# hw1 - Derivative Securities Fall 2007 Homework 1...

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Derivative Securities, Fall 2007 – Homework 1. Distributed at Lecture 1. Due in class at Lecture 3 (9/18/07 Kohn, 9/19/07 Allen). 1. The present exchange rate between US dollars and Euros is 1.34 \$/Euro. The price of a domestic 180-day Treasury bill is \$97.60 per \$100 face value. The price of the analogous Euro instrument is 97.40 Euros per 100 Euro face value. (a) What is the theoretical 180-day forward exchange rate? (b) Suppose the 180-day forward exchange rate available in the marketplace is 1.34 \$/Euro. This is more than the theoretical forward exchange rate, so an arbitrage is possible. Describe a risk-free strategy for making money in this market. How much does it gain, for a contract size of 100 Euro? 2. Let B ( t, T ) be the cost at time t of a risk-free dollar at time T . (a) Suppose B (0 , 1), B (0 , 2) and B (1 , 2) are all known at time 0 (i.e. interest rates are deterministic). Show that the absence of arbitrage requires B (0 , 1) B (1 , 2) = B (0 , 2). (b) Now suppose B (0 , 1) and B (0 , 2) are known at time 0 but B (1 , 2) will not be known until time 1. What goes wrong with your argument for (a)? Show that

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