put call forward parity question

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h21

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Determine if a forward contract is correctly priced by using put–call–forward parity. The option exercise price is 90, the risk-free rate is 5 percent, the options and the forward contract expire in two years, the call price is 15.25, the put price is 3.00, and the forward price is 101.43.

Hi all, can some kind soul help me answer this based on the old simple

C+X/(1+r)^t=P+S

i am so confused
 
You’re not so dumb.
Nobody ever presents forward put-call parity by giving the simple formula I wrote. I don’t know why, but they don’t.
 
They just throw away the derived formula
c+(X-Ft)/(1+r)^t = p
while the derivation rests on that simple idea
Recall original put-call parity
c+X/(1+r)^t=p+S
Now substitute S by the forward price
S=Ft/(1+r)^t
And you get the same parity but using forwards
c+X/(1+r)^t=p+Ft/(1+r)^t
which matematically boils down to
c+(X-Ft)/(1+r)^t = p
 
h21 wrote:
Determine if a forward contract is correctly priced by using put–call–forward parity. The option exercise price is 90, the risk-free rate is 5 percent, the options and the forward contract expire in two years, the call price is 15.25, the put price is 3.00, and the forward price is 101.43.

Hi all, can some kind soul help me answer this based on the old simple

C+X/(1+r)^t=P+S

i am so confused
Click to expand...
You are not given the spot price, so find it using the Put-Call Parity you already know. After that, we will calculate the forward price using that spot price and the risk-free rate the problem provided.
C + X/(1+r)^t = P + S
Free the S:
S = C + X/(1+r)^t - P
S = 15.25 + 90/(1+0.05)^(2) - 3
S= 93.88
Now calculate the forward price of the stock:
FP = 93.88 x (1.05)^2
FP = 103.51
Compare it with the forward price provided. As we see it is not correctly priced.
 
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