After all the fancy securities and sophisticated tools you learnt during your time at Leeds, you have ended up working for an agricultural firm in Wyoming. Everything said it's neither hot or humid, so you are beating all those that went into the Street and/or moved South. At last your firm seems to really need those derivative skills that you learnt in Colorado - the company has decided to start trading derivatives on two crops: potatoes and oranges. You look up to your Bloomberg screen and find the following information on forward contracts on potatoes and on oranges. Oranges Maturity Forward price 33.835 38.880 0.5 1.0 Maturity 0.5 1.0 Potatoes Maturity 0.5 1.0 The current spot price for oranges is $30, whereas the current spot price for potatoes is $20. You also learn that zero-coupon Treasury bonds with a face value of $100 have the following prices. Forward price 20.591 21.600 Bond price 97.129 92.593 Strike price K = 17.5 K = 20 K = 22.5 Forward and spot markets for potatoes and oranges are very liquid, as well as Treasury bond markets, so you can ignore transaction costs (i.e. the bid-ask spread is negligible). 1. If you knew the price of a put option on potatoes with a one-year maturity and a strike price of $20 is $1.265, what would you estimate the price of a call option with the same strike and maturity to be? 2. The SIBIOI, an options market, is currently quoting the following prices for one-year options on potatoes. Calls Puts Bid Ask Bid Ask 4.25 4.35 0.45 0.55 2.70 2.80 1.25 1.30 1.60 1.65 2.55 2.65 Is there an arbitrage opportunity? How would you take advantage of it? Assume potatoes and Treasury bonds are trading at the prices given before and the bid-ask spreads for both potatoes and bonds are negligible. Be specific in terms of the profits you earn per trade that you can execute at the given prices. 3. You know that neither potatoes nor oranges carry a significant convenience yield. What do you learn about these two commodities from the forward prices given above? Be as specific as you can.