For problems 1 to 5, consider two firms, XYZ and Teleco. Firm XYZ mines copper, with fixed costs of $0.50/1b and variable costs of $0.40/1b. Teleco sells the telecommunications equipment and uses copper wire as an input. Suppose Teleco earns a fixed revenue of $6.20 for each unit of wire it uses. The wire price is the price of copper/lb plus $5. The 1-year forward price of copper is $1/lb. The 1-year interest rate is 6%. The 1-year option prices for copper are C(0.9500) = 0.0649, C(0.9750) 0.0500, C(1.0000) = 0.0376, = C(1.0250) = 0.0274, C(1.0500) = 0.0194, P(0.9500) = = 0.0178, P(0.9750) = 0.0265, P(1.0000) = 0.0376, P(1.0250) = 0.0509, P(1.0500) = 0.0665 1. Suppose XYZ buys a put option with a strike of $0.95, $1.00, or $1.05. Draw a graph of the hedged profit in each case. 2. Suppose XYZ buys collars with the following strikes. Draw a graph of the hedged profit in each case. a. $0.95 for the put and $1.00 for the call b. $0.975 for the put and $1.025 for the call c. $1.05 for the put and $1.05 for the call 3. If Teleco does nothing to mange copper price risk, what is its profit 1 year from now, per pound of copper that it buys? If it hedges the price of wire by buying copper forward, what is its estimated profit 1 year from now? Construct graphs illustrating both unhedged and hedged profit. 4. Compute estimated profit in 1 year if Teleco buys a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case. 5. Compute estimated profit in 1 year if Teleco sells collars with the following strikes: a. $0.95 for the put and $1.00 for the call b. $0.975 for the put and $1.025 for the call c. $0.95 for the put and $0.95 for the call 6. A BCD stock pays a $1 dividend every 3 months. The current price is $50 and the first dividend coming 3 months from now. The con- tinuously compounded risk-free rate is 6%. What is the price of the prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? What is the price of a forward contract that expires at the same time? 7. A BCD stock pays an 8% continuous dividend. The current price is $50 and the continuously compounded risk-free rate is 6%. What is the price of a prepaid forward contract that expires 1 year from today? What is the price of a forward contract that expires at the same time? 8. Suppose you are a market maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0. a. What is the no-arbitrage forward price for delivery in 9 months? b. Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending? c. Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending? For problems 1 to 5, consider two firms, XYZ and Teleco. Firm XYZ mines copper, with fixed costs of $0.50/1b and variable costs of $0.40/1b. Teleco sells the telecommunications equipment and uses copper wire as an input. Suppose Teleco earns a fixed revenue of $6.20 for each unit of wire it uses. The wire price is the price of copper/lb plus $5. The 1-year forward price of copper is $1/lb. The 1-year interest rate is 6%. The 1-year option prices for copper are C(0.9500) = 0.0649, C(0.9750) 0.0500, C(1.0000) = 0.0376, = C(1.0250) = 0.0274, C(1.0500) = 0.0194, P(0.9500) = = 0.0178, P(0.9750) = 0.0265, P(1.0000) = 0.0376, P(1.0250) = 0.0509, P(1.0500) = 0.0665 1. Suppose XYZ buys a put option with a strike of $0.95, $1.00, or $1.05. Draw a graph of the hedged profit in each case. 2. Suppose XYZ buys collars with the following strikes. Draw a graph of the hedged profit in each case. a. $0.95 for the put and $1.00 for the call b. $0.975 for the put and $1.025 for the call c. $1.05 for the put and $1.05 for the call 3. If Teleco does nothing to mange copper price risk, what is its profit 1 year from now, per pound of copper that it buys? If it hedges the price of wire by buying copper forward, what is its estimated profit 1 year from now? Construct graphs illustrating both unhedged and hedged profit. 4. Compute estimated profit in 1 year if Teleco buys a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case. 5. Compute estimated profit in 1 year if Teleco sells collars with the following strikes: a. $0.95 for the put and $1.00 for the call b. $0.975 for the put and $1.025 for the call c. $0.95 for the put and $0.95 for the call 6. A BCD stock pays a $1 dividend every 3 months. The current price is $50 and the first dividend coming 3 months from now. The con- tinuously compounded risk-free rate is 6%. What is the price of the prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? What is the price of a forward contract that expires at the same time? 7. A BCD stock pays an 8% continuous dividend. The current price is $50 and the continuously compounded risk-free rate is 6%. What is the price of a prepaid forward contract that expires 1 year from today? What is the price of a forward contract that expires at the same time? 8. Suppose you are a market maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0. a. What is the no-arbitrage forward price for delivery in 9 months? b. Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending? c. Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending
