MODELING, FORECASTING THE CRYPTOCURRENCY MARKET VOLATILITY AND VALUE AT RISK DYNAMICS OF BITCOIN

Due to the illiquidity of inventories pledged, the essential of price risk management of supply chain finance is to long-term price risk measure. Long memory in volatility, which attests a slower than exponential decay in the autocorrelation function of standard proxies of volatility, yields an additional improvement in specification of multi-period volatility models and further impact on the term structure of risk. Thus, long memory is indispensable to model and measure long-term risk. This paper sheds new light on the impact of the existence and persistence of long memory in volatility on inventory portfolio optimization. Firstly, we investigate the existence of long memory in volatility of the inventory returns, and examine the impact of long memory on the modeling and forecasting of multi-period volatility, the dependence structure between inventory returns and portfolio optimization. Secondly, we further explore the impact of the persistence of long memory in volatility on the efficient frontier of inventory portfolio via a data generation process with different long memory parameter in the FIGARCH model. The extensive Monte Carlo evidence reveals that both GARCH and IGARCH models without accounting for long memory will misestimate the actual long-term risk of the inventory portfolio and further bias the efficient frontier; besides, through A sensitive analysis of long memory parameter d, it is proved that the portfolio with higher long memory parameter possesses higher expected return and lower risk level. In conclusion, banks and other participants will benefit from the long memory taken into the long-term price risk measure and portfolio optimization in supply chain finance.

Long memory in variance or volatility refers to a slow hyperbolic decay in autocorrelation functions of the squared or log-squared returns. The conventional volatility models extensively used in empirical analysis do not account for long memory in volatility. This chapter revisits the Indian stock market by using the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model. For empirical modeling, daily values of 14 indices from the National stock exchange (NSE) and Bombay Stock Exchange (BSE) from June 1997 to March 2010 are used. The results of the study confirm the presence of long memory in volatility of index returns. This shows that FIGARCH model better describes the persistence in volatility than the conventional GARCH models. Against the evidence of fractional behavior of volatility in Indian stock market, it is essential to factor the long memory in derivative pricing and value at risk models.

This research applied closing price return for ASEAN ETFs. Comparing the long memory in volatility and asymmetric volatility of ASEAN ETFs, this research used four models, fractional autoregressive integrated moving average (ARFIMA), a hybrid of ARFIMA and fractionally integrated generalized autoregressive conditional heteroscedasticity (ARFIMA-FIGARCH), ARFIMA with fractionally integrated asymmetric power autoregressive conditional heteroscedasticity (ARFIMA-FIAPARCH) and ARFIMA with hyperbolic generalized autoregressive conditional heteroscedasticity (ARFIMA-HYGARCH) models. The results show that by using closing price return data samples ASEAN ETF have a long memory in volatility and negative asymmetric volatility. ARFIMA-FIAPARCH model perform better to investigate long memory in volatility and asymmetric volatility for ASEAN ETF. This findings can be evaluated by academicians, financial risk managers, investors, and regulators.

This article attempts to verify the presence of long memory in volatility in the Indian foreign exchange market using daily bilateral returns of the Indian Rupee against the US dollar from 17/02/1994 to 08/11/2013. In the first part of the analysis the presence of long-term dependence is confirmed in the return series as well as in two measures of unconditional volatility (absolute returns and squared returns) by employing three measures of long memory. Next, the presence of long memory in conditional volatility is tested using ARMA-FIGARCH and ARMA-FIAPARCH models under various distributional assumptions. The results confirm the presence of long memory in conditional variance for two models. In the last part, the presence of long memory in conditional mean and conditional variance is verified using ARFIMA-FIGARCH and ARFIMA-FIAPARCH models. It is also found that long-memory models fare well compared to short-memory models in sample forecast performance.

