Question

(i) How do you understand volatility? (ii) How do we forecast volatility?

Answer 1

Volatility can be described as the uncertainty associated with a future outcome. For example, a stock price may be expected to be $78 in a month's time but it can never be predicted with 100% certainty. So, along with the forecast, a range will be provided as the best estimate like the stock price will be $78 with a volatility of +/- 10%. It basically says that the price will be within a range of $70.2 to $85.8.

The following methods are used for volatility forecasting:

1). Historical volatility models - which are created using historical realized volatility over a give period of time. These are the easiest models to create.

2). Random walk - This works on the assumption that tomorrow's volatility is best predicted by today's volatility.

3). Historical mean - This takes the average of the historical volatility over a given time period with equal weights to all data points.

4). Moving average - In this, a sample average volatility is estimated by using volatility observations (or data points) for a fixed length of time and a fixed weight is awarded to all data points, so all data points contribute equally to the overall volatility calculation.

5). Exponentially Weighted Moving Average (EWMA) - In this model, more weight is given to recent data points as compared to older ones. This improves the predictive ability of the model.

6). Discrete historical models - These models use historical rolling time periods. The weights are assigned to each time period but the weights assigned to individual data points inside each time period are kept constant.

7). Autoregressive Moving Average (ARMA) models - These models add autoregression to the moving average model so that the weights of the observations are adjusted such that the forecast is optimized over a sample time period.

8). ARCH models - In the Autoregressive Conditional Heteroskedasticity model, the volatility of the next period is only conditional upon the last period’s volatility. An upgrade to the ARCH model is the GARCH (or Generalized ARCH) model which captures the dependence of volatility on time.

9). Implied standard deviation models - These models use volatility which is implied by the pricing of options in the options market.