article
Creating Synthetic Callable Debt Using Swaptions
October 28, 2014

The following article was written by Bill Whitehead, Vice President & Director, Research, at Federal Farm Credit Bank Funding Corporation. Bill is a long time user of FINCAD Analytics Suite.

## Overview

The Farm Credit System is a Government-Sponsored Enterprise (GSE) which, through a Cooperative network of banks and associations, provides more than $90 billion in loans to more than a half million borrowers, including farmers, ranchers, rural homeowners, agricultural cooperatives, rural utility systems and agribusiness. The Farm Credit Banks issue callable bonds to fund mortgage assets that often contain prepayment options. The issuer of the callable bond is long an embedded call option that (approximately) offsets the short loan prepayment option granted to the agricultural mortgage borrower. The Farm Credit Banks issue bonds through their fiscal agent, the Federal Farm Credit Banks Funding Corporation (FFCB) in Jersey City, NJ. Because the option embedded in an agency callable bond is similar in many respects to an option on an interest rate swap, it is possible to replicate the cash flows for a callable bond using a combination of an interest rate swap and a swaption. Monitoring pricing relationships in the swap and swaption markets can provide an issuer of callable bonds with useful information. We are interested in how the callable bond pricing indications we receive from bond dealers compare to the levels we estimate for "synthetic" callable bonds. While the following analysis uses a common and frequently issued agency callable bond (4-year final maturity bond, callable once after the first year[1]) to illustrate how the synthetic callable bond can be structured, the technique is perhaps more valuable when used to estimate pricing levels for callable bond structures that are not issued regularly within the agency callable bond market. This is perhaps where indications developed from the liquid swap and swaption markets are most useful for the issuer. This article illustrates how the FFCB used FINCAD Analytics Suite functionality to: I. Create a Synthetic Callable Bond II. Calculate the Callable Bond Pricing Spreads To download the latest trial version of FINCAD Analytics Suite, contact a FINCAD Representative. ## I. Create a Synthetic Callable Bond To create a synthetic callable bond, two swaps are used: 1) 1 year pay fixed/receive floating swap, and 2) 1 year option to enter into a 3 year pay fixed swap FFCB's conventional short-term debt provides the underlying funding. ## II. Calculate the Callable Bond Pricing Spreads #### A. Data Required To develop the callable bond pricing spread, the following data is required: 1. A swap discount factor curve - The swap curve will be used to calculate what the coupon rate will be for the fixed leg of the swap. To build the curve, the following rates may be used: Swap rates, treasury benchmarks, LIBOR, and Eurodollar futures. 2. Swaption volatility matrix - Because we are attempting to replicate a 4/1-year, 1Xcall, callable bond, the relevant volatility input is for a (European) option that is exercisable one year from now to enter into a 3-year, pay-fixed interest rate swap. The relevant cell in the volatility table is circled, the volatility indication is 38.9% The following is a representation of the swaption volatility levels on March 5, 2004.. 3. Swap Structure and Swap deal details such as effective and terminating date, payment frequency and accrual method of the fixed and floating leg, reset rate frequency of the floating leg, business day convention, + or - margin added to the reset rate, etc. #### B. Calculations 1. Generate a discount factor curve by using a curve building function such as aaSwap_crv3. The curve will be used as an input in determining the fixed coupon rate and swaption value. Creating Synthetic Callable Debt Using Swaptions 2/7 2. Calculate the par swap rate (fixed coupon rate) - By using the function aaSwp_cpn with the discount factor curve as input, we will be able to determine what the par swap rate would be. This rate is then used as the fixed coupon rate of the fixed leg of the swap. Other functions that calculate the par swap rate include aaParSwap and aaSwp_cpnl. Creating Synthetic Callable Debt Using Swaptions 3/7 3. Define the swaption details and calculate its cost - The swaption price for a right to pay fixed 1 year forward, 3 year swap is calculated using the function aaSwpnBli (an old function, a newer function would be aaSwaption1_BL). To validate the fair value output of FINCAD Analytics Suite, the same swaption structure is priced in Bloomberg Finance LP's OVSW screen, below. The results are very close. Any differences are probably due to intra-day differences in the input yield curves and, possibly, due to differences in the way the Bloomberg Finance LP* calculator (default) and FINCAD Analytics Suite discount factor curves were specified. FINCAD Analytics Suite Black Swaption Model 4. Finance the upfront option premium at the pay fixed swap rate. The 1-year swap rate is used for year 1, the forward, 3-year swap rate is used for years 2 through 4 5. Make an assumption regarding the cost of conventional floating-rate funding over the four year horizon (vs. LIBOR). 6. In this example a simple IRR function is used to derive the synthetic callable bond's equivalent all-in cost. 7. The forecasted cash flows required by the IRR function are calculated using the synthetic callable bond's assumed par amount ($1 million) + the upfront swaption premium.
8. Once the equivalent all-in cost is estimated, we back out the yield impact of our standard underwriting fees to calculate the equivalent coupon rate for a 4/1-year euro callable bond issued with a par price.
9. The callable bond pricing indications we receive from bond dealers are typically quoted on a coupon spread to Treasury benchmark yield. We subtract the interpolated 4-year Treasury yield from the synthetic callable bond's equivalent coupon rate to derive the quoted pricing spread.

