3_volatility

# 3_volatility - VOLATILITY definition and other basics...

This preview shows pages 1–7. Sign up to view the full content.

VOLATILITY J. Wei, Department of Management, U of T 1 MGTD78 definition and other basics weighted moving average model GARCH(1, 1) maximum likelihood estimation of GARCH volatility forecasting and volatility term structure

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
VOLATILITY J. Wei, Department of Management, U of T 2 MGTD78 Definition of volatility : standard deviation of the variable Variance rate (or variance) : square of volatility Calendar days or trading days (see Business Snapshot 9.1)? volatility seems to be generated by trading; we therefore count only trading days – 252 days in a year. Example: annual variance is 0.0625. Then annual volatility is 0.25; daily variance is 0.0625 / 252 = 0.000248; daily volatility is 0.25/sqrt(252) = 0.01575. Implied volatility: volatility implied from option prices (C71) VIX (Fig 9.1)
VOLATILITY IN FINANCIAL VARIABLES J. Wei, Department of Management, U of T 3 MGTD78 Black-Scholes model assumes normal distribution of returns Financial returns are usually not normal. Example in Table 9.2 (10-year period, 12 exchange rates): % days on which realized FX is n standard deviations away from mean: real world(%) Normal distribution(%) > 1 SD 25.04 31.73 > 2 SD 5.27 4.55 > 3 SD 1.34 0.27 > 4 SD 0.29 0.01 > 5 SD 0.08 0.00 > 6 SD 0.03 0.00 large / extreme changes are more likely than predicted by normal: heavy-tail or fat-tail distributions (see Figure 9.1)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
POWER LAW J. Wei, Department of Management, U of T 4 MGTD78 Alternative to normal distribution when extreme values are considered It is an approximation, applicable to many situations The Power Law: when x is large, the value of variable v approximately satisfies Prob(v > x) = Kx α , where K and α are constants Application: use not-so-extreme values of x to estimate K and α , then calculate probability for extreme realizations Example: the probability that v > 6 is 0.004 when K = 10.368 and = 4. Then we can calculate the α following:
STANDARD METHOD OF ESTIMATION J. Wei, Department of Management, U of T 5 MGTD78 Review of C71 (on day n, going back m days): where In risk management, we make three changes use percentage change (reflecting reality): assuming to be zero (for simplicity) replace m -1 by m (conforming to ML estimate) ( 29 u u 1 - m 1 σ m 1 i 2 i - n 2 n = - = u m 1 u , S S ln u m 1 i i n 1 - i i i = - = = and 1 - i 1 - i i i S S S u - = u u m 1 σ m 1 i 2 i - n 2 n = =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
WEIGHTING SCHEME J. Wei, Department of Management, U of T 6 MGTD78 Standard method assigns equal weight (1/m) to all observations Make sense to assign more weights to recent observations: The weighting scheme ( α i ) varies. The most common is to
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 19

3_volatility - VOLATILITY definition and other basics...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online