The current price of crude oil is $32.00 per barrel. Forward prices for 3, 6, 9,...

 

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The current price of crude oil is $32.00 per barrel. Forward prices for 3, 6, 9, and 12 months are $31.37, 830.75, $30.14, and $29.54. Assuming a 2% continuously-compounded annual risk-free rate. (i) Suppose there is an active leasing market for crude oil with continuously-compounded annual lease rate q. What is the lease rate q for each maturity? Question 4: Commodity Forward Contracts with Convenience Yield (3/10) (This question is designed to help you understand why forward prices can be different across different investors. This question is very difficult and will not be tested in exams. However, the question is written in a way that you can solve with the skills from class.) The market spot price of soybeans is S, and the continuously-compounded interest rate is re at time t. Suppose that there are no storage costs, lease markets, carry costs or transacation fees. Suppose that there is one lender in the market who has convenience yield e. Suppoe that you are a trader for an investement bank. (1) Suppose an investor comes to you and wants to enter a long forward position on one unit of soybeans with maturity T, and Fe (St. T), the forward price, is determined by you. What other positions / operations does the investor need in order to make the payoff of his portfolio, which includes the forward contract, zero at time T? You can assume the lender needs to be paid e(T-t) units of soybean at time T for each unit it lends at time t due to convenience yield, and the investor can only trade the soybeans and bonds directly in addition to the long position of the forward contract. (2) What is the payoff of the portfolio (1) to the investor at time t? If the payoff is positive, there is an arbitrage opportunity for the investor. Derive a condition for the forward price such that the arbitrage opportunity does not exist. The current price of crude oil is $32.00 per barrel. Forward prices for 3, 6, 9, and 12 months are $31.37, 830.75, $30.14, and $29.54. Assuming a 2% continuously-compounded annual risk-free rate. (i) Suppose there is an active leasing market for crude oil with continuously-compounded annual lease rate q. What is the lease rate q for each maturity? Question 4: Commodity Forward Contracts with Convenience Yield (3/10) (This question is designed to help you understand why forward prices can be different across different investors. This question is very difficult and will not be tested in exams. However, the question is written in a way that you can solve with the skills from class.) The market spot price of soybeans is S, and the continuously-compounded interest rate is re at time t. Suppose that there are no storage costs, lease markets, carry costs or transacation fees. Suppose that there is one lender in the market who has convenience yield e. Suppoe that you are a trader for an investement bank. (1) Suppose an investor comes to you and wants to enter a long forward position on one unit of soybeans with maturity T, and Fe (St. T), the forward price, is determined by you. What other positions / operations does the investor need in order to make the payoff of his portfolio, which includes the forward contract, zero at time T? You can assume the lender needs to be paid e(T-t) units of soybean at time T for each unit it lends at time t due to convenience yield, and the investor can only trade the soybeans and bonds directly in addition to the long position of the forward contract. (2) What is the payoff of the portfolio (1) to the investor at time t? If the payoff is positive, there is an arbitrage opportunity for the investor. Derive a condition for the forward price such that the arbitrage opportunity does not exist.

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1 For the investor to have zero payoff in addition to the long forwa... View the full answer