Question

Suppose that the current spot price of a continually paying dividend asset is $222, the interest rate is r = 3% and the dividend yield is q = 2%.
(a) What are the one-month and eight-month forward prices for the asset in an arbitrage-free market?
(b) Let X be a portfolio on time interval [0, T] consisting of three positions startng from time 0: borrow $222 at the rate 3%, long 1 unit of the asset, and short the three-month forward at the forward price F = $222.56. Is an arbitrage portfolio? If your answer is no, show a proof. If your answer is yes, explain how you can make a profit by taking the arbitrage opportunity.

Answer 1

As per the Forward Pricing Theory :

S = Spot Price = 222

r = Risk-Free Rate = 03% = 0.03

q =  dividend yield = 02% = 0.02

Answer a)

When

Time T = 01 Month = 01 / 12

= 222.19

Time T = 08 Month = 08 / 12

= 223.48

Ans: Three Month and Eight Months Forward Prices are   $ 222.19 & $ 223.48

Answer b)

three-month forward at the forward price F = $222.56

Using

Forward Pricing Theory :

S = Spot Price = 222

r = Risk-Free Rate = 03% = 0.03

q =  dividend yield = 02% = 0.02

Time T = 03 Month = 03 / 12

= 222.56

Now As per Forward pricing theorem and the current price of forward both are Same There is No arbitrage opportunity. (Ans)