Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

A Note on the Term Structure of Implied Volatilities for the Yen/U.S. Dollar Currency Option

This paper tests the relationship between short dated and long dated implied volatilities obtained from Tokyo market currency option prices by employing three different volatility models: a mean reverting model, a GARCH model, and an EGARCH model. We document evidence that long dated average expected volatility is higher than that predicted by the term structure relationship during the dramatic appreciation of yen/dollar exchange in the early 1990's. This revised version was published online in August 2006 with corrections to the Cover Date.     

Forecasting Intraday Volatility and Value-at-Risk with High-Frequency Data

In this paper, we develop modeling tools to forecast Value-at-Risk and volatility with investment horizons of less than one day. We quantify the market risk based on the study at a 30-min time horizon using modified GARCH models. The evaluation of intraday market risk can be useful to market participants (day traders and market makers) involved in frequent trading. As expected, the volatility features a significant intraday seasonality, which motivates us to include the intraday seasonal indexes in the GARCH models. We also incorporate realized variance (RV) and time-varying degrees of freedom in the GARCH models to capture more intraday information on the volatile market. The intrinsic tail risk index is introduced to assist with understanding the inherent risk level in each trading time interval. The proposed models are evaluated based on their forecasting performance of one-period-ahead volatility and Intraday Value-at-Risk (IVaR) with application to the 30 constituent stocks. We find that models with seasonal indexes generally outperform those without; RV can improve the out-of-sample forecasts of IVaR; student GARCH models with time-varying degrees of freedom perform best at 0.5 and 1 % IVaR, while normal GARCH models excel for 2.5 and 5 % IVaR. The results show that RV and seasonal indexes are useful to forecasting intraday volatility and Intraday VaR.     

Modelling conditional heteroscedasticity and jumps in Australian short-term interest rates

The present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.     

On measuring volatility and the GARCH forecasting performance

We apply a new algorithm based on Fourier analysis to compute the volatility of a diffusion process. By using simulations of the continuous-time GARCH model, we show that our method performs well in computing integrated volatility. We show that linear interpolation of high frequency observations induces a downward bias in estimating integrated volatility. By measuring ex post volatility with our method, we find that the forecasting performance of the GARCH model is improved with respect to what is established when classical methods are employed. These results are confirmed by the analysis of exchange rate high frequency time series.     

中国和台湾地区经济波动的实证研究

本文利用ARCH类模型对中国和台湾地区的实际GDP增长率的波动进行了实证分析,结果表明,中国实际GDP增长率的波动有ARCH效应,并且GARCH模型拟合效果最好,而台湾地区实际GDP增长率的波动没有ARCH效应。这表明中国经济波动率是变化的,实际GDP的增长率是对称的,而台湾地区的GDP的波动率是不变的。     

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.     

Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System

We construct a series of 3‐, 4‐ and 5‐variable multivariate GARCH models of exchange rate volatility transmission across the important European Monetary System (EMS) currencies including the French franc, the German mark, the Italian lira, and the European Currency Unit. The models are estimated without imposing the common restriction of constant correlation on both daily and weekly data from April 1979–March 1997. Our results indicate the importance of checking for specification robustness in multivariate Generalized Autoregressive Conditional Heleroskedasticity (GARCH) modeling, we find that increased temporal aggregation reduces observed volatility transmission, and that the mark plays a dominant position in terms of volatility transmission.     

Boom–Bust Cycles and the Forecasting Performance of Linear and Non-Linear Models of House Prices

The tremendous rise in house prices over the last decade has been both a national and a global phenomenon. The growth of secondary mortgage holdings and the increased impact of house prices on consumption and other components of economic activity imply ever-greater importance for accurate forecasts of home price changes. Given the boom–bust nature of housing markets, nonlinear techniques seem intuitively very well suited to forecasting prices, and better, for volatile markets, than linear models which impose symmetry of adjustment in both rising and falling price periods. Accordingly, Crawford and Fratantoni (Real Estate Economics 31:223–243, 2003) apply a Markov-switching model to U.S. home prices, and compare the performance with autoregressive-moving average (ARMA) and generalized autoregressive conditional heteroscedastic (GARCH) models. While the switching model shows great promise with excellent in-sample fit, its out-of-sample forecasts are generally inferior to more standard forecasting techniques. Since these results were published, some researchers have discovered that the Markov-switching model is particularly ill-suited for forecasting. We thus consider other non-linear models besides the Markov switching, and after evaluating alternatives, employ the generalized autoregressive (GAR) model. We find the GAR does a better job at out-of-sample forecasting than ARMA and GARCH models in many cases, especially in those markets traditionally associated with high home-price volatility.