Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps

By Cecilia Mancini. 2006

456 citations recorded by the source corpus.

Abstract. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/efc003fd7c27df4582402cfe6a0034db1c0a8085

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Statistics and Probability

Citations in the corpus

Estimation of integrated volatility of volatility with applications to goodness-of-fit testing (2011, methodology): “For this reason, it appears as if the truncation method due to [22] can be applied, and a similar intuition holds for the bias correction as well.”
The Risk Premia Embedded in Index Options (2015, background): “For mn = n, V̂ (n,mn) t is the truncated variation (see, e.g., Mancini (2009)), which provides a consistent estimate of the integrated diffusive variance over [t − 1, t].”
Tails, Fears and Risk Premia (2010, unknown): “These measures for the continuous and jump variation were first proposed by Mancini (2009). They are based on the intuitive idea that over short time intervals, the continuous component of the price will be normally distributed with variance proportional to the length of the time interval.”
Quarticity and other functionals of volatility: Efficient estimation (2012, background): “2) if it is the case, in the spirit of [9, 10]), and under the additional assumptions that ct itself is an Itô semimartingale and that, when X jumps, these jumps are summable, which are exactly the same assumptions under which the truncated versions of Un(f) in (1.”
Systemic Co-Jumps (2017, methodology): “Remark 2.”
Large-dimensional factor modeling based on high-frequency observations (2019, unknown): “20The thresholding approach has first been proposed by Mancini (2009) and Lee and Mykland (2008).”
IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS (2012, background): “We consider here the modified versions of the quantities vnr,l and w n defined in Barndorff-Nielsen and Shephard (2004a) because, by Theorem A.1, ṽnr,l and w̃ n exclude from the sums the terms affected by jumps.”
Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting (2010, methodology): “Mancini (2009) also establishes a central limit theorem for TRV and provides the quarticity estimator (A.3), see Appendix A.”
The Realized Laplace Transform of Volatility (2011, unknown): “In order to “net out” the effects of the price jumps, the top right panel also shows the LT×LT plot for the Truncated Variance of Mancini (2009) as well15, because the relevant comparison is the spot to the integrated variation, exclusive of the contribution of squared price jumps.”
Identifying Jumps in Financial Assets: A Comparison Between Nonparametric Jump Tests (2011, methodology): “, 2006), threshold estimators (Mancini, 2009), the median or the minimum realized variation (Andersen et al.”
Anticipating Long‐Term Stock Market Volatility (2014, unknown): “(10) Following Mancini (2009), the latter measure adjusts for outliers by excluding squared returns above the threshold rN = N −0.99 which depends on the average number N of days within a quarter.”
Exploiting the errors: A simple approach for improved volatility forecasting (2016, methodology): “aswell as the TruncatedRQestimator based on the ideas ofMancini (2009), formally defined by,”
Realised quantile-based estimation of the integrated variance (2010, background): “most notably the influential bi-power variation of Barndorff-Nielsen and Shephard (2004) and the threshold estimators of Jacod (2008); Mancini (2004a, 2006) .”
Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks (2010, unknown): “Then, provided sufficiently weak cross-asset dependencies in the idiosyncratic risks (see Ross (1976) and Chamberlain and Rothschild (1983)), the absence of arbitrage implies that E(ri) = rf + λ0βi, where rf and λ0 denote the risk free rate and the premium for bearing systematic factor risk, respect”