Arbitrage with Financing and Two-Curve Discounting
This chapter covers two topics, which turn out to be related. The first topic is arbitrage pricing in bond and swap markets under realistic financing arrangements. The second is pricing swaps when the riskless investable rate (e.g., fed funds) is not the same as the swaps' floating rate index (e.g., three-month London Interbank Offered Rate (LIBOR)).
So as not to overwhelm the reader with the nuances of this chapter at the start of the book, Chapter 1 showed that discounting is shorthand for arbitrage pricing of bonds under simplified financing arrangements. In particular, it was assumed that the proceeds from shorting one set of bonds could be used to purchase other bonds. However, as described in Chapter 12, bonds are shorted through repos that require sale proceeds to be posted as collateral. This means that the long side of an arbitrage has to be financed by borrowing money in the repo market and introduces the complication that the financing rates on the short and long side of an arbitrage need not be the same. This chapter1 begins by deriving the connection between discounting and arbitrage pricing for bonds under these more realistic financing arrangements. It turns out that the results of Chapter 1, which comprise the basic tool box for fixed income practitioners, hold true under the following additional conditions. First, all bonds finance at the same rate. Second, interim mispricings can be financed at that ...