Basis Convergence and Long Memory in Volatility When Dynamic Hedging with Futures

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.

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.

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.

The Effect of Long Memory in Volatility on Stock Market Fluctuations

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.

Asymmetric Effect of Basis on Dynamic Futures Hedging: Empirical Evidence from Commodity Markets

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.

This work studies wavelet-based Whittle estimator of the fractionally integrated exponential generalized autoregressive conditional heteroscedasticity (FIEGARCH) model often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behavior of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation. In particular, a localized version of our estimator becomes attractive in small samples.

Chapter 9 A Source of Long Memory in Volatility

Bitcoin volatility was investigated with various symmetric and asymmetric models in the study. In addition, value at risk (VaR) was calculated by using the Kupiec LR test and the error prediction performances of the models were compared. As a result of the work, the long memory of volatility in Bitcoin returns was found. It means the cryptocurrency market is not efficient. According to the FIAPARCH asymmetric model, it was determined that positive information shocks reaching the Bitcoin market increased volatility more than negative information shocks. Comparing the error prediction performance of the models by calculating VaR, the HYGARCH model prediction results were found to be superior to other models included in the study. Thus, it was determined that the most suitable model in predicting the volatility, namely the risk of Bitcoin in short and long positions for those who consider investing in Bitcoin, is the asymmetric model HYGARCH.

The volatility of the Scandinavian international future energy market is examined based on a well known intra-day range-based measure of volatility. The main purpose of the paper is to identify determinants of the energy market's intra-day volatility. Firstly, the investigation is a contract-by-contract, range-based volatility measure. The findings are (1) long memory in volatility the longest contracts (year), but not for the shortest (month), (2) the first difference contemporaneous and one-day lagged trading volume measures influences daily volatility positively and consistently over all contracts, (3) trading volume seems to dominate the Samuelson (maturity) and the open-interest hypotheses thus manifesting earlier findings of future markets. Secondly, the paper applies a relatively new methodology to cope with dynamic panel data models, where every contract in the market is organized as a panel. The GMM-type estimator for dynamic panel-data of Arellano [1] is therefore implemented. The results show appropriate specification residual tests and demonstrate firstly the importance of volatility serial correlation. This estimator also shows that the change in daily trading volume is the major determinant of intra-day volatility. In contrast to the segmented analyses, time to maturity shows increased intra-day volatility influence while the measures of bid-ask spread and open interest show decreased significance. The main GMM findings are therefore that the change in trading volume (including lags) and time to maturity are major determinants of intra-day volatility.

Dependence and mean reversion in stock prices: The case of the MENA region

A novel time-varying FIGARCH model for improving volatility predictions

Rescaled variance and related tests for long memory in volatility and levels