why when calculating the call option value : c = hS + PV (-hS- + C-) is not equivalent with c = hS + PV (-hS+ + C+) on the book say it is equivalent ?
They are mathematically equal either way up or down. Maybe you need to watch the signs (+) & (-)
are you referring to the example in the Shweser book ?
Referring the sample, let say: S=50, X=50, S+=62.5 and S-=40, RFR= 7%
can you post the size of up-move and down-move and i’ll calculate both methods for you
sorry my bad you posted S+ and S- give me a minute
1st method
size of an up move = 1.25
size of a down move = 0.8
probability of up move = 60%
probability of down move = 40%
Payoff C+ = 12.5
payoff C- = 0
Expected value (call) = (0.6 x 12.5) + (0.4 x 0) = 7.5
Value of the call = 7.5/1.07 = 7.01
2nd method
h = (12.5 - 0)/(62.5 - 40) = 0.555556
c = hS + PV (-hS- + C-) = 7.011 (due to rounding)
c = hS + PV (-hS+ + C+) = 7.008 ( due to rounding)
thanks Nicolas! yeah…maybe due to rounding when I calculate the h ratio I rounded it to 0.56 thats why there is a different in the c value. Thanks for your effort and explanation.
My pleasure !
at 0.56 ( rounding ) one will be at 6.97 and the other at 7.2
seems like a big difference, hence for this particular topic i suggest to take the figure as is and your numbers will reconcile.