Question

1. A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

1. What are the forward price and the initial value of the forward contract?
2. Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

Answer 1

We can find the present value of the dividend which is expected to be paid in 2 months and 5 months, and is given as

PV of the dividends = + = 0.9868 + 0.9672 = $1.954

The forward price F₀ is given by

F₀ = = $50.01

Hence, initial value is F₀-S₀ = 50.01-50 = 0.01 (Consider it to be 0) (The value of a forward contract at initiation is always 0)

After 3 months,

PV of the dividend = = $0.9868

Forward price = =$47.9629

The delivery price K = $50.01. Value of short position in the forward contract after 3 months is given as :

f = = $2.0065 = $2.01 (rounding off)