic of is well acknowledged, most studies are based on cross-sectional calibration with parametric models. On statistical side, previous works conducted over daily or longer return horizons, few them have carefully its estimation, especially high-frequency data. However, estimation important because...

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed the relationship between observation times and price process. In this paper, we establish a central limit theorem for realized volatility in general endogenous time setting. We also tricity under hypothesis that there is no endogeneity, which propose test document endogeneity present financial data.

Abstract Nonlinear experiments involve response and regressors that are connected through a nonlinear regression-type structure. Examples of models include standard regression, logistic probit regression. Poisson gamma inverse Gaussian so on. The Fisher information associated with experiment is typically complex function the unknown parameter interest. As result, we face an awkward situation. Designing efficient will require knowledge parameter, but purpose to generate data yield estimates!...

We propose a methodology for evaluating the hedging errors of derivative securities due to discreteness trading times or observation market prices, both. Utilizing weak convergence approach, we derive asymptotic distributions as disappears in several situations. First, examine error discrete‐time when true strategy is known, which generalizes result Bertsimas, Kogan, and Lo (2000) continuous Itô processes. Then consider data‐driven strategy, unknown. This free parametric model assumptions,...

Inference on the parametric part of a semiparametric model is no trivial task. On other hand, if one approximates infinite dimensional by function, obtains that in some sense close to model; and inference may proceed method maximum likelihood. Under regularity conditions, assuming approximating fact generated data, ensuing likelihood estimator asymptotically normal efficient (in model). Thus sequence estimators growing models approximate and, intuitively, limiting {`}semiparametric{'} should...

The availability of high frequency financial data has generated a series estimators based on intra-day data, improving the quality large areas econometrics. However, estimating standard error these is often challenging. root problem that traditionally, errors rely theoretically derived asymptotic variance, and this variance involves substantially more complex quantities than original parameter to be estimated. Standard are important: they used assess precision in form confidence...

The paper investigates the structure of self-consistent estimators (SCE) and nonparametric maximum likelihood estimator (NPMLE) for doubly censored data. An explicit sufficient necessary condition an SCE to be NPMLE is given. Based on this, algorithms computing are provided. relation between our EM algorithm studied.