Suppose that there are two securities, RAIN and SUN. RAIN pays $100 if there is any rain on the day of the soccer world cup final, $0 otherwise. SUN pays $100 if there is no rain, $0 otherwise. Suppose the soccer world cup final is 1 year from today, and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70.
(a) If you buy 1 share of RAIN and 1 share of SUN, what is your payoff after 1 year, depending on the weather?
(b) What does the No-Arbitrage Condition imply about the price of a 1-year zero coupon bond with face value $100 (Assume no trading costs.)
(c) Suppose that a 1-year zero coupon bond with face value $100 is trading at $90. Show how you would set up a transaction to earn a risk less arbitrage profit (Assume no trading costs).
(d) Suppose that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost $2 per $100 face value. Can you still make an arbitrage profit?