Volatility

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(t1)
• 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 -gt volatility
• Advantage
• Forward looking
• Disadvantage
• Different options
• Depens on Black/Scholes

10
VIX and Implied Volatility

• VIX is index of implied volatility for the SP

11
VIX versus SP
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