We note that the resulting spread is within a few tenths of a basis point of the spread quoted by Bear Stearns, one of Farm Credit's selling group members.

 4-year Interpolated Treasury 2.401% Synthetic Callable Bond est. All-in Cost 3.1348% Less standard concession - 0.046 Equivalent coupon rate 3.089% Spread to Treasury +68.8 bps Bear Stearns estimate* (4/1 euro) +68.53 bps, 3.10% coupon rate

Notes:

Risks

One of the assumptions required when comparing an actual callable bond to a "synthetic" callable bond created using pay fixed swaps is the cost of the underlying short-term, floating-rate funding that is issued to raise the actual funding. A GSE typically has several alternatives for raising short-term, floating-rate funding including issuing agency discount notes, floating-rate notes indexed to LIBOR, or swapping non-callable, fixed-rate "bullet" bonds to pay floating. If the GSE funded the synthetic callable bond with debt that had to be "rolled over" at some point during the life of the synthetic issue the GSE would be subject to basis risk in the relationship between the cost of the short-term debt and the LIBOR rate designated for the floating-leg of the swaps.

In the example, we assumed we could issue short-term funding over the four year horizon at a cost of 3-month LIBOR less 6 basis points. This level represents where we estimate we could have issued a 4-year, non-callable fixed-rate bond and swapped to receive fixed and pay floating. The equivalent sub-LIBOR cost for a 3-month agency discount note was actually lower.

Another question is how to recover (or, how to account for) the unamortized option premium if the swaption expires without being exercised. This concern is similar to the accounting challenge of dealing with unamortized concessions (underwriting fees) when conventional callable debt is called.

The synthetic callable bond's equivalent coupon rate is an approximation, projected interest cost for the synthetic during the first year is considerably less (1-year swap rate) with cost stepping up if the swaption is exercised.

*Bear Stearn's estimate for an agency 4/1-year euro callable bond was taken from the daily pricing indications sheet Funding Corp receives. The Treasury benchmark yield used by Bear Stearns to quote the estimated 4/1 euro callable bond coupon rate appears to have been slightly different, again probably due to intraday change, than the 4-year Treasury yield we used to estimate the spread on the synthetic callable bond.

The derived synthetic 4/1-year 1X callable bond estimated coupon level is at a +68.8 basis point spread to the 4-year Treasury benchmark yield. The synthetic is right on top of the +68.5 basis point spread indication received from the bond dealer.

In March 2004, the GSE's prevailing LIBOR-equivalent funding target for callable bonds with a 1-year non-call period was probably in the neighborhood of 3-month LIBOR minus 15 to 18 basis points. We've shown that a 4/1-year 1X callable bond priced at +68.5 bps to Treasury is equivalent to 3-month LIBOR minus 6 basis points making it unlikely that a GSE would issue a 4/1-year euro at this level unless this type of funding was urgently needed. It is more likely that the GSE would hold out for a lower coupon rate before issuing which would either require the dealer to use a lower volatility input when pricing the agency callable bond or for the investor to accept a lower option-adjusted spread to Treasury (which could be viewed as the credit risk component of the agency issuer's callable bond spread).

[1] A 4/1-year European callable bond. We use the abbreviation 1X to indicate the "one-time" call exercise feature. The Farm Credit System also routinely issues callable bonds where the call may be exercised on any interest payment date after the first call date (Bermudan option, "discretely callable") and bonds that may be called any time after the first call date (American option, "continuously callable").