We consider the estimation of a random level shift model for which the series of interest is the sum of a short memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1−α) and is a random variable with probability α. Our estimation...

This paper shows how one can obtain a continuous-time preference-free option pricing model with a path-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete-time GARCH model of Heston and Nandi (1997) that allows asymmetry between returns and volatility. For the continuous-time model, one can directly compute closed...

The paper studies a factor GARCH model and develops test procedures which can be used to test the number of factors needed to model the conditional heteroskedasticity in the considered time series vector. Assuming normally distributed errors the parameters of the model can be straightforwardly estimated by the method of maximum likelihood. Inefficient but computationally simple preliminary esti...

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...

This paper compares the forecasting performance of the conditional autoregressive range (CARR) model with the commonly adopted GARCH model. We examine two major stock indices, FTSE 100 and Nikkei 225, by using the daily range data and the daily close price data over the period 1990 to 2000. Our results suggest that improvements of the overall estimation are achieved when the CARR models are use...

We measure global real and nominal macroeconomic uncertainty and analyze its impact on individual countries’ macroeconomic performance. Global uncertainty is measured through the conditional variances of global factors in inflation and output growth, estimated from a bivariate dynamic factor model with GARCH errors. The impact of global uncertainty is measured by including the conditional varia...

A semiparametric extension of the GJR model (Glosten et al., 1993. Journal of Finance 48, 1779–1801) is proposed for the volatility of foreign exchange returns. Under reasonable assumptions, asymptotic normal distributions are established for the estimators of the model, corroborated by simulation results. When applied to the Deutsche Mark/US Dollar and the Deutsche Mark/British Pound daily ret...

Value at Risk (VaR) has become the industry standard to measure the market risk. However, the selection of the VaR models is controversial. Simulation Results indicate Historical Simulation has significant positive bias, while GARCH (1,1) has has significant negative bias. Also HS adapts structural change slowly but stable, while GARCH adapts structural break rapidly but less stable. Thus the m...

Characterizing asset return dynamics using volatility models is an important part of empirical finance. The existing literature on GARCH models favors some rather complex volatility specifications whose relative performance is usually assessed through their likelihood based on a time-series of asset returns. This paper compares a range of GARCH models along a different dimension, using option p...

This paper analyzes the application of the Markov-switching ARCH model (Hamilton and Susmel, 1994) in improving value-at-risk (VaR) forecast. By considering a mixture of normal distributions with varying variances over different time and regimes, we find that the “spurious high persistence” found in the GARCH model is adjusted. Under relative performance and hypothesis-testing evaluations, the ...