1. Fin250f: Lecture 11.1 Spring 2010 Volatility

2. Outline • Volatility features • Why does volatility change? • Simple forecast methods • Historical • Intra-day, High-Low • Implied • Volatility 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 • High/Low range • Implied • Model based (GARCH) similar to historical

6. Why Forecast Volatility • Risk measures • Option pricing • Portfolio optimization

7. Moving Average of Volatility • Rolling moving average of returns squared

8. Exponential Filter: Riskmetrics • h(t) = variance at time t • Smooth weighting of past volatility

9. Intraday/High-low • Two methods • Estimate volatility for day t using intraday data (15 minute returns): v(t) • Estimate volatility for day t using High/Low range information • Build time series (ARMA) model for v(t) • Use to forecast v(t+1)

10. High Low Range Volatility

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

12. VIX and Implied Volatility • VIX is index of implied volatility for the S&P

13. Stylized Facts: 1.) Autocorelation Patterns • Absolute value of returns • High/low range • AR(1) model • volsimple.m • Very persistent vol

14. Stylized Facts:2.) Standardized returns • Returns(t)/std(t) • Smooths out volatility • Trims down fat tails • A lot, but not all of the mysteries of returns