3. Gold (20 points) Three months ago, you shorted one six-month gold forward contract. The contract is on 1kg(1000g) of gold, and prices are expressed per gram of gold. When you started shorting, the gold price was $54.00 (per gram), and the forward price was $55.00. Three months later, you are examining your portfolio, and you are trying to find out the value of your existing short position (which has delivery in three months). Unfortunately, you no longer have access to data about gold forwards, so you do not observe today's forward prices. Instead, you see that the spot price of gold has dropped to $53.00 (per gram). You also observe the following zero rates, all expressed per annum with continuous compounding For this question, suppose that it is costless to store gold. (a) (5 points) Using the information given, what is the price of a gold forward with a delivery date that matches the contract you already have? Express your answer in dollars per gram to two decimal places. (b) (8 points) What is the value to you of your existing position in the gold forward market? (c) (7 points) Suppose you did observe the gold futures market. You observe a 3-month gold futures price of $53.20 per gram, which should be different than the forward price you calculated in (a). Does this seem to suggest the existence of an arbitrage opportunity? As a reminder, gold prices tend to rise when interest rates fall, and vice versa. Explain your answer in at most 3 sentences