BSM model

I know we do not need to remember the BSM model. But I was wondering… There are 2 BSM models for European call options

C0 = S0N(d1) – e–rTXN(d2)

C0 = PV {S0erTN(d1) – XN(d2)}.

Why are we not getting the same answer given S0 = $50 N(d1) = 0.779 N(d2) = 0.723 X = $45 r = .03 T = 6 months or 0.5

If you’re not getting the same answer, rest assured that you’re doing something wrong on your calculator.

Who told you we don’t need to remember the BSM model? Reading 41, learning objectives G-K all scream “MEMORIZE BSM!”. You need to know what every term means (e.g. N(d2) is the probability of the option expiring in the money, N(d1) is the hedge ratio, x is the strike price, e-rt is the discount term, ergo you need to know the formulas).

You should memorize the first formula: C0 = S0N(d1) – e–rTXN(d2)

And realize it is very similar to the other formula (binomial model): C0 = hS0 + (-hS++C+)/(1+Rf)

The first component in both is the # of stock needed to buy and the 2nd component is what is needed to borrow.

If PV = e-rT, then both expressions should be identical. The second expression is simply the first with PV factored out.

Thanks for the response. I got a $0.10 difference. Could that be a rounding error? C0 = S0N(d1) – e–rTXN(d2) C0 = PV {S0erTN(d1) – XN(d2)}. Co = [$50* (.779)] - [(e ^-.03*.5)* ($45)* (.723)] = 6.8994 Co = [$50* (e ^.03 * .5)] * [(.779) - $45 * (.723)] / 1.03 = 6.7997

Would I be safe to assume that for the 2nd formula, I would need to discount the the value by the risk free rate to get the present value?

Thanks @Tatics I appreciate your comment as well!

Discounting error, not rounding.

Thank you. I mad appreciate it yo. You da real Breadmaker