Question #54, Afternoon BSAS **SPOILER** index, why, understand, following, potential

bchadwick

Index Price:890
Call option with X=1000 strike price on the index= $68
Risk-Free Rate 1.5%
Discrete Dividend Yield of Index=3.22%
“To avoid any potential arbitrage opportunities, which of the following is closest to the premium of the one-year in-the-money put with an exercise price of X=1000?”
1) I don’t understand why an option derived using Black-Scholes-Merton can have a dividend yield (because of the assumption of no cash flows with the BSM model), but anyway…
2) I don’t know how they solve this. They say use put-call parity, but they take the risk-free and dividend yield rates and make them continuous [ln(1+i)=continuous rate]. They say you have to “reduce the index price by its continously compounded dividend yield factor.”
They claim Put option=Call option + 1000e^(continuously compounded risk-free rate) - 890e^(continuously compounded dividend yield rate).
What freaking put-call parity formula are they using

stalkey

C+X/(1+rf)^t = P+S
1/(1+rf)^t = e^(-rfc*T) – if continuously compounded
continuous risk free rate: ln(1+.015) = 0.01489
Since there is a continuous dividend at ln(1.0322) = 0.0317
68+1000*e^(-0.01489*1)=P+890*e^-0.0317
P=1053.22 - 862.22 = 191.$

manchester88

Why does 1/(1+rf)^t=e^(-rfc*T)? Does it have something to do with derivative of ln(1+rf)=1/(1+rf)? Is there any way you can tell me mathematically, or should I just memorize that:
Co+ Xe^(-rfc*T)=P+So*e^(-rdc*T)?

troymo

I get a slightly different answer with the regular formula, C+PV(X)=P+S-PVCF; I get $191. Is that a rounding error and thus usable on the test, or should I suck it up and memorize the continuous dividend yield/risk-free rate thingie formula?