Assignment: Investments and Security Markets
Questions
1. The stock of the Miami Tower Company (MTC) is currently worth $100. Over each of the next two years, the stock price will either move up to 115% of the beginning-of-year stock price or down to 90% of the beginning of year price. You do not know which one will happen, nor how likely these are. The risk-free interest rate is 3% per year. MTC will also pay a $2 per share dividend at the end of year
1. Assume that it is possible to observe the stock price at the end of year 1, exercise any option you might hold immediately (should you choose to do so), and still qualify for the dividend if exercise gives ownership of the underlying.
(a) What is the price of a two-year European Call Option with strike price $95, written on MTC stock?
(b) What is the price of a two-year American Call Option with strike price $95, written on MTC stock? For full credit, you must show whether early exercise is profitable in each state of the world.
(c) What is the price of a two-year American Put Option with strike price $95, written on MTC stock? For full credit, you must show whether early exercise is profitable in each state of the world.
(d) What is the price of a two-year American Put Option with strike price $105, written on MTC stock? For full credit, you must show whether early exercise is profitable in each state of the world.
2. (a) What is the no-arbitrage price for a 1-year UK Pound Sterling foreign-exchange forward denominated in US Dollars, if the current exchange rate is $1.65/£, the risk-free interest rate in the UK is 3% per year, and the risk-free interest rate in the US is 2% per year?
(b) Carefully outline the steps a US investor must undertake in order to invest $1000 in UK Gilts (risk-free bonds), assuming his current wealth is in US Dollars, and that he wants to consume his money in US Dollars afterwards. Assume he uses the foreign-exchange forward you priced in the previous part in converting his money back to Dollars at the end of his investment.
(c) When pursuing this strategy, is the investor exposed to any foreign-exchange rate risk? Why or why not?