Question 1: You note that Sony stock is selling at $25. Each month, it either goes up 10% or down 8%. The interest rate is 1% per month.
a. What is the value of a two-month call option to buy Sony at $26?
b. What is the value of a two-month put option with an exercise price of $26?
Question 2: You note that platinum sells for $750 per ounce and know that it will sell for either $850 or $750 in one year. There are call options and put options for platinum. There are also futures markets for platinum. The safe rate of interest is10%. You can ignore all storage and transportation costs.
a. You observe a derivative contract (some unknown combination of calls, puts, written calls, written puts) that pays off $90 if platinum is selling for $850 in a year and pays off $110 if is selling for $750. In a competitive market with no arbitrage opportunities, what should the cost be for this derivative?
b. Also in a competitive market with no arbitrage opportunities, what should the futures contract for delivery of one ounce of platinum in one year be selling for today?