Ramgarajan K. Sundaram Derivatives Module MS in Risk Management New York University Examination Notes 1. There are four problems in this exam. You are required to do all of them for full credit. 2. You may use the text and class notes to assist you. But please remember: No taking help from each other or any other source. 1
Question 1 You live in a country where the government has xed the price of wheat at S = $300 per metric ton. Assume that the xed price is credible and is denitely not expected to change over the next month. Suppose you can take long and short positions in wheat with equal facility and costlessly (i.e., no transactions costs, no shorting costs, etc). Assume there are no holding costs or benets associated with wheat. The one-month interest rate is r = 6% in continuously-compounded and annualized terms. Show that it is NOT possible to dene an arbitrage-free one-month forward price for wheat in this setting. Explain intuitively why this is the case. Comment One way to show that no arbitrage-free forward price exists is to use the following steps: 1. The usual cost-of-carry formula suggests F = SerT as the candidate forward price. Using S = 300, r = 0:06, and T = 1=12, calculate F. Using the standard arguments developed in class, show that if the forward price is not equal to F, there is always an arbitrage. 2. Next, show that in this setting if the forward price is not equal to the xed spot price S, there is always an arbitrage. 3. Since the forward price cannot simultaneously be equal to S and F = SerT , there is no arbitrage-free forward price possible. 2
Question 2 A company manufactures and supplies gold wire to customers. Delivery is made one month after the customer order is received. Company practice is to buy gold on the day the order is received. Let date 0 denote the date of order and date T denote the date of delivery. Customers are given a choice between date-of-order and date-of-delivery price. (The choice is made after the date of…