Kim Christensen’s research while affiliated with Aarhus University and other places

... Additionally, the findings of Christensen et al. (2023) based on high-frequency data indicate limited price discovery in the days following earnings announcements. However, their findings are confined to 50 liquid firms due to the extensive size of high-frequency data, while we look at all US stocks and aim to capture the speed of price discovery using daily data. ...

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Jump Clustering, Information Flows and Stock Price Efficiency

... The SV framework has inspired extensive methodological developments: Tauchen and Pitts [19] and Taylor [20] pioneered the application of stochastic principles to financial volatility modeling; Chib, Nardari, and Shephard [21] advanced Bayesian estimation techniques for high-dimensional multivariate SV models with time-varying correlations; Jensen and Maheu [22] introduced a semiparametric Bayesian approach incorporating Markov chain Monte Carlo methods to address distributional uncertainty; Fernández-Villaverde, Guerrón-Quintana, and Rubio-Ramírez [23] developed computationally efficient particle filtering algorithms tailored for large-scale SV models. Recent innovations continue to expand the SV paradigm, as evidenced by contributions from Rømer [24], Yazdani, Hadizadeh, and Fakoor [25], Bolko, Christensen, Pakkanen et al. [26], and Chan [27], among others. Notwithstanding these advancements, SV models remain computationally intensive, particularly for parameter estimation and short-term forecasting. ...

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Semiparametric Estimation and Application of Realized GARCH Model with Time-Varying Leverage Effect

... Researchers must tackle multiple moving elements to predict market volatility with confidence. Traditional approaches predicting market volatility failed because financial markets remain unpredictable and volatile (Rouf et al., 2021;Christensen et al., 2023). As a result, there has been growing interest in employing Machine Learning to enhance volatility forecasting as Machine Learning technology proves more effective than prior methods as Zhang and Lei (2022) explained. ...

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Leveraging Machine Learning Techniques to Forecast Market Volatility in the U.S.

... I find it even more interesting that, although the same random variables enter the transformation (19) for different r, we have an independence based on the next two auxiliary lemmas. ...

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Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age

... 3 Our paper also contributes to a burgeoning body of literature that examines the intricate dynamics of asset prices that the standard jump-diffusion models cannot capture. Recent studies provide increasing evidence on "abnormal" intraday price behaviour, including temporary explosive trends and gradual jumps that lead to persistent returns (Christensen et al., 2022;Andersen et al., 2023;Laurent et al., 2024;Shi and Phillips, 2024), as well as excessive price staleness and sluggish adjustments that result in an unexpectedly high fractions of small in-traday returns (Bandi et al., 2017(Bandi et al., , 2020(Bandi et al., , 2024. These anomalies in asset prices violate standard models for the efficient price process, and autocovariances of returns are no longer zeros over all horizons. ...

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Multi-Horizon Test for Market Efficiency

... M.) introduced in 2000 the Multifractal Random Walk (MRW) model [21,22,28], which formally corresponds to H − → 0 + . Later, this super-rough regime was also observed in real data [12,13,23,28,29], as clarified recently in [24] (more on this later, and see also [3]). ...

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Why is the volatility of single stocks so much rougher than that of the S&P500?

... On a microstructural level, HFTs are especially suspected of exhibiting harmful behavior during sudden intraday shocks, as pointed out by Bellia et al. (2022), who show that electronic designated market makers consume liquidity when it is most needed. As such, there seems to exist a trade-off between the greater liquidity and efficiency provided by market-making HFTs in normal times and the disruptive consequences of their quoting and trading activity in times of market stress. ...

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Revisiting the trading activity of high-frequency trading firms around ultra-fast flash events

... Vetter (2015) develops empirical estimations of integrated volatility of volatility and Bull (2017) uses a wavelet-thresholding. Ebner et al. (2018) applies Fourier inference for stochastic volatility models. Christensen et al. (2019) builds a new test based on a nonparametric estimator of the empirical distribution function of stochastic variance or, more recently, Li et al. (2021) considers tests where jumps are present. ...

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Estimation and specification test for diffusion models with stochastic volatility

... In the present section, we examine the effect of the NVAT on market quality in extreme market events, such as flash crashes and bubbles. In accordance with Bellia et al. (2018), we identify a mini-bubble (crash) as a strong and rapid price increase (drop), at least by 1.5% of the initial level, followed by a violent burst (recovery), within at most 12 minutes (24 rounds in our simulations). To be identified as a bubble (crash), the log price should retrace at least one-third of its initial rise (decline) within the above-mentioned time window. ...

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Non-Value-Added Tax to improve market fairness and quality

... Several estimators of the intraday volatility curve has emerged over the years, e.g. Bollerslev (1997, 1998) propose a parametric model for periodicity in volatility, whereas Boudt, Croux, and Laurent (2011) and Christensen, Hounyo, and Podolskij (2018) develop nonparametric jump-and microstructure noise-robust estimators from high-frequency that verify the existence of a pervasive structure in the intraday volatility. ...

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A nonparametric test for diurnal variation in spot correlation processes