Question

A stock is expected to pay a dividend of $5 per share in 2 months .

At initiation, the stock price is $100, and the risk-free rate of interest is 6% per annum with
continuous compounding for all maturities. An investor takes a short position in a
9-month forward contract on the stock.

It is calculated for you that the present value of the dividend, i.e. I is 4.95.

Six months later, the price of the stock is $90 and the risk-free rate of interest is
still 6% per annum for all maturities. What are the forward price and the value of the short position in the forward contract? What is the delivery price K for this forward contract?

(note there is only one dividend during the life of this forward).

Answer 1

As per the Carry of Cost model,

Forward Price = Stock price + Interest cost - Dividend forgone

Stock price = 100

Dividend after 2 months = 5

r = 6% o.a continuous compounding. ie r for 9 months = 6/12 * 9 = 4.5% ie r for 3 months = 6/12*3 = 1.5

Forward price =( current stock price - Present value of Dividends)* e^r

= ( 100 - 4.95) *e^0.045

=95.05 * 1.04602786

= $99.42

After six months present value of Forward Price = Forward price / e^ r

= 99.42  / e^0.015 = 99.42 /1.015113065 = 97.94

Value for a forward contract where the person is short the forward contract

= Present value of forward contract - Stock price after 6 months

=97.94 - 90

=$ 7.94