Question

The current price of YBM stock S is $101. European options with a strike price K = $100 and maturing in T = 6 months trade on YBM. The continuously compounded, risk-free interest rate r is 5 percent per year. A dividend of $1.10 is paid out after three months. If the put price p is $4.03, the call price c is:

Answer 1

Solution: the Put call parity for a dividend paying stock is given by:

(S - PV(D) ) + P = C + PV(X)

We have Now , C = (S- PV(D)) + P - PV(X)

Where S is the stock price ,

PV(D) -> Present Value of the dividend = D * e^(-r*t) , We have D=1.10(given) , r =0.05 , t =3/12 = .25

PV(D) = 1.10 * e^(-.05*.25) = 1.10 * .9875 = 1.0863

P ->Put Price, C -> Call Price

PV(X) -> Present value of the strike price = X * e^(-r*t)

PV(X) =100 * e^(-0.05 * .5) { t -> .5 given}

= 100 * .9753 = 97.53

Putting all the values in the PCP equation we get

C =(101 - 1.0863) + 4.03 - 97.53

C = 99.9137 + 4.03 - 97.53 = 103.9437 - 97.53 = 6.4137

The value of the call option comes out to be 6.4137