In their study on the applicability of volatility forecasting for risk management applications, [2] stress the importance of long-term volatility dependencies under longer forecast horizons. The present contribution addresses multiple-period value-at-risk (VaR) prediction for equity markets under long memory in return volatilities. We account for long memory in the τ-step ahead volatility forecast of GJR-GARCH(1,1) by using a novel estimator considering the slowly declining influence of past volatility shocks. Our empirical study of established equity markets covers daily index returns during the period 1975 to 2007. We study the out-of-sample accuracy of VaR predictions for five, ten, 20 and 60 trading days. As a benchmark model we use the parametric GARCH setting of Drost and Nijman (1993) and the Cornish-Fisher expansion as an approximation to innovation quan-tiles. The backtesting results document that our novel approach improves forecasts remarkably. This outperformance is only in part due to higher levels of risk forecasts. Even after controlling for the unconditional VaR levels of the competing approaches, the long memory GJR-GARCH(1,1) approach delivers results which are not dominated by the benchmark approach.

The Effect of Long Memory in Volatility on Stock Market Fluctuations

This study investigates calendar anomalies and their impact on returns and volatility patterns in the cryptocurrency market, focusing on day-of-the-week effects before and during the COVID-19 pandemic. Using advanced statistical models from the GARCH family, we analyze the returns of Binance USD, Bitcoin, Binance Coin, Cardano, Dogecoin, Ethereum, Solana, Tether, USD Coin, and Ripple. Our findings reveal significant shifts in volatility dynamics and day-of-the-week effects on returns, challenging the notion of market efficiency. Notably, Bitcoin and Solana began exhibiting day-of-the-week effects during the pandemic, whereas Cardano and Dogecoin did not. During the pandemic, Binance USD, Ethereum, Tether, USD Coin, and Ripple showed multiple days with significant day-of-the-week effects. Notably, positive returns were generally observed on Sundays, whereas a shift to negative returns on Mondays was evident during the COVID-19 period. These patterns suggest that exploitable anomalies persist despite the market’s continuous operation and increasing maturity. The presence of a long-term memory in volatility highlights the need for robust trading strategies. Our research provides valuable insights for investors, traders, regulators, and policymakers, aiding in the development of effective trading strategies, risk management practices, and regulatory policies in the evolving cryptocurrency market.

When market returns follow a long memory volatility process, standard approaches to estimating dynamic minimum variance hedge ratios (MVHRs) are misspecified. Simulation results and an application to the S&P 500 index document the magnitude of the misspecification that results from failure to account for basis convergence and long memory in volatility. These results have important implications for the estimation of MVHRs in the S&P 500 example and other markets as well.

This paper tests for long memory in volatility of fixed‐income returns; specifically, South Africa's local currency 10‐year government bond, given that the characterisation of stochastic long‐memory volatility is of interest and importance in portfolio and risk management. The long‐memory parameter is estimated using methods based on wavelets, which have gained prominence in recent years. Evidence of long memory in fixed‐income return volatility is conclusively demonstrated across a variety of volatility measures and wavelet forms. This finding suggests a pattern of time dependence, which may potentially be exploited to generate improved volatility forecasting performance especially over long horizons. This paper further extends the extant literature by comparing the predictive power of long‐memory forecasts with those obtained from a standard (short‐memory) generalised autoregressive conditional heteroskedasticity (GARCH) process. The results of this exercise suggest that the information content of long‐memory models does not lead to improved forecast accuracy. The GARCH(1,1) model is shown to provide the best forecasts across most horizons (i.e.daily, weekly and monthly). Forecast performance is further revealed to be sensitive to the choice of volatility proxy used. Finally, the derived volatility forecasts are generally very close, and in some cases, almost indistinguishable.

A class of robust M-estimators for generalised autoregressive conditional heteroscedastic (GARCH) type models are used for the prediction of value-at-risk (VaR) of Karachi Stock Exchange (KSE). To better understand the impact of global financial crisis on KSE, the daily stock return data is divided into three sub-periods: the pre-crisis period (3 January 2005 to 31 December 2007), the crisis period (2 January 2008 to 30 June 2009), and the post-crisis period (1 July 2009 to 31 December 2013). Symmetric and asymmetric GARCH models that capture the most common stylised facts about index returns such as volatility clustering and leverage effect are fitted to these time periods and in-sample and out-of-sample estimates of VaR are obtained. Our results show that M-estimators provide accurate and reliable estimates of VaR in low and high volatile time. Our findings also show that the asymmetric model provides better fit than the symmetric model for the KSE.

