5.26. The spot price of oil is $80 per barrel and the cost of storing a barrel o

Question

5.26. The spot price of oil is $80 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free interest rate is 5% per annum continuously compounded. What is an upper bound for the one-year futures price of oil? 5.27. A stock is expected to pay a dividend of S1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a 6-month forward contract on the stock. (a) What are the forward price and the initial value of the forward contract? (b) Three months later, the price of the stock is S48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

Explanation / Answer

1) risk free rate , r = 5% = 0.05

cost of storing barrel of oil , c = 3

present value of storage cost, p = c/(er ) = 3/(e0.05 ) = 2.853688

upper bound for one year future price =( spot price+p)*e0.05 = (80+2.853688)*e0.05 = $87.10

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