Question

A stock index currently stands at 280. The risk-free interest rate is 10% per annum (with semiannual compounding) and the dividend yield on the index is 5% per annum (continuously compounded). The futures price for a six-month contract is closest to the which of following value:________

a. $235.07
b. $287.09
c. $277.11
d. $340.21

Answer 1

b. $287.09

Step-by-step explanation:

The computation of the future price of a six month contract is shown below;

Given that

Current stock index = 280

Risk free rate = 10% or 0.10

Dividend yield = 5% or 0.05

Periods (n) = 6 months or 0.5 year

now

Futures price = Current stock index × e^(risk free rate - dividend yield) × n

= 280 × e^(0.10 - 0.05) × 0.5

= 280 × e^(0.05) × 0.5

= 280 × e^(0.025)

= 280 × 1.025315

= $287.09