Serving the Quantitative Finance Community

 
User avatar
tw
Topic Author
Posts: 592
Joined: May 10th, 2002, 3:30 pm

Hull on futures options

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
 
User avatar
Aaron
Posts: 4
Joined: July 23rd, 2001, 3:46 pm

Hull on futures options

August 13th, 2002, 7:27 pm

No, the important cash flow takes place at option exercise. It's the difference between the option exercise price and the futures settle price. If that's large enough, the interest earned by exercising early is greater than the remaining time value of the option. The margin cash flows between option exercise and futures delivery are seldom enough to cause early exercise.