Question

Suppose that you enter into a six-month forward contract on a non-dividend-paying stock when the stock price is $30 and the risk-free interest rate (with quarterly compounding) is 12% per annum.

a) What is equivalent continuously compounding rate?

b) What is the forward price?

Answer 1

a) Effective quarterly rate = 12%/4 = 3%

Effective annual rate = (1 + 0.03)^4 - 1 = 0.12550881 = 12.550881%

Equivalent continuously compounding rate = e^(rt) - 1 = 2.718281828^( 0.12550881 * 1) - 1

Equivalent continuously compounding rate = 13.3725157%

b) F = Spot * e^(rt)

t = 0.5 years

F = 30 * 2.718281828^(0.12550881 * 0.5)

F = 30 * 1.064765306

F = $31.94295918

Can you please upvote? Thank you :-)