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Forecasting stock volatility

B. Venkatesh

FORECASTING a stock's volatility is a key aspect in determining pricing, especially in the options market. Volatility refers to the fluctuations in the stock price. Forecasting these fluctuations is important to an option trader, as higher fluctuation in the stock price means higher option price, and hence more profits.

A simple way to forecast a stock's volatility is to assume that its historical volatility holds. You can, therefore, calculate the volatility as the standard deviation (std) of the stock returns. The normal procedure is to calculate the std of daily returns, and then scale it.

For instance, if you want the 14-day volatility, you have to multiply the daily volatility by the square root of 14. This is based on Einstein's equation (called the T to the one-half rule) to find the distance travelled by a particle in a brownian motion! Now, the above equation assumes that volatility remains the same through the 14-day period. But assuming volatility to remain the same is not always correct. Studies have shown that high volatility on a particular day is followed by high volatility the next day. Similarly, low volatility on a day is followed by low volatility the next day. Statistically, volatility is said to follow a positive serial correlation.

So, this means that we need to use different volatility estimates for different time periods; one-day volatility should be different from 14-day volatility. Researchers have developed various models to counter this problem. The commonly used model is called the Generally Autoregressive Conditional Heteroskedasticity (GARCH). This model assumes that future volatility will depend on the past volatility, and is, hence, conditional. Autoregressive is the process whereby the past observations are incorporated into the present.

GARCH then is a model that uses past volatility data to forecast future volatility. Other models include stochastic volatility and various forms of GARCH, such as EGARCH, MGARCH.

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