Bond Valuation Using OAS
Properly used, option-adjusted spread analysis is a powerful tool. But for the unwary it can also hold hidden dangers.
By Andy Kalotay
We’re pleased to be kicking off Kalotay Analytics’ entry into the blogosphere with a series of posts on option-adjusted spread (OAS) analysis. The term was coined in the mortgage research group at Salomon Brothers in the mid-1980’s. Today OAS is the standard quantitative tool used for trading and risk management of all investment-grade fixed income products. By taking into account the volatility of interest rates, OAS enables investors to directly compare fixed income instruments which have similar characteristics, but trade at different prices because of the embedded options.
Broadly speaking, the OAS approach is a two-stage process. Starting with a benchmark yield curve, we first create an interest rate tree that depicts possible evolutions of the yield curve over time. We then use this tree to determine the price of a security given its OAS, or the OAS given the price. In the case of bonds, the computational algorithm is ‘backward recursion’; see Fabozzi’s Handbook of Fixed Income Securities, or Tuckman’s Fixed Income Securities: Tools for Today's Markets for details. But be aware that industrial-strength implementation bears little resemblance to a textbook coding exercise.
Properly deployed, OAS delivers accurate measures of interest rate risk, such as effective duration and effective convexity. However, implementation is frequently deficient, although most investors are blissfully ignorant of these deficiencies -- they have little idea of what is missing from under the hood. Over the course of these posts, we will take an in-depth look at the proper handling of the following areas:
- Options - call, put, and sinking fund
- Interest rate process, including mean reversion and volatility term structure
- After-tax valuation, incorporating the treatment of discount munis
- Scenario analysis - scenario specification, option exercise, and reinvestment rate
Let’s start with the most readily observable aspect of a system: computational speed. Back in the ‘80’s computers were much slower, taking hours to calibrate the interest rate lattice. By the time the run finished, interest rates changed so much that the results were practically meaningless.
Beyond faster chips, more proficient implementation -- such as using trinomial or tetranomial trees instead of binomial trees with equal step sizes -- dramatically improved performance. Can you guess the magnitude of improvement? Take the Kalotay Analytics Speed Demo for a test run.
Our next post will cover the most complex bond structure – sinking fund bonds. Did you know that they can have as many as four interrelated options?
A Model for Valuing Bonds and Embedded Options
Financial Analysts Journal (May/June 1993)
Andrew Kalotay, George Williams and Frank Fabozzi
This seminal article explains in concrete detail and in layman’s terms how to compute a fair value for any bond, including callables and other structures with one or more embedded options. The technique requires building a binomial interest rate tree that models the evolution of interest rates and the yield curve.
About Kalotay Analytics
For more than twenty-five years, Kalotay Analytics’ flagship BondOAS™ has been at the core of the world’s most sophisticated fixed income valuation systems. From real-time pricing of bond ETF’s to instantaneous risk analysis, BondOAS performs computationally intensive calculations with the precision and speed required by today’s highly demanding market participants.