An exponential continuous time GARCH process

In this paper we introduce an exponential continuous time GARCH(p,q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p,q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p,p) model

The risk-return tradeoff: A COGARCH analysis of Merton's hypothesis

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953-2007 in order to test for Merton's theorised relationship between risk and return. Like some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time GARCH models but also using a COGARCH - a newly developed continuous-time GARCH model which allows for a rigorous analysis of unequally spaced data. When a risk-return relationship symmetric to positive or negative returns is postulated, a significant risk premium of the order of 7-8% p.a., consistent with previously published estimates, is obtained. When the model includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomes insignificant. These results are robust to the use of a value weighted or equally weighted index.The COGARCH model properly allows for unequally spaced time series data. As a sidelight, the model estimates that, during the period from 1953 to 2007, the weekend is equivalent, in volatility terms, to about 0.3-0.5 regular trading days

Comparing the Performance of Alternative Generalised Autoregressive Conditional Heteroskedasticity Models in Modelling Nigeria Crude Oil Production Volatility Series

Communication in Physical Sciences 2019, 4(2): 87-94 Authors: A. E. Usoro, C. E. Awakessien and C. O. Omekara  There is no gainsaying the fact that crude oil production remains a major factor to the Nigeria economic growth given its significant contribution to the nation’s gross domestic product. Preponderance of the researches in the oil sector dwell more on oil prices, with less focus on the volatility of crude oil production. What cannot be overemphasized in oil sector is the production volatility effect which is mostly caused by unstable production quantity due to certain nation’s economic, social, political factors. In this paper, volatility of crude oil production was considered, and different Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models were fitted to Nigeria crude oil production volatility series. Data for the work were monthly crude oil quantity data from January 2010 to August 2019 (NNPC ASB) from which the crude oil production volatility was measured. The suggested GARCH models included GARCH (0,1), GARCH (0,2), GARCH (1,1), GARCH (1,2), GARCH (2,1) and GARCH (2,2). Using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Schwarz’s Information Criterion (SIC), GARCH (1,2) and GARCH(2,1) competed favourably. The MSE of forecast revealed GARCH (2,1) to perform better for the forecast of crude oil production volatility. Further findings will reveal other alternative models as the crude oil production pattern changesin the future

Conditional heteroskedasticity in crypto-asset returns

In a recent contribution to the financial econometrics literature, Chu et al. (2017) provide the first examination of the time-series price behaviour of the most popular cryptocurrencies. However, insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a Gauss-Kronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature