a) A one-year-long forward contract on a non-dividend-paying stock is entered into when the stock price is $200 and the risk-free interest rate is 8% per annum (continuous compounding). Three months later, the price of the stock is $140 and the risk-free interest rate remains unchanged. What is the value of the forward contract for the delivery of one share?
b) Discuss the key differences between futures and forward contracts.
a) A company wishes to hedge its fuel cost using futures contracts on heating oil in the next three months. The company will lose $2 million for each 1 cent increase in the per-gallon price of the fuel. The correlation between the (spot) fuel price and the heating oil futures price is 0.60, and the fuel price change has a standard deviation that is 50% greater than of the price change in heating oil futures. Each contract for heating oil is for 42,000 gallons. How many heating oil futures contracts should be traded to achieve the full hedge?
b) Suppose that you observe the following price information on gold spot and futures contracts. Assuming short-selling is possible and there are no transactions costs, describe an arbitrage strategy to profit from the quoted price. What factors should you consider before making such an arbitrage trade? The risk-free rate is 5% per annum (continuously compounded).
a) Compute the price of a European call option (on a non. dividend-paying stock) when the stock price is $90 and the strike price is $85. The risk-free interest rate is 5% per annum (continuously compounded), the stock volatility is 30% per annum, and the time to maturity is nine months. The d, and d2 of the Black-Scholes-Merton option pricing model are given below.
b) Using the result obtained in (a), derive a price of the put option with the same maturity and strike price as the call option by using the put-call parity relationship.
c) Discuss the VIX index and its construction method.