Floating-rate bonds

Credit risk Fixed and floating-rate bonds are both subject to changes of credit risk. 

In Chapter 8, we described several models to measure the term structure of credit spread and we introduced the model proposed by Longstaff and Schwartz (1995) for pricing fixed-rate debt. The authors propose also a model to valuing floating-rate notes. The equation derived for pricing floating-rate bonds is given by (10.2) ... 

Buy 50 million par value of a 5-year floating-rate bond that pays 6-month EURIBOR every six months. 

The cash flows for this transaction are set forth in Exhibit 19.1. The second column of the exhibit shows the cash flows from purchasing the 5-year floating-rate bond. There is a 50 million cash outlay and then 10 cash inflows. The amount of the cash inflows is uncertain because they depend on future levels of 6-month EURIBOR. The next column shows the cash flows from borrowing 50 million on a fixed-rate basis. The last column shows the net cash flows from the entire transaction. As the last column indicates, there is no initial cash flow (no cash inflow or cash outlay). In all 10 6-month periods, the net position results in a cash... 

EXHBIT 19.1 Cash Flows for the Purchase of a 5-Year Floating-Rate Bond... 

The subscript for EURIBOR indicates the 6-month EURIBOR as per the terms of the floating-rate bond at time t. 

It can be seen from the net cash flow in Exhibit 19.1 that a fixed-rate payer has a cash market position that is equivalent to a long position in a floating-rate bond and a short position in a fixed-rate bond— the short position being the equivalent of borrowing by issuing a fixed-rate bond. 

Floating-rate bonds, often referred to as floating-rate notes (FRNs), also exist. The coupon rates of these bonds are reset periodically according to a predetermined benchmark, such as 3-month or 6-month LIBOR (London interbank offered rate). LIBOR is the official benchmark rate at which commercial banks will lend funds to other banks in the interbank market. It is an average of the offered rates posted by all the main commercial banks, and is reported by the British Bankers Association at 11.00 hours each business day. For this reason, FRNs typically trade more like money market instruments than like conventional bonds. 

Since a floating-rate bond is valued on its principal value at the start of a swap, a swaption may be viewed as the value on a fixed-rate bond, with a strike price that is equal to the face value of the floating-rate bond. 

Equation (7.24) essentially states that PVBP of the swap equals the difference between the PVBPs of the fixed- and floating-rate bonds. This value is usually calculated for a notional principal of 1 million, based on the duration and modified duration of the bonds (defined in chapter 2) and assuming a parallel shift in the yield curve. 

Note that the swap PVBP, 425, is lower than that of the 5-year fixed-coupon bond, which is 488.45. This is because the floating-rate bond PVBP reduces the risk exposure of the swap as a whole by 63.45. As a rough rule of thumb, the PVBP of a swap is approximately the same as that of a fixed-rate bond whose term runs from the swaps next coupon reset date through the swap s termination date. Thus, a 10-year swap making semiannual payments has a PVBP close to that of a 9.5-year fixed-rate bond, and a swap with 5.5 years to maturity has a PVBP similar to that of a 5-year bond. 

Floating rate notes (FRNs) are bonds that have variable rates of interest the coupon rate is linked to a specified index and changes periodically as the index changes. An FRN is usually issued with a coupon that pays a fixed spread over a reference index for example, the coupon may be 50 basis points over the six-month interbank rate. Since the value for the reference benchmark index is not known, it is not possible to calculate the redemption yield for an FRN. The FRN market in countries such as the United States and United Kingdom is large and well-developed floating-rate bonds are particularly popular with short-term investors and financial institutions such as banks. 

It was suggested earlier that a swap be seen as a bundle of cash flows arising from the sale and purchase of two cash-market instruments a fixed-rate bond with a coupon equal to the swap rate and a floating-rate bond with the same maturity and paying the same rate as the floating leg of the swap. Considering a swap in this way, equation (7.23) can be rewritten as (7.24). 

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