hw1sol

hw1sol - Math 194 Winter 2010 Homework 1 Solutions 1 A...

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Math 194, Winter 2010 Homework 1 — Solutions 1. A forward contract is an agreement to buy or sell an asset at a certain future time for a certain price (called the forward price ). At the time a forward contract is entered into, no money changes hands. The investor who agrees to buy the asset at the future time is said to hold the long position in the contract and the investor who agrees to sell the asset is said to hold the short position in the contract. Suppose that a stock is currently selling for \$20 per share. A (long position in a) forward contract is available to buy 100 shares of the stock 3 months from now for \$20.20 per share. Suppose that a bank is offering interest at the rate of 5% per annum (compounded continuously) on a 3-month deposit. Describe a strategy for creating an arbitrage profit and compute the amount of the profit. Solution. At time 0, we borrow 100 shares of the stock, sell them immediately for \$2000, and put this money in the bank. After 3 months the bank account has grown to \$2000 · exp( . 05 · (3 / 12))
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