Heavy Tail and Changing Volatility

[Liming]

Dear David,
I’ve had some confusion, misunderstanding and doubts when doing 09 Level I Annotated Boot Camp. Appreciate your kind help on this!

A basic concept to verify: if heavy tail necessarily implies changing volatility and vice versa?

Thank you for your enlightenment and correction!
Cheers
Liming
16/11/09

 

[David Harper CFA FRM]

Hi Liming,

No, not implied and not the same.
Heavy tail is (4th moment) property of a static distribution; every distribution has a kurtosis. Heavy tailed is kurtosis > 3
Heteroskedasticity (changing volatility or, I prefer, time-varying volatility) implies a sequence of errors (in regression terms), or in our case generally, a time series: the variance is changing over time.

e.g., GBM = constant volatility
GARCH = conditional normal (not fat) but time-varying variance with implication of unconditional fat tail

so (i) a distribution can be fat/not (normal/heavy) and then, it is a separate question whether (2) the variance of the distribution is constant/changing over time

we can have
* a normal distribution with time-varying variance, or
* a heavy tailed distribution (e.g., student's t) with time-varying variance

David