Question

Assume that a stock is trading at $100, and that it will pay a single cash dividend of $2 exactly one month from now. Interest rate = 1.5%. Calculate the 3-month forward price. If the 3-month put with strike K=$100 is worth $2. What would be the value of the call with the same strike?

Answer 1

3 Month Forward Price.

Suppose someone Purchases one stock at $100 and sells one stock in 3 month forward.

He borrows $100 at 1.5% rate for 3 months.

Interest for 3 months =(1.5*(3/12))=0.375%=0.00375

Future value of $100 at the end of 3 months =100*(1+0.00375)=100.375

Amount to be returned with interest=100.375

If he invests dividend of $2 for 2 months at 1.5% annual interest

Interest for 2 months =(1.5*(2/12))%=0.25%=0.0025

Future value of $2 =2*1.0025=2.005

3 Months forward Price =X

X+2.005=100.375

X=100.375-2.005=$98.37

3 month Forward Price=$98.37

3 Month Forward Price

$98.37

Put Call Parity Equation

C+X/(1+r)^t=S0+P

C=Call premium

P=Put premium=$2

X=Strike price of Put and Call=$100

r=annual interest rate=1.5%

t=Time in years=(3/12)=0.25

S0=Initial price of underlying=$100

C+(100/((1+0.015)^0.25))=100+2

C+99.63=102

C=102-99.63=$2.37

Value of the call option at Strike Price of $100

$2.37