Open AccessPosted Content
A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales
Reads0
Chats0
TLDR
In this paper, the realised bipower variation process (BPS) is defined, and it is shown that it converges locally uniformly in time, in probability, to a limiting process V(Y;r,s)Abstract:
Consider a semimartingale of the form Y_{t}=Y_0+\int _0^{t}a_{s}ds+\int _0^{t}_{s-} dW_{s}, where a is a locally bounded predictable process and (the "volatility") is an adapted right--continuous process with left limits and W is a Brownian motion. We define the realised bipower variation process V(Y;r,s)_{t}^n=n^{((r+s)/2)-1} \sum_{i=1}^{[nt]}|Y_{(i/n)}-Y_{((i-1)/n)}|^{r}|Y_{((i+1)/n)}-Y_{(i/n)}|^{s}, where r and s are nonnegative reals with r+s>0. We prove that V(Y;r,s)_{t}n converges locally uniformly in time, in probability, to a limiting process V(Y;r,s)_{t} (the "bipower variation process"). If further is a possibly discontinuous semimartingale driven by a Brownian motion which may be correlated with W and by a Poisson random measure, we prove a central limit theorem, in the sense that \sqrt(n) (V(Y;r,s)^n-V(Y;r,s)) converges in law to a process which is the stochastic integral with respect to some other Brownian motion W', which is independent of the driving terms of Y and \sigma. We also provide a multivariate version of these results.read more
Citations
More filters
Journal ArticleDOI
Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise ∗
TL;DR: In this article, realised kernels are used to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions, where the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem.
Journal ArticleDOI
The Relative Contribution of Jumps to Total Price Variance
Xin Huang,George Tauchen +1 more
TL;DR: In this paper, the authors examine tests for jumps based on recent asymptotic results; they interpret the tests as Hausman-type tests and find that microstructure noise biases the tests against detecting jumps, and a simple lagging strategy corrects the bias.
Journal ArticleDOI
Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps
TL;DR: In this paper, a stochastic process driven by diffusions and jumps is considered and a technique for identifying the times when jumps larger than a suitably defined threshold occurred is proposed.
Journal ArticleDOI
Variance Risk-Premium Dynamics: The Role of Jumps
TL;DR: In this paper, the temporal variation in the market variance risk premium was investigated using high-frequency stock market data and variance swap rates, and the results indicated that investors fear of future jumps are especially sensitive to recent jump activity and that their willingness to pay for protection against jumps increase signiflcantly immediately after the occurrence of jumps.
Journal ArticleDOI
Measuring downside risk-realised semivariance.
TL;DR: In this paper, a new measure of risk based entirely on downward moves measured using high frequency data is proposed, based on the theory of probability theory, drawing on some new results from probability theory.
References
More filters
Book
Limit Theorems for Stochastic Processes
Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
Posted Content
Modeling and Forecasting Realized Volatility
TL;DR: In this article, the authors provide a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions.
Journal ArticleDOI
Econometric analysis of realized volatility and its use in estimating stochastic volatility models
TL;DR: In this paper, the moments and the asymptotic distribution of the realized volatility error were derived under the assumption of a rather general stochastic volatility model, and the difference between realized volatility and the discretized integrated volatility (which is called actual volatility) were estimated.
Posted Content
Econometric analysis of realised volatility and its use in estimating stochastic volatility models
TL;DR: In this article, the moments and the asymptotic distribution of the realised volatility error were derived to estimate the parameters of stochastic volatility models, which can then be used to predict the expected volatility.
Dissertation
Theoremes limites pour des processus discretises
TL;DR: In this article, a processus de depart sont des semi-martingales quasi-continues a gauche a crochet absolument continu par rapport a mesure de lebesgue.