# Mathematical Modeling in Economics and Finance

#### Questions

1. What is the difference between the retail or client market and the wholesale or interbank market for foreign exchange?
2. Who are the market participants in the foreign exchange market?
3. What is meant by a currency trading at a discount or at a premium in the forward market?
4. Why does most interbank currency trading worldwide involve the U. S. dollar?
5. Banks find it necessary to accommodate their clients’ needs to buy or sell FX forward, in many instances for hedging purposes. How can the bank eliminate the currency exposure it has created for itself by accommodating a client’s forward transaction?
6. A CD/\$ bank trader is currently quoting a small figure bid-ask of 35-40 when the rest of the market is trading at CD1. 3436-CD1. 3441. What is implied about the trader’s beliefs by his prices?
7. What is triangular arbitrage? What is a condition that will give rise to a triangular arbitrage opportunity?

#### Problems

1. Using the American term quotes from Exhibit 5., calculate a cross-rate matrix for the euro, Swiss franc, Japanese yen, and the British pound so that the resulting triangular matrix is similar to the portion above the diagonal in Exhibit 5.
2. Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how would he profit if he has \$1,000,000 available for this purpose.
3. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting €0. 7627/\$1. 00 and Credit Suisse is offering SF1. 1806/\$1. 00. You learn that UBS is making a direct market between the Swiss franc and the euro, with a current €/SF quote of  6395.

#### Sales using each of the following:

• a) A 3 – month moving average
• b) A 6 – month weighted average using 0. 1, 0. 1, 0. 1, 0. 2, 0. 2, and 0. 3 with the heaviest weights applied to the most recent months.
• c) Exponential smoothing using an = 0. 3 and a September forecast of 18
• d) A trend projection With the data given, which method would allow you to forecast next March sales?

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