Ray Yeutien Chou

ARCH modeling in finance: A review of the theory and empirical evidence

Although volatility clustering has a long history as a salient empirical regularity characterizing high-frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of explicitly modeling time-varying second-order moments. Instrumental in most of these empirical studies has been the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982). This paper contains an overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data. Several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and the pricing of derivative assets, are also discussed.

Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model

We propose a dynamic model for the high/low range of asset prices within fixed time intervals: the Conditional Autoregressive Range Model (henceforth CARR). The evolution of the conditional range is specified in a fashion similar to the conditional variance models as in GARCH and is very similar to the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998). Extreme value theories imply that the range is an efficient estimator of the local volatility, e.g., Parkinson (1980). Hence, CARR can be viewed as a model of volatility. Out-of-sample volatility forecasts using the S&P500 index data show that the CARR model does provide sharper volatility estimates compared with a standard GARCH model.

Measuring risk aversion from excess returns on a stock index

Abstract Measuring risk aversion from excess returns on a stock index presents two obstacles: 1. the time path of the stock-index variance needs to be modeled and estimated, and 2. other components of wealth must be accounted for. We distinguish two measures that relate the risk premium to variance: 1. the measure of risk aversion which, by the single-factor CAPM, would be the slope coefficient in the linear relation between the mean excess return and the variance of the overall risky portfolio of the representative investor, and 2. the slope coefficient in the linear relationship between the mean excess return on a stock index and its variance. Even when risk aversion is constant, the latter can vary significantly with the relative share of stocks in the risky wealth portfolio, and with the beta of unobserved wealth on stocks. We introduce a statistical model with ARCH disturbances and a time-varying parameter in the mean (TVP ARCH-M). The model decomposes the predictable component in stock returns into two parts: the time-varying price of volatility and the time-varying volatility of returns. The relative share of stocks and the beta of the excluded components of wealth on stocks are instrumented by macroeconomic variables. The ratio of corporate profit over national income and the inflation rate are found to be important forces in the dynamics of stock price volatility.

Market volatility and the demand for hedging in stock index futures

This study examines the relation between stock market volatility and the demand for hedging in S&P 500 stock index futures contracts. Open interest is used as a proxy for hedging demand. The analysis employs unique data that identify separately the open interest of large hedgers, large speculators, and smaller traders. Volatility estimates are decomposed into expected and unexpected components, to assess whether traders’ reactions to volatility depend upon its predictability. Results indicate that daily open interest for hedgers increases when unexpected volatility increases. Increases in unexpected volatility may cause hedgers to raise their estimates of future expected volatility, and hence increase their demand for hedging. Open interest of speculators is not related to expected volatility, and is only weakly related to unexpected volatility. The increase in the participation of hedgers in periods of higher volatility is significantly larger than the increase in the participation of speculators. The results suggest that increases in stock market volatility increase the demand for hedging.

Testing time reversibility without moment restrictions

In this paper we propose a class of new tests for time reversibility. It is shown that this test has an asymptotic normal distribution under the null hypothesis and non-trivial power under local alternatives. A novel feature of this test is that it does not have any moment restriction, in contrast with other time reversibility and linearity tests. Our simulations also confirm that the proposed test is very robust when data do not possess proper moments. An empirical study of stock market indices is also included to illustrate the usefulness of the new test.

Cointegration of International Stock Market Indices

In this paper, we derive evidence on the integration of international stock markets from the cointegration properties of international stock market prices. Using the multivariate cointegration test of Johansen, we find that the set of six country stock price indices, including that of the United States, Canada, the United Kingdom, France, Germany, and Japan are cointegrated. The results suggest that there are long-run equilibrium relationships among the stock market prices. Subsample and subgroup analyses also indicate that the cointegration relationships have become stronger over time. This is consistent with greater stock market integration amid the increasing liberalization and globalization of capital markets.

Modeling the Asymmetry of Stock Movements Using Price Ranges

It is shown in Chou (2005). Journal of Money, Credit and Banking, 37, 561–582that the range can be used as a measure of volatility and the conditional autoregressive range (CARR) model performs better than generalized auto regressive conditional heteroskedasticity (GARCH) in forecasting volatilities of S&P 500 stock index. In this paper, we allow separate dynamic structures for the upward and downward ranges of asset prices to account for asymmetric behaviors in the financial market. The types of asymmetry include the trending behavior, weekday seasonality, interaction of the first two conditional moments via leverage effects, risk premiums, and volatility feedbacks. The return of the open to the max of the period is used as a measure of the upward and the downward range is defined likewise. We use the quasi-maximum likelihood estimation (QMLE) for parameter estimation. Empirical results using S&P 500 daily and weekly frequencies provide consistent evidences supporting the asymmetry in the US stock market over the period 1962/01/01–2000/08/25. The asymmetric range model also provides sharper volatility forecasts than the symmetric range model.

Range Volatility Models and Their Applications in Finance

There has been a rapid growth of range volatility due to the demand of empirical finance. This paper contains a review of the important development of range volatility, including various range estimators and range-based volatility models. In addition, other alternative models developed recently, such as range-based multivariate volatility models and realized ranges, are also considered here. Finally, this paper provides some relevant financial applications for range volatility.

Determinants of geographic differentials in the Savings and Loan failure rate: A heteroskedastic TOBIT estimation

This article has empirically studied determinants of interstate differentials in the S&L failure rate. The heteroskedastic-TOBIT model used in estimation turns out to perform much better than either OLS or the homoskedastic-TOBIT. Significant efficiency gain is obtained in formulating the multiplicative heteroskedasticity. Four types of variables are important: regional economic conditions, asset/liability management, regulatory structure, and politics.

es modéles ARCH en finance : un point sur la théorie et les résultats empiriques

Although volatility clustering has a long history as a salient empirical regularity characterizing high frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of explicitly modeling time varying second order moments. Instrumental in most of these empirical studies has been the Autoregressive Conditionnal Heteroskedasticity (ARCH) model introduced by Engle (1982). This paper contains an overview of some of the developments in the formulations of ARCH models and a survey of numerous empirical applications using financial data. Several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies and the pricing of derivative assets, are also discussed.