Consider a forward contract written on 50 tonnes of zinc, a metal that is currently trading at $1,000 per tonne in the cash or spot market. Contract settlement is by making or taking delivery of 50 tonnes of zinc on contract settlement date. Zinc storage costs are $12 per tonne per month, payable at the end of each month, and the risk-free rate is 3% per annum on a continuously compounded basis. Question: Calculate the theoretical price of a zinc forward contract with three months to settlement.
Question
Consider a forward contract written on 50 tonnes of zinc, a metal that is currently trading at 12 per tonne per month, payable at the end of each month, and the risk-free rate is 3% per annum on a continuously compounded basis. Question: Calculate the theoretical price of a zinc forward contract with three months to settlement.
Solution
To calculate the theoretical price of a zinc forward contract with three months to settlement, we need to consider the following steps:
Step 1: Calculate the spot price of the zinc The spot price of the zinc is given as $1,000 per tonne.
Step 2: Calculate the storage costs The storage costs are given as 12 * 3 = $36 per tonne.
Step 3: Calculate the total cost of carrying the zinc for three months The total cost of carrying the zinc for three months is the sum of the spot price and the storage costs. So, the total cost is 36 = $1,036 per tonne.
Step 4: Calculate the present value of the total cost The present value of the total cost is calculated by discounting the total cost at the risk-free rate for the period of the contract. The risk-free rate is given as 3% per annum on a continuously compounded basis. So, the present value of the total cost is 1,036 * e^(-0.0075) = $1,027.27 per tonne.
Step 5: Calculate the theoretical price of the forward contract The theoretical price of the forward contract is the present value of the total cost multiplied by the number of tonnes in the contract. So, the theoretical price of the forward contract is 51,363.50.
Therefore, the theoretical price of a zinc forward contract with three months to settlement is $51,363.50.
Similar Questions
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