August 13th, 2002, 1:41 pm
From Hull, fourth edition, section 12.9 (p.295):"Traded futures options are, in practice usually American. Assuming that the risk-freerate of interest, r, is positive, there is always some chance that it will be optimal to exercise an American futures option early."On the facing page, he quotes Black's result for the value of futures options.c=exp(-rt)*[FN(d1)-xN(d2)]p=exp(-rt)*[xN(-d2)-FN(-d1)]d1=(ln(F/X)+sigma^2t/2)/(sigma.sqrt(t))d2=(ln(F/X)-sigma^2t/2)/(sigma.sqrt(t))Now.c(F)>exp(-rt)*max(F-X,0)p(F)>exp(-rt)*max(X-F,0)(the RHS is discounted by a value appropriateto the cashflow occuring at the option's expiry).This would seem to imply that, for Hull's argumentto be correct, early exercise would yield cashflow beforeeither option expiry or futures maturity, presumably throughthe margin account. Is this how it would work? Is theresome other argument as to why there is "some chance of early exercise"? cheers,Tom