Question

Smith holds a long position for a Stock index futures contract which is four months from maturity. A stock index currently stands at 350. The risk-free interest rate is 8% per annum (with continuous compounding) and the dividend yield on the index is 4% per annum.

a) What should the futures price for a four-month contract be?

b) Suppose one month later the stock price is 351. The dividend yield and index are the same. What is the value of the contract now?

Answer 1

Current value of stock index, S0 = 350

risk free rate , r= 8%

dividend yield , d= 4%

where m = no. of compounding periods in 1 year

maturity of contract , T= 4 months

Future price = S0*[e^{(r - d)*(T/12)}] = 350*[e^{(0.08-0.04)*(4/12)}] = 350*1.013422619 = 354.697916 or 354.70 ( rounding off to 2 decimal places)

b) S0 = 350

T = 3

Future price = S0*[e^{(r - D)*(T/12)}] = 350*[e^{(0.08-0.0392207)*(3/12)}] = 350*1.010050167 = 353.51755848 or 353.52 ( rounding off to 2 decimal places)