Question

Suppose you enter into a 9-month long forward contract on a non-dividend-paying stock when the stock price is S₀ = $125 and the risk-free rate is 2.0% per annum with continuous compounding.

(a) What are the forward price (F₀) and the initial value of the forward contract?

(b) Three months later, the price of the stock (S₀) is $112, and the risk-free remains 2.0%. What are the forward price (F₀) and the value of the forward contract?

(c) Another month later (4 months from today), the risk-free rate increases to 2.25% while the stock price stays $112. What are the forward price and the value now?

(d) Suppose now that another month later (5 months from today) the risk-free rate stays 2.25%, but the stock price goes up to $130. How much could you sell your forward contract for?

Answer 1

a]

Forward price = spot price * e^rt,

where r = continuously compounded risk free rate

t = time to expiration of contract in years

Here, the time left to expiration is 9 months, hence t = (9/12) years.

Forward price = $125 * e^0.02*(9/12) = $126.89

Value of forward contract = zero (the value of a forward contract at initiation is zero)

b]

Here, the time left to expiration is 6 months, hence t = (6/12) years.

Forward price = $112 * e^0.02*(6/12) = $113.13

Value of forward contract = price of forward now - price of forward at initiation

Value of forward contract = $113.13 - $126.89 = -$13.76

c]

Here, the time left to expiration is 5 months, hence t = (5/12) years.

Forward price = $112 * e^0.025*(5/12) = $113.17

Value of forward contract = price of forward now - price of forward at initiation

Value of forward contract = $113.17 - $126.89 = -$13.72

d]

Here, the time left to expiration is 4 months, hence t = (4/12) years.

Forward price = $130 * e^0.025*(4/12) = $131.09