European Option with futures-style margining

hichmoul · January 7th, 2008, 12:24 pm

Hi,Consider 2 European calls on a stock that pays no dividends before the option's expiry,under the assumptions of the Black Scholes Merton framework,1 with the premium being paid upfront (at trade time),2 the other has futures-style margining, where the premium is paid/received over its life 1 c = S N(d1) - X e(-rT) N(d2) d1 = ( ln (S/X) + (r+ v*v/2) ) / v sqrt(T)2 How would the 2nd call be priced?

daveangel · January 7th, 2008, 12:33 pm

the margined option will be priced as follows:C = c * exp(rT)ie it is the forward value of the standard option.

hichmoul · January 8th, 2008, 7:10 am

i see. thanks,basically, with the upfront payment, we discount the expected payoff at expiry,margining the option removes the need for discounting.makes sense.how about the difference between a european option settled in cash and one settled with delivery of the stock(assuming the stock is delivered or the cash is paid/received right at the expiry).No difference i suppose?

hichmoul · November 13th, 2008, 9:32 am

Hello,Returning to the initial question, what about american options?The only difference between an upfront paid american and futures-styleamerican is also C = c * exp(rT)rds,

hichmoul · August 12th, 2009, 7:50 am

daveangel, what about the 3rd case if the option premium is paid at expiry?