Financial Risk Management of Insurance Enterprises Valuing Interest Rate Swaps

Interest Rate Swaps Swaps are used frequently by insurers Importance of swaps requires us to look more deeply into their pricing What are some market conventions? How to we value swaps? –How do we value the floating side? –How do we determine the fixed rate?

Review Recall that in an interest rate swap, two parties exchange periodic interest payments on a notional principal amount Typically, one interest rate is a floating rate and the other is the fixed rate Markets refer to swap positions based on fixed vs. floating position –Purchasing a swap or being long a swap refers to paying the fixed rate (receiving floating)

The Most Common Contract We look at the most common contract because it has quotes which are readily available –Quarterly settlement (four payments per year) –Floating rate is 90-day (3-month) LIBOR “flat” Other swap contracts may be less liquid and have a higher spread –May require a moderate amount of calculations We will price swaps assuming this common contract

Conventions in Fabozzi vs. Our Convention The book uses the following conventions –A 360-day year is assumed –Payments are based on the interest rate prorated by the actual number of days in the quarter (called “actual/360 basis”) Others use actual/365 for the fixed side NOTE: FOR SIMPLICITY, WE WILL USE COMMON SENSE AND NOT MARKET CONVENTIONS –One-quarter year is ¼, not “actual/360”

Pricing Swaps - Overview Recall that Eurodollar CD futures are based on the 3-month LIBOR contract –Underlying is the 3-month, future LIBOR See WSJ for Eurodollar futures prices –Recall from Chapter 10, the future LIBOR is 100 minus the index price Hedging arguments require liquidity –Eurodollar futures are the most heavily traded futures contracts in the world –Liquidity is excellent for 5-7 years

Pricing Swaps - Overview (p.2) By establishing a hedging argument, we can “replicate” the swap with Eurodollar futures A swap can be decomposed into two pieces: a position in a floating rate bond and the opposite position in a fixed rate bond –If long a swap, you are long the fixed bond and short the floating bond

Valuing the Floating Side Essentially, we are pricing a floating rate bond –Cash flow depends on what the coupon is based on (e.g. LIBOR, Treasuries) If the floating payments are based on LIBOR, as in the swap case: –We can use Eurodollar CD futures to determine an implied future floating rate –This gives us the “unknown” future floating payment on the swap

Determining the Fixed Rate As in the simple two period case, we want swap NPV=0 Use trial-and-error (or some solver) to determine the fixed rate which will have the same present value as the floating side Pricing an interest rate swap becomes a question of finding the fixed rate

An Example What is the fixed rate for a 2-year swap given the following Eurodollar future prices? Assume it is December 1997, the current 3- month LIBOR is 4.50%, and the notional amount is $1 million

Example - Eurodollar Futures Prices

Example - Floating Rate Value

Example - Sample Calculations

Note About Discount Factors This approach gives us another source of interest rate information –We use the Eurodollar Futures contracts –Previously, we used the Treasury curve There will be a difference in the interest rates represented by LIBOR vs. Treasuries due to credit risk –LIBOR has credit risk

Determine the Fixed Rate Use the discount rates to “guess” a fixed rate of the swap Equate the fixed side value of the swap to the floating side value

Example - Finding the Fixed Rate Using Goal Seek in Excel, Fixed Rate of Swap is 5.91%

Valuing an Off-Market Swap Off-market means that the fixed rate is not the rate in a new swap –Therefore, NPV is not necessarily 0 Value the floating payments using Eurodollar futures as before Value the fixed side using the discount rates for the floating side Difference of floating side and fixed side is the value of the swap

Reminder!!! Exam 2 is Tuesday, November 12 Open book, open note