Question

(a) On January 1st 2017 a share has a price of £15 and is expected to pay a dividend of £0.95 in 1 year and a further dividend of £1.00 in 2 years. The relevant risk-free interest rate is 3% per annum with continuous compounding. What should be the price of a forward contract, written on this share, which matures immediately after the second coupon is paid and what is the initial value of the forward contract? (40 marks) (b) Immediately after the first dividend payment the share is trading at £16.50. What will be the new forward price and the current value of the long forward position which was opened in January 2017? (40 marks) (c) Explain why the prices and valuations in parts (a) and (b) must hold. (20 marks)

Answer 1

a) 15 Futures Price = (Stock Price - Present Value of Dividend) x (1 + Risk Free Interest Rate) Futures Price Stock Price #VALUE! #VALUE! Dividend after 1st year 0.95 Dividend after 2nd year Risk Free Interest Rate 3% PV of Dividend given after year 1 0.92 PV of Dividend given after year 2 0.94 Hence, FP = (15-0.92-0.94)*((1.03)^2) 13.94 Current Stock Price 16.5 0.84486218 #REF! Dividend at end of year Risk Free Interest Rate 3% PV of Dividend 0.97 Hence, FP = (16.5-0.97)*(1.03) 16.00 and current value of long position = 16-13.94 = 2.06 The valuations are based on risk free rate, actual stock price & dividend paid Hence, a) must hold In case of b) the underlying assets value has increased and hence the FP has increased. b)