# Question

Suppose that LMN Investment Bank wishes to sell Auric a zero-cost collar of width 30 without explicit premium (i.e., there will be no cash payment from Auric to LMN). Also suppose that on every option the bid price is $0.25 below the Black Scholes price and the offer price is $0.25 above the Black-Scholes price. LMN wishes to earn their spread ($0.25 per option) without any explicit charge to Auric.

What should the strike prices on the collar be? (Note: Since the collar involves two options, LMN is looking to make $0.50 on the deal. You need to find strike prices that differ by 30 such that LMN makes $0.50.)

•XYZ mines copper, with fixed costs of $0.50/lb and variable cost of $0.40/lb.

•Wirco produces wire. It buys copper and manufactures wire. One pound of copper can be used to produce one unit of wire, which sells for the price of copper plus $5. Fixed cost per unit is $3 and noncopper variable cost is $1.50.

•Telco installs telecommunications equipment and uses copper wire fromWirco as an input. For planning purposes, Telco assigns a fixed revenue of $6.20 for each unit of wire it uses.

The 1-year forward price of copper is $1/lb. The 1-year continuously compounded interest rate is 6%. One-year option prices for copper are shown in the table below.17

In your answers, at a minimum consider copper prices in 1 year of $0.80, $0.90, $1.00, $1.10, and $1.20.

What should the strike prices on the collar be? (Note: Since the collar involves two options, LMN is looking to make $0.50 on the deal. You need to find strike prices that differ by 30 such that LMN makes $0.50.)

•XYZ mines copper, with fixed costs of $0.50/lb and variable cost of $0.40/lb.

•Wirco produces wire. It buys copper and manufactures wire. One pound of copper can be used to produce one unit of wire, which sells for the price of copper plus $5. Fixed cost per unit is $3 and noncopper variable cost is $1.50.

•Telco installs telecommunications equipment and uses copper wire fromWirco as an input. For planning purposes, Telco assigns a fixed revenue of $6.20 for each unit of wire it uses.

The 1-year forward price of copper is $1/lb. The 1-year continuously compounded interest rate is 6%. One-year option prices for copper are shown in the table below.17

In your answers, at a minimum consider copper prices in 1 year of $0.80, $0.90, $1.00, $1.10, and $1.20.

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