The main purpose of this paper is to estimate the volatility in global fertilizer prices. The endogenous structural breakpoint unit root test and alternative volatility models, including the generalized autoregressive conditional heteroskedasticity (GARCH) model, Exponential GARCH (EGARCH) model, and GJR model are estimated for six global fertilizer prices and the crude oil price. Weekly data f...

Traditional GARCH models fail to explain at least two of the stylized facts found in financial series: the asymmetry of the distribution of errors and the leverage effect. The leverage effect stems from the fact that losses have a greater influence on future volatilities than do gains. Asymmetry means that the distribution of losses has a heavier tail than the distribution of gains. We test whe...

Over the past years, cryptocurrencies have drawn substantial attention from media while attracting many investors. Since then, cryptocurrency prices experienced high fluctuations. In this paper, we forecast high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling to select best model. We propose various generalized autore...

When using trees to price options, the standard practice is to increase the number of partitions per day, n, to improve accuracy. But increasing n incurs computational overhead. In fact, raising n makes the popular Ritchken-Trevor tree under non-linear GARCH (NGARCH) grow exponentially when n exceeds a typically small threshold. Worse, when this happens, the tree cannot grow beyond a certain ma...

The skewness in physical distributions of equity index returns and the implied volatility skew in the risk neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introd...

The margin system is a clearinghouse’s first line of defense against the default risk. From the perspectives of a clearinghouse, the utmost concern is to have a prudential system to control the default exposure. Once the level of prudentiality is set, the next concern is the opportunity cost to the investors. It is because high opportunity cost discourages people from hedging futures and thus d...

It is well known that volatility asymmetry exists in financial markets. This paper reviews and investigates recently developed techniques for Bayesian estimation and model selection applied to a large group of modern asymmetric heteroskedastic models. These include the GJR-GARCH, threshold autoregression with GARCH errors, threshold GARCH and Double threshold heteroskedastic model with auxiliar...

a r t i c l e i n f o JEL classification: C53 G17 Keywords: GARCH Higher conditional moments Approximate predictive distributions Value-at-Risk S&P 500 Treasury bill rate Euro–US dollar exchange rate It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency...