BL MetPrec ltd. needs to purchase 100,000 tonnes of steel. The purchase is set to occur in 3 months' time. The risk free rate of interest is 1% p.a. continuously compounded. The continuously compounded storage cost and convenience yield are both 3% p.a..

The current price of steel is 115/tonne, but it is very unstable - the implied volatility is at 25% p.a. - and in a downturn. Further, there is a counterparty willing to sell the desired amount of steel in three months, namely CompElect inc., which has an estimated probability of default of 1.5% over the next 3 months. BL MetPrec is considering the possibility of using either futures or forward contracts.

Q1. Design the required forward transaction for BL MetPrec with CompElect inc. as counterparty, and determine the sale price and the value of the forward contract ignoring counterparty credit risk. If, instead, counterparty credit risk is taken into account, what is the value of the contract? If, also, the price of default of the counterparty is fully incorporated by the sale price, will the sale price be larger or smaller than the non-arbitrage forward price? Explain.

Q2. Ignoring counterparty credit risk and assuming that the log-returns of steel are normally distributed with zero mean and standard deviation equal to the implied volatility, quantify the 3-month 99% confidence level VaR of the forward position of BL MetPrec ltd. Interpret the number you have obtained.

Q3. Assume that the steel is purchased at the prevailing market price in three months, and BL MetPrec wants to hedge this transaction using futures contracts (which are cash-settled). Futures on steel are traded on the LME, with a contract size of 10 tonnes. The contract closest to maturity expires in 5 months. Assuming a standard deviation of futures price of 21% p.a. and a correlation of futures and spot prices of 0.95, design the required optimal futures hedge for BL MetPrec. Explain how the hedge should be managed, the sale price and the cost of the hedge due to counterparty credit risk.

Many thanks for your time and help!!