Valuation Commentary

How to Validate an Interest Rate Model?
Part I: Pricing Swaps & Bonds
by Alex Levin

Mortgage practitioners are more liberal and grateful consumers of term structure modeling analytics than typical Street derivative traders. They pay much less attention to such things as the assumed rate distribution (leave that to statisticians - they've got to earn their bread somehow), pricing standard rate derivatives struck away from at-the-money (ATM) or exotics (who cares?). Symptomatically, MBS complexity that traces its roots to the behavioral uncertainty often masks the need for rigor.

Yet, most good models can and should be tested using a few simple steps. Below, I outline several validation exercises for readers and describe how AD&Co.'s financial engineering ensures positive results. In upcoming Pipeline issues, I will discuss the testing of volatility calibration and options.

Test 1: Valuation of fixed-rate swaps and option-free bonds

It may seem trivial, but let us follow Ronald Reagan's favorite Russian saying "Trust, but verify!" Pay attention to swap and bond maturities used as inputs (AD&Co. offers up to 14 entry points), and price the bond or swap with some other maturity. For example, a user may input rates for the 5-yr swap and the 10-yr swap (among others), but opt to skip the 7-yr point. What 7-yr rate is calculated by the system? Our OAS spreadsheet easily enables a user to turn a pass-through MBS entry into a bullet bond. And our library is equipped with even more tools to run various tests with non-MBS instruments.

We would first set volatility to zero and find that the 7-yr bond or swap has an internally interpolated rate of, say, 4.5%. Let us introduce volatility into the system and rerun the analysis. The rate on an option-free instrument should not change, should it? Increase volatility further and see if the system holds and reports the same rate or the same value for the bond or swap. How did AD&Co. pass this test? We used three financial engineering methods: