Content uploaded by Fulvio Corsi
Author content
All content in this area was uploaded by Fulvio Corsi
Content may be subject to copyright.
A preview of the PDF is not available
The Volatility of Realized Volatility
Abstract and Figures
In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.
Figures - uploaded by Fulvio Corsi
Author content
All figure content in this area was uploaded by Fulvio Corsi
Content may be subject to copyright.
... is used to calculate the realized volatility of both markets. The existing body of literature widely concurs that employing high-frequency data for calculating realized volatility demonstrates superior performance compared to relying solely on daily returns (e.g.,Martens 2001; Andersen et al. 2003;Koopman et al. 2005;Lyócsa, et al. 2021), and it has subsequently become popular in empirical studies for forecasting the volatility of oil and equity returns (e.g.,Bollerslev and Zhou 2006;Corsi et al. 2008;Wei 2012;Souček and Todorova 2013;Sévi 2014;Luo and Ji 2018; Bonato et al. 2020; Cui et al. 2021a;Grønborg et al. 2022; Maghyereh et al. 2022a,b; Maghyereh 2022, 2023a,b; among many others).Consider a logged price process p t that evolves as a continuous Brownian motion:where µ s is a predictable drift and locally bounded, σ s is the continuous part of volatility, and W s is a standard Brownian motion. If we sample M intraday observations for T days, ...
The paper extends the literature by examining whether real economic policy (the business condition risk (ADS)) can derive the risk connectedness in the oil–stock nexus during the COVID-19 outbreak using the multivariate wavelet coherency (MWC) and partial wavelet coherency (PWC) methods. The wavelet methods allow to isolate the effect of different global risk indices (such as the US economic uncertainty index (EPU), the crude oil volatility index (OVX), and the geopolitical risk index (GPR)) on the level of risk connectedness. Based on the daily data for the period January 2018–December 2020, we find that very strong impact of real economic uncertainty indices on risk connectedness. This impact is time-varying and frequency-sensitive, and it exhibits event-specific patterns. We find stronger MWC and PWC between real economy uncertainty indices and risk connectedness at lower frequencies. However, during the coronavirus disease 2019 (COVID-19) crisis, higher coherencies are found at higher frequencies; conditional to the effect of each global risk factor (EPU, GRP, and OVX), we also find higher PWC between oil and equity volatilities at lower frequencies. This study provides useful guidance to regulators and portfolio risk diversifiers. JEL Classifications : G12; G15; G18 ; G01; F3; E44
... The ARMA-GARCH model is the combination of ARMA and GARCH, proposed and developed by Engle (1982) and Bollerslev (1986), respectively. The realized volatility equation based on lagged values is also used in heterogeneous autoregression type models (Audrino and Knaus 2016;Corsi 2009;Corsi et al. 2008;Degiannakis and Livada 2016;Patton and Sheppard 2015;Qiu et al. 2019;Todorova and Souček 2014;Wang et al. 2016). Ling and McAleer (2003) study the theoretical properties of the multivariate ARMA-GARCH model, which Nakatsuma and Tsurumi (1996), Li et al. (2002), and later Ghahramani and Thavaneswaran (2006) ...
Using transaction-level tick-by-tick data of same-day and next-day settlement of the Russian Rouble versus the US Dollar exchange rate traded on the Moscow Exchange Market during the period 2005-2013 we analyse the impact of trading hours extensions on volatility. During the sample period, the Moscow Exchange extended trading hours three times for the same-day settlement and two times for the next-day settlement of the RUB/USD rate. To analyse the effect of the implementations, various measures of historical and realised volatility are calculated for 5-minute and 15-minute intraday intervals spanning a period of 3 months both prior to and following trading hours extensions. Besides historical volatility measures, we also examine volume and spread. We apply an ARMA-GARCH model utilising realised volatility and a trade classification rule to estimate the probability of informed trading. The extensions of trading hours cause a significant increase in both volatility and volume for further analysing the reasons behind volatility changes.
Volatility changes mostly occur after the opening of the market. We document that the length of the extension has a significant positive effect on realised volatility. The results show that informed trading increased substantially after the opening for the rate of same day settlement, whereas this is not observed for next day settlement. The findings demonstrate that although trading hours extensions raise opportunities for more transactions and liquidity in foreign exchange markets, they may also lead to higher volatility in the market. Furthermore, this distortion is found to be more significant at opening and midday. A potential explanation for the increased volatility mostly at the opening is, that the trading hours extension attracts informed traders rather than liquidity providers.
