One method to price options is the so-called "Binomial Tree" method, the basics of which I will walk you through in this assignment.

Assume that today's spot exchange rate is $1.20/.

Also assume that every week, the dollar will either appreciate or depreciate against the euro by 2% (note: a 1% appreciation would result in an exchange rate of $1.20/ * 1/(1.01) = $1.188.../). Assume that these are the only two possible things that can happen. For simplicity, you may also assume that you can borrow or lend at a rate of 0%.

Consider a call option on the euro with a strike price of $1.20/ that matures in 1 week.

a.What possible payoffs can it have?

b.Assume that you long or short a futures contract on the euro at a price of $1.20/ for any maturity. Can you make a portfolio using a futures contract that will mimic the payoffs of the option at every possible outcome? Hint: You will need to borrow or lend in addition to the future.

c.How much did the portfolio you created in (b) cost to set up? By the law of one price, since your portfolio should have the exact same payoffs as the option, it should have the same price. Going forward, you may assume that there are no arbitrage opportunities and therefore that this is the price that the option would have.

d.Now consider an option that matures in 2 weeks. What will the price of this option be?

Note: To mimic the payoffs of this option, you may need to modify your futures position throughout the duration. You may assume that the futures price is equal to the spot price for all maturities.