Question

1) Suppose that an Intel single-stock futures contract expires in four months. The stock pays a dividend in two months. We have the following information. Annualized, continuously compounded risk-free interest rate for 2-month period: r = 3.86%. Annualized, continuously compounded risk-free interest rate for 4-month period: r = 4.95%. Current spot price of Intel stock: $30 per share. Dividend per share of $0.24 in two months. What must the futures price equal in order than no arbitrage opportunity exist?

2) The spot price of an investment asset is $47 per unit and the annualized risk-free rate for all maturities (with continuous compounding) is 6%. The asset provides an income of $1.68 per unit at the end of the first and second years. Assuming no arbitrage opportunities exist, what is the forward price on a forward contract that matures in 3 years?

Answer 1

Solution:

Question 1.

Current spot price = $30 , Dividend = $0.24

Interest rate for 2 months =  3.86%, Interest rate for 4 months = 4.95%

Since dividend will be paid in 2 months hence the current value of dividend = $0.24 * exp ( -interest rate*time)

= $0.24 * exp ( -3.86%*2/12) = $0.24 * 0.9936 = 0.2385

In order to have no arbitrage opportunity future price will be

Future Value = (Spot price- present value of dividend) * Exp (interest rate*time) = ($30-0.2385) * exp (4.95%*4/12) = 29.762 * 1.01664 =30.26

So future price should be 30.26

Question 2.

Spot price = $47

interest rate = 6% , Fixed income is $1.68 in year 1 and year 2

The current value of fixed income that will be paid in year 1 = $1.68 * exp ( -6%*1) = $1.68 *0.942 = 1.582

The current value of fixed income that will be paid in year 2 = $1.68 * exp ( -6%*2) = $1.68 *0.887 = 1.49

Forward price for 3 year = (47-1.582-1.49) * exp ( 6% *3) = 43.927 *1.1972 = $52.59

Forward price = $52.59