1. Volatility Fin250f: Lecture 5.1 Fall 2005 Reading: Taylor, chapter 8

2. Outline  Volatility features  Why does volatility change?  Simple forecast methods Historical Intra-day Implied  Volatility and the stylized facts

3. Volatility Features  Persistent (very persistent)  Correlations diminish for longer horizons  Connected to trading volume  Equity: Negatively related to current returns

4. Why Does Volatility Change?  Information arrivals Business/versus clock time Number of events per day Question:  Why is this so persistent?  Other explanations Liquidity and heterogeneous traders

5. Volatility Forecast Methods  Historical Moving average Weighted average Intraday  Implied  Model based (GARCH) similar to historical

6. Moving Average of Volatility  Rolling moving average of returns squared

7. Weighted Average  h(t) = variance at time t  Smooth weighting of past volatility

8. Intraday  Estimate volatility for day t using intraday data (15 minute returns): v(t)  Build time series (ARMA) model for v(t)  Use to forecast v(t+1)  Modification: Use high/low range as proxy for volatility at t

9. Implied Volatility  Options prices depend on volatility (Black/Scholes)  Run Black/Scholes backwards Option price -> volatility  Advantage Forward looking  Disadvantage Different options Depens on Black/Scholes

10. VIX and Implied Volatility  VIX is index of implied volatility for the S&P

11. VIX versus S&P

12. Forecast Performance  Implied  Intraday/High-Low  Daily historical

13. Volatility and Stylized Facts

14. This Generates  Fat tails in returns  Uncorrelated returns  Positive correlation in squared returns