Assume that the risk–free rate is 3% per annum and storage costs are 0.5 % per

annum both continuously compounded.

a) Assume that a barrel of oil trades for $ 100 on the spot market. What is the oil

forward price for delivery in one year?

b) Assume that you sell 100,000 barrels forward for delivery in one year. Six

months later the oil spot price is $ 93 dollar per barrel. What is the new forward

price for delivery in six months? What is the present value of your forward short

position? (i.e. mark to market) What would your profit be if you were to close

your position?

Assume that you are a professional oil trader; you may borrow/lend in two separate

markets cash or oil. Currently, you may borrow/lend cash at 6% per annum and

borrow/lend oil at 2% per annum. The interest rates on the two loans are simple annual

rates. Hence, if oil is borrowed interest must be repaid in oil. Thus 100 barrels borrowed

today would require 102 barrels to be repaid in one year. If cash is borrowed, $ 100

borrowed today would require $ 106 to be repaid in one year.

Assume that the current oil spot price is $ 100 per barrel, the risk–free rate is 3% per

annum and storage costs are 0.5 % per annum both continuously compounded

c) Using the forward market price (from a)), which lending/borrowing strategy

would you initiate to take advantage of the situation (assume a nominal cash

amount of $1,000,000)? What would the present value of your profit be?

Assume now that you need to price a 3 year maturity swap contract where you receive

cash at 6% per annum and pay oil at 2% per annum. As before, the swap rates are simple

annual rates and swap payments are exchanged at the end of each year (the first payment

will occur a year from now) on a principal value of $ 100,000,000 for the cash leg and

1,000,000 barrels for the oil leg. Also assume that the current oil spot price is $ 100 per

bbl, the risk–free rate is 3% per annum and storage costs are 0.5 % per annum both

continuously compounded for all maturities.

d) What is the present value of the swap if the principal values are exchanged at

maturity?

e) What is the present value of the swap if instead the principal values are NOT

exchanged at maturity?

f) Assume that you maintain a 2% oil swap rate, which cash swap rate should be

quoted so the present value of the swap would be zero if the principal values are

exchanged at maturity? What should be this rate if instead the principal values

are NOT exchanged at maturity?

Subject | Business |

Due By (Pacific Time) | 02/26/2013 05:30 pm |

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