Understanding market, credit and operation risk

[[email protected]]

Hi
Would FAT tail appear only in unconditional distributions and not in
conditional distributions...

Regards

 

[David Harper CFA FRM]

Hi vinoth,

Fat tail (kurtosis > 3) is firstly a feature (4th moment function) of a distribution; so, many distributions can be unconditionally fat tailed; e.g., student's t.

But further, your phrase is associated with GARCH(1,1): with regard to stochastic processes, GBM (used in black scholes) is sort of our baseline and, as it assumed constant volatility and i.i.d. returns, GBM process is normal return (lognormal price level) both conditionally and unconditionally; i.e, not fat tailed.

GARCH(1,1) however does not assume constant volatility. Rather, the variance update is *conditional* and therefore time-varying. So, we say about GARCH: the conditional returns are normal (not fat) but the unconditional returns are heavy-tailed. My metaphor is a skiing: if your skis are a constant width and you ski by swerving, the width is constant at each cross section (normal) but if you stop and look back at the total width carved out (left to right) it will be wider due to the swerving (just a metaphor).

David