Trust but Verify
Accuracy Critical for OAS Analytics
by Andy Kalotay
Industrial-strength OAS analytics should provide comprehensive coverage of embedded bond options and generate accurate results. In my last post I discussed coverage, and observed that some systems ignore complex options, for example, those in sinking fund bonds. Such deficiencies may be an indication of larger problems. In this post, I will focus on testing the accuracy of the results.
In the wake of the 2008 banking crisis, Dodd-Frank imposed onerous model validation requirements on financial institutions, ranging from evaluating conceptual soundness to reviewing documentation. Here, I discuss a narrow part: are the reported results correct? Determining 100% accuracy is practically impossible; systematically checking for potential flaws is much easier. The discovery of a single mistake should call into question the credibility of the entire system.
The suggested tests below fall into four broad categories:
- Numerical precision
- Theoretical principle
- Relative measures
- Extreme values
A bond with an embedded option, such as a call or a put, is comprised of two distinct pieces: an underlying optionless bond and an option. Its value is the sum of the values of the components, each of which should be validated independently.
Valuing an optionless bond is a back-of-the envelope calculation, provided that your system discloses cashflows and discount factors. Otherwise, use a flat yield curve and compute the cashflows and discount factors. The value of an optionless bond is the sum of the present values (PV’s) of the individual cashflows, each discounted at the appropriate rate. Note that interest volatility does not enter into this ‘off-lattice’ calculation.
Now you know the true value of the optionless bond. However, OAS analytics determine value by lattice-based recursive number-crunching, rather than by a PV formula. Because the lattice does depend on volatility, you would expect the result to be close, but not exactly equal, to the (off-lattice) PV. In fact, the results are likely to be identical: the OAS analysis matches the PV, for any volatility. This is because the system recognizes that the bond is optionless, and reports the PV obtained off-lattice — a trick of the trade.
Let’s try to outsmart the system by embedding an option of no value, say, a put at 10 or a call at 200. Because this forces the system to value the bond on the lattice, the expected result should differ slightly from the PV of the optionless bond calculated earlier. But you’ll be surprised to find that the ‘on-lattice’ value equals the PV, without rounding error. This is another trick of the trade that I will leave you to ponder.
Turning to option values, the simple checks below will help you detect possible flaws. First and foremost, the system should not violate the principle of put-call parity. In particular, the difference between the value of a European put option and a like call option on the same underlying bond should not depend on the interest rate volatility. While the individual option values increase with volatility, their difference should be constant, as illustrated below.
You should also validate putable-extendible parity. Consider two bonds with the same coupon, one maturing in year M and putable by the investor in year P, the other maturing in Year P and extendible by the investor to year M. Their values should be the same – can you see why?
If the prevailing interest rate is below the coupon, investors will not put the putable bond and will extend the extendible bond. If the rate is above the coupon, they will put/will not extend. In both cases the cashflows generated by the putable and the extendible bonds will be the same; therefore, their values must be the same.
Finally, here are some relative measure tests of OAS system outputs:
- Option values should increase with volatility (as in put-call parity test above)
- Increasing the call price or lowering the coupon should reduce the value of a call option (the opposite for a put option)
- Value of European option < Bermudan < American
- Shorter lockout should increase option value
I hope I’ve given you some ammunition to test the accuracy of your favorite OAS analytics. Accepting the results on faith is risky. As Reagan said to Gorbachev, “Doveryai, no proveryai.” Trust but verify!
Stay tuned for my next post, which will discuss the subtleties of after-tax valuation.