An index put option with a three month maturity has a strike price of 6000. The current underlying stock index is trading at 5900 and it has a volatility of 30 per cent per year. The risk-free rate is 3.5 per cent per year continuously compounded. Using one-month steps compute the price of the option if it is American-style and can be exercised early. Comment on whether early exercise is likely. A commodity has a spot price of $3650 and the four month futures price is $3545. The four month continuously compounded risk-free interest rate is 4.5 per cent per year. The storage costs for the commodity is 1.5 per cent per year continuously compounded. Calculate the convenience yield on the commodity.