Dynamics Of Realized Volatility Research Articles

Fractional gaussian noise: Spectral density and estimation methods

The fractional Brownian motion (fBm) process, governed by a fractional parameter , is a continuous‐time Gaussian process with its increment being the fractional Gaussian noise (fGn). This article first provides a computationally feasible expression for the spectral density of fGn. This expression enables us to assess the accuracy of a range of approximation methods, including the truncation method, Paxson's approximation, and the Taylor series expansion at the near‐zero frequency. Next, we conduct an extensive Monte Carlo study comparing the finite sample performance and computational cost of alternative estimation methods for under the fGn specification. These methods include two semi‐parametric methods (based on the Taylor series expansion), two versions of the Whittle method (utilising either the computationally feasible expression or Paxson's approximation of the spectral density), a time‐domain maximum likelihood (ML) method (employing a recursive approach for its likelihood calculation), and a change‐of‐frequency method. Special attention is paid to highly anti‐persistent processes with close to zero, which are of empirical relevance to financial volatility modelling. Considering the trade‐off between statistical and computational efficiency, we recommend using either the Whittle ML method based on Paxson's approximation or the time‐domain ML method. We model the log realized volatility dynamics of 40 financial assets in the US market from 2012 to 2019 with fBm. Although all estimation methods suggest rough volatility, the implied degree of roughness varies substantially with the estimation methods, highlighting the importance of understanding the finite sample performance of various estimation methods.

The Role of Binance in Bitcoin Volatility Transmission

ABSTRACT We analyse high-frequency realized volatility dynamics and spillovers between centralized crypto exchanges that offer spot and derivative contracts for bitcoin against the US dollar or the stable coin tether. The tether-margined perpetual contract on Binance is clearly the main source of volatility, continuously transmitting strong flows to all other instruments and receiving very little volatility from other sources. We also find that crypto exchanges exhibit much higher interconnectedness when traditional Western stock markets are open. Especially during the US time zone, volatility outflows from Binance are much higher than at other times, and Bitcoin traders are more attentive and reactive to prevailing market conditions. Our results highlight that market regulators should pay more attention to the tether-margined derivatives products available on most self-regulated exchanges, most importantly on Binance.

Flexible HAR model for realized volatility

Abstract The Heterogeneous Autoregressive (HAR) model is commonly used in modeling the dynamics of realized volatility. In this paper, we propose a flexible HAR(1, . . . , p) specification, employing the adaptive LASSO and its statistical inference theory to see whether the lag structure (1, 5, 22) implied from an economic point of view can be recovered by statistical methods. The model differs from Audrino and Knaus (2016) [Audrino, F. and S. D. Knaus. 2016. “Lassoing the HAR model: A model selection perspective on realized volatility dynamics.” Econometrics Review 35: 1485–1521]. where the authors apply LASSO on the AR(p) model, which does not necessarily lead to a HAR model. Adaptive LASSO estimation and the subsequent hypothesis testing results fail to show strong evidence that such a fixed lag structure can be recovered by a flexible model. We also apply the group LASSO and related tests to check the validity of the classic HAR, which is rejected in most cases. The results justify our intention to use a flexible lag structure while still keeping the HAR frame. In terms of the out-of-sample forecasting, the proposed flexible specification works comparably to the benchmark HAR(1, 5, 22). Moreover, the time-varying model combinations show that when the market environment is not stable, the fixed lag structure (1, 5, 22) is not particularly accurate and effective.

Testing the Lag Structure of Assets’ Realized Volatility Dynamics

A (conservative) test is applied to investigate the optimal lag structure for modelingrealized volatility dynamics. The testing procedure relies on the recent theoretical results that showthe ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combinee cient parameter estimation, variable selection, and valid inference for time series processes. In anapplication to several constituents of the SP (ii) in many cases the relevant information for prediction is included in the first 22lags, corroborating previous results concerning the accuracy and the diffculty of outperforming outof-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of theoptimal lag structure can be identified across assets belonging to the same market segment or showinga similar beta with respect to the market index.

Modeling Realized Volatility Dynamics with a Genetic Algorithm

AbstractThe heterogeneous autoregressive model of realized volatility (HAR‐RV) is inspired by the heterogeneous market hypothesis and characterizes realized volatility dynamics through a linear function of lagged daily, weekly and monthly realized volatilities with a (1, 5, 22) lag structure. Considering that different markets can have different heterogeneous structures and a market's heterogeneous structure can vary over time, we build an adaptive heterogeneous autoregressive model of realized volatility (AHAR‐RV), whose lag structure is optimized with a genetic algorithm. Using nine common loss functions and the superior predictive ability test, we find that our AHAR‐RV model and its extensions provide significantly better out‐of‐sample volatility forecasts for the CSI 300 index than the corresponding HAR models. Furthermore, the AHAR‐RV model significantly outperforms all the other models under most loss functions. Besides, we confirm that Chinese stock markets' heterogeneous structure varies over time and the (1, 5, 22) lag structure is not the optimal choice. Copyright © 2016 John Wiley & Sons, Ltd.

Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics

Realized volatility computed from high-frequency data is an important measure for many applications in finance, and its dynamics have been widely investigated. Recent notable advances that perform well include the heterogeneous autoregressive (HAR) model which can approximate long memory, is very parsimonious, is easy to estimate, and features good out-of-sample performance. We prove that the least absolute shrinkage and selection operator (Lasso) recovers the lags structure of the HAR model asymptotically if it is the true model, and we present Monte Carlo evidence in finite samples. The HAR model's lags structure is not fully in agreement with the one found using the Lasso on real data. Moreover, we provide empirical evidence that there are two clear breaks in structure for most of the assets we consider. These results bring into question the appropriateness of the HAR model for realized volatility. Finally, in an out-of-sample analysis, we show equal performance of the HAR model and the Lasso approach.

Testing the Lag Structure of Assets' Realized Volatility Dynamics

A (conservative) test is constructed to investigate the optimal lag structure for forecasting realized volatility dynamics. The testing procedure relies on the recent theoretical results that show the ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combine efficient parameter estimation, variable selection, and valid inference for time series processes. In an application to several constituents of the SP (ii) in many cases the relevant information for prediction is included in the first 22 lags, corroborating previous results concerning the accuracy and the difficulty of outperforming out-of-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of the optimal lag structure can be identified across assets belonging to the same market segment or showing a similar beta with respect to the market index.

Monte Carlo option pricing with asymmetric realized volatility dynamics

What are the advances introduced by realized volatility models in pricing options? In this short paper we analyze a simple option pricing framework based on the dually asymmetric realized volatility model, which emphasizes extended leverage effects and empirical regularity of high volatility risk during high volatility periods. We conduct a brief empirical analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001–2004 period. The results indicate that as expected the superior forecasting accuracy of realized volatility translates into significantly smaller pricing errors when compared to models of the GARCH family. Most importantly, our results indicate that the presence of leverage effects and a high volatility risk are essential for understanding common option pricing anomalies.