# Volatility of Stock

Nowadays it is a key issue to forecast the stock market. Forecasting stock market depends on forecasting the volatility by different linear or non-linear models. The volatility of asset returns is time-varying and predictable, but forecasting the future level of volatility is very difficult. Hence, in this study we have provided a simple, yet highly effective framework for forecasting a stock market by considering the transition probability and long run probability of different classified state of volatility. Using DSE 20 index data for January 2001 to October 2010, this paper has tried to use transition probability and limiting probability to make an idea about the future phenomena of the Dhaka stock exchange.

Introduction

The stock market for an economy, what a clinical thermometer is to a human body, reflects the health of the economy. In an economy with a sizeable private corporate sector, aspects like security price stability, investors’ confidence, stable capital market and general economic development are so interwoven that the state of the economy, especially the investment climate in the country can easily be guessed by a mere review of the behavior of the stock market. There are different financial variables in stock market such stock price, share index etc. This share prices may fall in some situation and may constant or rise in another situation. These move up or down is termed as volatility. A volatile stock would be one that sees very large swings in its stock price. If there is a high volatility in the stock market, i.e. the market is not inconsistent position and the country’s economy will be threatened. Volatility indicates to the fluctuations in security prices that are the function of a variety of factors such as interest rates, industrial production, commodity prices, savings, investments, employment, political and economic developments and stability, technological changes, corporate profits, earnings or dividend, investors’ feelings and ‘rumor’. Forecasting the future level of volatility is difficult for at least three reasons. First, volatility forecasts are sensitive to the specification of the volatility model. Second, correctly estimating the parameters of a volatility model often be difficult. Third, Volatility forecasts are anchored at noisy proxies or estimates of the current level of volatility, (Brandt, M. W., and Jones, C. S., 2006). However, the volatility forecasting is very complex and the model selection is too much difficult. In this paper, my main focus is to judge the market behavior and then tries to forecast the future movement of stock market by estimating the transition probability of switching in different state (low, medium, high) and also estimate the long run probability of such state, which is very necessary in forecasting purpose. If one can know the long run

A study on volatility switching of Dhaka Stock Exchange

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probability of switching of volatility in different state that may very helpful to him to understand the future fluctuation or consistency of a stock market and to safe invest.

Literature Review

There is a large literature on forecasting volatility. Many econometric models have been used. The Auto Regressive Conditional Heteroscedasticity (ARCH) model introduced by Engel and Bollerslev’s Generalized ARCH (GARCH) model conveniently accounted for time varying volatility. In ARCH, the conditional variance is equal to a linear function of past squared errors. In GARCH model, the conditional variance of the current error is specified as a function of past conditional variances and past errors. Only the magnitude of the errors affects volatility, but their signs do not. The GARCH models have been applied to study stock market volatility by poon and Taylor, Engel and Ng and Kearns and Pagan. The character of asymmetry in the distribution of stock returns allows an unexpected positive return to cause less volatile than an unexpected negative...

References: Brandt, M. W., and Jones, C. S. (2006), “Volatility Forecasting With Range-Basedd EGARCH Models”, Journal of Business and Economic Statistics, Vol. 24, pp.470-486. Dewett, K. K. and Chand A. (1986). Modern Economic Theory, 21strevised ed., Shyam Lal Charitable Trust, Ram Nagar, New Delhi. Gujarati, D. N.(2003). Basic Econometrics, 4th ed, McGraw-Hill. Gonzalez-Rivera, G. (1998) “Smooth Transition GARCH Models”, Studies in Nonlinear Dynamics and Econometrics, Vol. 3, pp. 61–78. Medhi, J. (1996). Stochastic Process, 2nd Ed, New Age International (P) Limited. Xu, J., (1999), “Modeling Shanghai stock market volatility”, Annals of Operations Research 87, pp. 141-152. Yu, J., (2002), “Forecasting Volatility in the New Zealand Stock Market”, Applied Financial Economics, Vol.12, pp. 193-202.

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