# Advances in Bond Analytics Speed

*How Far We Have Come*

*How Far We Have Come*

*by Andy Kalotay*

*by Andy Kalotay*

Finance is a relatively young academic discipline. Markowitz’s paper on efficient portfolios was published in 1952, and the Black-Scholes option valuation formula in 1973. But finance is a very old profession (the second oldest?), and analytics have always been an integral part of it.

Price-yield conversion is the most basic calculation in the bond world. The underlying mathematics of computing a yield entails solving a high-degree polynomial. In the absence of a formula, in 1921 Darville and Johnson heralded the speed of their patent-pending Bond Yield Chart: “*Problems are answered on the one chart without the necessity of referring to different books, turning many pages and pro-rating between prices and maturities.*” Now, we take this calculation for granted; it is virtually instantaneous on a low-end computer. If you are interested in the evolution of price-yield conversion speed, take a look at my 2003 presentation to the Bond Market Association (now SIFMA).

Today, option-adjusted spread (OAS) analysis is the standard approach for bonds and MBS. The brute force number-crunching involved places a high demand for processing power on analytics vendors. My Bond Valuation Using OAS post briefly discussed the advances in computational speed since the introduction of the approach in the mid-'80s. Back then, depending on the quality of the implementation, just calibrating the interest rate lattice (the ‘binomial tree’) took anywhere from several minutes to as long as an hour.

The live BondOAS demo at Kalotay.com gives a good sense of just how far computational speed has progressed. It analyzes a portfolio of roughly 6,000 callable agency bonds in two phases, on a low-end PC. In Phase 1 it values the portfolio, in about **0.3 seconds**, based on the current LIBOR swap curve and an interest rate volatility specified by you. Phase 2 calculates standard risk measures – duration, convexity, OAS, and multi-scenario horizon analysis based on the US Treasury yield curve. As you will see, the risk analysis of 6,000 bonds takes about **1.0 second**.

How about the speed of MBS analytics? The live MBS demo running on the same low-end PC values 4,000 pass-throughs in **3 seconds**, and then calculates the risk measures in **8 seconds**. This performance is accomplished by modeling an MBS as a portfolio consisting of 10 bonds, and then valuing each bond using OAS.

Due to the I/O required, these demos understate the true performance of the underlying analytical libraries, which are displayed in the figure below. As indicated, in 1 minute Kalotay Analytics can value 13 million bullets, 1.6 million callable bonds, and about 150,000 agency pass-throughs on a basic PC.

Now that we have an appreciation of the attainable speed for OAS calculations, the challenge is how to effectively utilize this technology. Real-time valuation and risk analysis, based on contemporaneous market information, naturally comes to mind. This is important for price discovery of bond ETFs, among other things. Also, hedge funds are now able to do millions of simulations to generate trading strategies.

While speed is impressive, it is useful only if the results are correct. Accuracy is critical. Comprehensive and accurate coverage of bond-embedded options are a must for bond analytics. See my post Trust by Verify on how to test whether an implementation is credible.

To recap, OAS analysis is computationally intensive and presents a major challenge to meet client demand for speed. There are clever algorithms to optimize the implementation. The textbook binomial tree approach is not used in industrial-strength systems; trinomial trees are most common. Kalotay Analytics builds a proprietary recombining tetranomial tree (you can’t learn everything from textbooks!). When it comes to iterative calculations, one must find the right balance between speed:* minimizing the number of iterations*, and accuracy: *convergence to the correct result*. Do your OAS analytics measure up? If not, it may be time to take it up with your vendor.

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