PurposeThe aim is to evaluate the performance of symmetric and asymmetric ARCH models in forecasting both the one‐day‐ahead Value‐at‐Risk (VaR) and the realized intra‐day volatility of two equity indices in the Athens Stock Exchange.Design/methodology/approachTwo volatility specifications are estimated, the symmetric generalized autoregressive conditional heteroscedasticity (GARCH) and the asymmetric APARCH processes. The data set consisted of daily closing prices of the General and the Bank indices from 25 April 1994 to 19 December 2003 and their intra day quotation data from 8 May 2002 to 19 December 2003.FindingsUnder the VaR framework, the most appropriate method for the Bank index is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one‐step‐ahead intra‐day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index.Originality/valueAs concerns the Greek stock market, there are adequate methods in predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.

Value at Risk (VAR) is a frequently used risk measure. Its concept based on determination of maximal loss for predetermined level of certainty is easy to understand. It is often used by various corporate professionals to measure different risks in the company, but predominantly banking and investment sector is responsible for growth of this approach. The rapid growth of instruments in financial market, support growth of VAR estimation methods, as well as methods for proper validation of this models. Presented paper goes beyond traditional financial instruments and tries to assess usefulness of three different VAR estimation models in cryptocurrency market. The motivation behind this research is to determine whether Normal, Historical or EWMA approaches of VAR estimation can be used for determination of maximal loss in cryptocurrency market with 95% and 99% probability. The performance of these VAR model is measure by number of violations and four different backtests: Basel’s Traffic light approach, Binomial test, POF test and TBF test. The results showed that performance of these VAR models differs based on the type of cryptocurrency and that VAR models perform differently at pre-COVID-19 and during COVID19 period.

The bitcoin market has exhibited highly volatile return movements, experiencing a sharp surge starting from in November 2022 to 2024. This significant fluctuation underscores the importance of analyzing the factors influencing bitcoin’s return dynamics. This study utilizes daily data with a final sample of 590 observations. All time-series variables must be stationary before being processed in the statistical model. The analysis was conducted using Stata 16 software. To ensure the absence of unit roots, the stationarity of the research variables was tested using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests. The findings indicate that market capitalization, gold, and litecoin have no significant impact on bitcoin returns. In contrast, miners’ revenue has a significant negative effect, while hashrate, mining difficulty, and the S&P 500 exhibit a significant positive influence on bitcoin returns. This study highlights bitcoin’s role as a store of value and investment asset, emphasizing the impact of hashrate and mining difficulty on its returns and integration into financial markets, particularly the S&P 500. The findings provide insights for investors on portfolio diversification and assets like a gold and equities. Additionally, the study underscores the importance of sustainable mining practices and regulatory policies to balance cryptocurrency’s economic potential with environmental sustainability. Keywords: Market capitalization; Mines’s Revenue; Hashrate; Mining difficulty; Commodity Asset, Cryptocurrency

ABSTRACTThis paper extends research concerned with the evaluation of alternative volatility forecasting methods under value at risk (VaR) modeling in the context of the Basle Committee adequacy criteria by broadening the class of generalized autoregressive conditional heteroscedasticity models, to include both asymmetric models and long memory models, in addition to the statistical methods commonly used in financial institutions. In the analysis of daily index data for eight emerging stock markets in the Asia – Pacific region, in addition to US and UK benchmark comparators, we find both asymmetric and long memory features to be important considerations in providing improved VaR estimates that minimize occasions when the minimum capital requirement identified by the VaR methodology would have fallen short of actual trading losses. More generally, our results illustrate the importance of adopting the stringent probability level stipulated in the regulatory framework, and of using fully out‐of‐sample forecast evaluation methods for the identification of forecasting models that mitigate the likelihood of inappropriately small VaRs and consequent regulatory intervention.

Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.