After receiving the quotes from Dealer A and then Dealer B, you realize there is an arbitrage opportunity (according to your calculation in part (b)). You still have Dealer B on the phone. If you decide to short yBZ1 and z BZ2 bonds with Dealer B, you then have to call back Dealer A and agree to buy x BC2 bonds. You believe that there is a 50 percent chance that Dealer A will still allow you to buy up to 10,000 BC2 bonds at $1,065 per bond, but there is also a 50 percent chance that Dealer A will increase the price of these bonds such that the arbitrage opportunity is no longer worth it (dealers often revise their prices after you call them back, as they realize you must not have any better outside options). In this case, your

Suppose that Dealer A provides quotes for coupon bonds in Firm XYZ (denote this bond BC2). This bond expires in two years, has a face value of $1,000, and an annual coupon rate of 6 percent. Dealer B provides quotes for zero-coupon bonds in Firm XYZ. The first bond expires in one year ( = 1) and has a face value of $1,000 (denote this bond BZ1). The second bond expires in two years ( = 2) and has a face value of $1,000 (denote this bond BZ2).

a) How many of bonds BZ1 and BZ2 do you have to purchase so that your payouts at = 1 and = 2 are equivalent to holding 10,000 of the BC2 bonds?

b) You call Dealer A. He says you can buy up to 10,000 BC2 bonds at $1,065 per bond. Following that, you call Dealer B. She says you can short up to 1,000 BZ1 bonds at $975 per bond and short up to 12,000 BZ2 bonds at $955 per bond. Describe the arbitrage opportunity involving these three bonds that also maximizes the profits you can make from this opportunity. This will involve buying x BC2 bonds, shorting y BZ1 bonds, and shorting z BZ2 bonds.

arbitrage attempt has failed, and you then have to call back Dealer B and repurchase your BZ1 bonds at $977 per bond and your BZ2 bonds at $957 per bond.

c) Dealer B is on the phone with the original quotes. Will you still go ahead with this arbitrage opportunity, knowing that there is a chance that Dealer A might no longer quote a purchase price of $1,065 per bond? For this question, you will need to calculate your profit or loss in each potential state of the world (Dealer A still gives you the original quote versus Dealer A revises his quote), and then calculate your expected profit across these states.