forward start option

[ajsa]

Hi David,

forward start option has the same value as an at the money option with the same time to maturity. So the time to maturity is from grant date or from the existence date? At the money is at the grant date or at the existence date? Why does it need to be at the money?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

It means forward call price (existence from T1 to T2) = call price today (if maturity = T2 - T1)
i.e., if "existence" is equal

Re: Why does it need to be at the money?
I wasn't sure ... so i created this XLS:
http://sheet.zoho.com/public/btzoho/oct14-forwardstart

and this shows it does not need to be ATM (!!). The foward call = c @ strike 80%/90%/110%/120%
see columns I & J (column J is the PV of the forward; column is today's call)

i love it ... you are pretty handy with that "why?"

David

 

[ajsa]

Hi David,

Thanks. so you mean PV(forward call price)=call price today, right? (what does the "BS" stand for?)
but on your spreadsheet, both forward call and call's terms are 1 year. does it mean the the forward call is from 0.5 yr to 1.5 yr while the call is from now to 1 yr? I thought both would expire at 1 yr time point..

your spreadsheet is very nice. thanks!

 

[David Harper CFA FRM]

Hi asja

BS = black scholes merton. prob should say BSM

Re: "PV(forward call price)=call price today." Exactly, that's Hull's assertion (I think) for the forward start, he's saying: PV(E[future value of call]) = call price today
Re term, not quite, he is requiring they have the same "term to maturity," so my XLS compares:

Col I (the usual): call option price today with 1 year term

Col J: Grow the stock price forward 0.5 years. Set strike equal to 80%/90%/etc this future stock price. Calculate BSM at that time (+0.5 years) for an option with 1 year maturity. So from today, it's an option granted T+0.5 with maturity T+1.5

...please let me know if you think that may not be consistent with the test?
...hull's text seems to imply non ATM won't hold up due to convexity, but it seems to be fine..

David

 

[ajsa]

Hi David,

I just feel it is not intuitive if the 2 options are equal while one expires 1 yr from now, and the other expires 1.5 yr from now. Coule you provide your insight?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

The options are the same (both have 1 year term to maturity), only the forward (instead of granting today) is granted in X months (0.5 months).
It's a *variation* (simplification of): what is the present value of the expected future stock price (St) in 0.5 months, when S0 = $1?
If E(St) = $1*exp(rate*0.5), the PV = discounted($1*exp(rate*0.5)) =exp(-rate*0.5)*$1*exp(rate*0.5) = $1

the call value (c) is expected grow, but that is offset exactly by the discount rate...David