Financial Risk Management of Insurance Enterprises

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 2005, 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, April 11 • Exam is 10-11:20 am in 430 Armory • Open book, open note

Exam 2 • Calculations and explanations • Focus is on lectures 13-20 • ALM • Duration and convexity • Stochastic processes • Interest rate models • Binomial method and simulation • Interest rate options • CMOs • Valuing swaps • Understand material prior to first exam • Derivatives • Need for financial risk management

Financial Risk Management of Insurance Enterprises