Bitcoin (BTC) perpetual futures contracts are highly leveraged speculative trading instruments with daily market trading of $45 Billion. BTC perpetual futures are derivative contracts, which depend upon the underlying BTC SPOT (current) price. Pricing perpetual futures fairly is hard, using traditional arbitrage arguments, because of the volatile nature of the so called funding rate, which is used as the replacement of risk free rate in the Cryptocurrency market. This work presents a novel technique for pricing BTC futures contracts using conditional volatility and mean models. Intra‐day high‐frequency futures' return volatility and mean are modelled using different ML and econometric techniques. A comparison is made using statistical measures to find the model that best captures the intra‐day conditional mean and volatility. Exponential generalized autoregressive conditional heteroskedasticity is shown to be an almost unbiased predictor of intra‐day volatility, while a constant autoregressive moving average (0, 0) model best captures the conditional mean of the returns. A market directional high frequency trading algorithm is developed using the volatility and mean models. The algorithm first prices the futures contract at some future point of time using the volatility and mean regression models. Next, the slope between the current futures price and the expected price are used to predict the market direction. A long or short position is taken depending upon the expected market direction movement. Extensive back‐testing results show absolute returns of 1500%–8000% depending upon the transaction fees and leverage used. On average, the market direction is predicted correctly 85% of the time by the best model. Finally, the trading technique is market neutral, in that it gives large positive returns, with low SD, in both bull and bear markets.
We propose a new realized volatility model which specifically accounts for memory-and leverage-effect through novel price pattern recognition based on an open-minded learning environment in convolutional neural networks (CNN), extending the heterogeneous autoregressive (HAR) model. More specifically, we investigate for the first time the inclusion of price patterns in forecasting high-frequency realized volatility. The HAR-JPEG models naturally extend the idea of heterogeneity to consider not time horizons, but also heterogeneity of information across market participants based on the noise-trader hypothesis. Rather than information heterogeneity emerging from market sentiment measures, price patterns (i.e., chart analysis) are considered the origin of information heterogeneity. The in-sample estimation of the HAR-JPEG model illustrates significant economic results and depicts best in-sample fitting across numerous well-established HAR extensions. The out-of-sample forecasting results improve realized volatility forecasting in which the CNN-based predictions are used as a new covariate, uncovering information heterogeneity from price pattern interpretation of market participants.
The COVID-19 crisis seriously impacted the global economy and supply chain system. Unlike previous studies, this paper examines the risk spillover effects within the supply chain system rather than between financial and other specific industries. The hypotheses are proposed by developing and simulating an agent-based model; the copula-conditional value at risk model is employed to empirically validate these hypotheses in China during the COVID-19 crisis. The findings reveal that risks are transmitted and amplified from downstream, through midstream to upstream. Additionally, the financial industry amplifies the risk spillover from the midstream to the upstream and downstream. Moreover, the risk spillovers exhibit significant time-varying characteristics, and policy interventions can potentially mitigate the effect of such spillovers. This paper provides a theoretical basis and empirical evidence for risk spillover in supply chain systems and offers suggestions for industrial practitioners and regulators.
In this chapter, we further extend the SV model by incorporating a model-free volatility estimator called realized volatility. The realized volatility, calculated from returns observed in a short interval such as 5 min, is a consistent estimator under certain conditions. The extended model can be seen as a hybrid model utilizing the information in realized volatility as well as daily returns. This hybrid model’s MCMC estimation algorithm is presented, as well as its extension with generalized hyperbolic skew Student’s t distribution. In an empirical study, we evaluate the models by comparing the one-day-ahead forecasts of volatility and daily return.
The normal inverse Gaussian distribution is defined as a variance-mean mixture of a normal distribution with the inverse Gaussian as the mixing distribution. The distribution determines an homogeneous Levy process, and this process is representable through subordination of Brownian motion by the inverse Gaussian process. The canonical, Levy type, decomposition of the process is determined, As a preparation for developments in the latter part of the paper the connection of the normal inverse Gaussian distribution to the classes of generalized hyperbolic and inverse Gaussian distributions is briefly reviewed. Then a discussion is begun of the potential of the normal inverse Gaussian distribution and Levy process for modelling and analysing statistical data, with particular reference to extensive sets of observations from turbulence and from finance. These areas of application imply a need for extending the inverse Gaussian Levy process so as to accommodate certain, frequently observed, temporal dependence structures. Some extensions, of the stochastic volatility type, are constructed via an observation-driven approach to state space modelling, At the end of the paper generalizations to multivariate settings are indicated.
Non-Gaussian processes of Ornstein-Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.
It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. The present work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the “usual” volatility estimator fails when the returns are sampled at the highest frequencies. If the noise is asymptotically small, our work provides a way of finding the optimal sampling frequency. A better approach, the “two-scales estimator,” works for any size of the noise.
Introduction to special Annals issue of papers presented at a conference in Cardiff, UK on July 9–11th 2000
