FORMULA SHEET ERRORS:
On page 18: The average, unconditional variance in GARCH(1,1) should read
Lv = alpha0/[1-(alpha1 + beta)], or equivalently
Lv = alpha0/[1 - alpha1 - beta]
Not incorrectly: alpha0/1 - alpha1 + beta
This follows from:
GARCH(1,1) = alpha0 + alpha1*(return^2) + beta*(lagged variance)
and alpha0 = Lv*gamma; i.e., gamma is the weight assigned to the long run variance (Lv)
As the weights must sum to 1.0, gamma + alpha1 + beta = 1, and therefore:
gamma = 1 - alpha1 - beta. And since Lv = alpha0/gamma, Lv must be:
Lv = alpha0/(1 - alpha1 - beta)
On page 51, the original version contained an error at the bottom
(but this was immediately fixed, version 1a does not contain this error)
Under LOSS GIVEN DEFAULT, the formula should start “LGD =” instead of “PD =”