# Problem 1. A trader wants to invest in gold. The trader can buy gold for \$250

September 11, 2016

Question
Problem 1. A trader wants to invest in gold. The trader can buy gold for \$250 per ounce and sell gold for \$249 per ounce. Zero coupon bonds with maturity 1 year can be bought for \$0.95 per bond and sold(issued) for \$0.9 per bond. For what range of forward prices on gold with delivery in one year does the trader have no arbitrage opportunities? (Hint: Find for which forward prices the trading strategies in the proof of Theorem 4.1 do not lead to arbitrage).

Problem 2. A company enters into a short futures contract to sell 5,000 bushels of wheat for \$2.5 dollars per bushel. The initial margin is \$3,000 and the maintenance margin is \$2,000. What price change would lead to a margin call? What price change will allow the company to withdraw \$1,500 from the margin account (without closing the futures position)?

Problem 3. The current price of silver is \$9 per ounce. The storage costs are \$0.24 per ounce per year payable quarterly in advance (e.g. you have to pay immediately storage costs of \$0.06 per ounce for the first quarter). Assuming that the continuously compounded interest rate is 10% per year, calculate the futures price of silver for delivery in ten months. (Hint: Regard storage costs as negative dividends)

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