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Kamakura Blog

Apr 17

Written by: Donald van Deventer
4/17/2012 4:27 AM 

Basel II required that regulated institutions implement an “internal capital adequacy assessment process” (“ICAAP”) as part of the pillar 2 component of regulations promulgated by the Basel Committee on Banking Supervision.  Even five years later, many thoughtful financial institutions risk managers have concerns about whether the approach followed by their institution for ICAAP can be improved.  This blog summarizes some of the key areas in which common practice in interest rate risk management (and by logical extension the associated ICAAP) can be improved.

The recent low interest rate period in the United States, combined with more than two decades of low interest rates in Japan, has highlighted many of the concerns that thoughtful interest rate risk managers have had with “common practice” interest rate risk analytics and risk systems:

1. Common practice interest rate risk (“ALM”) systems typically use a one factor term structure model (2 factor models are rare), but yield curve movements almost always show a twist in rates that is inconsistent with one factor models.
2. Common practice interest rate risk (ALM) systems typically assume that interest rate volatility is either constant (as in the Ho and Lee and Merton term structure models, implying a parallel shift in the yield curve) or declining with maturity (as in the Vasicek and extended Vasicek or Hull-White models), but this is inconsistent with historical data from the U.S. Treasury market, one of the deepest fixed income markets in the world.
3. Common practice interest rate risk systems have difficulty dealing with the observed interest rate volatility, which shows a strong correlation between the level of short term interest rates and short term volatility and a much weaker link between rate level and volatility level at longer maturities.

In a recent series of blogs, we have shown how multi-factor interest rate models based on the Heath-Jarrow-Morton “no arbitrage” restrictions can deal with these three issues very successfully:

van Deventer, Donald R. “Heath Jarrow and Morton Example One: Modeling Interest Rates with One Factor and Maturity-Dependent Volatility,” Kamakura blog, www.kamakuraco.com, March 2, 2012.

van Deventer, Donald R. “Heath Jarrow and Morton Example Two: Modeling Interest Rates with One Factor and Rate and Maturity-Dependent Volatility,” Kamakura blog, www.kamakuraco.com, March 6, 2012.

van Deventer, Donald R. “Heath Jarrow and Morton Example Three: Modeling Interest Rates with Two Factors and Rate and Maturity-Dependent Volatility,” Kamakura blog, www.kamakuraco.com, March 13, 2012.

van Deventer, Donald R. “Heath Jarrow and Morton Example Four: Modeling Interest Rates with Three Factors and Rate and Maturity-Dependent Volatility,” Kamakura blog, www.kamakuraco.com, March 28, 2012.

In this blog, we show the implications of a multi-factor model and realistic empirical interest rate volatility assumptions for ICAAP analysis.  We use the 3 factor Heath-Jarrow-Morton model and the interest rate volatility assumptions for those three factors outlined in the March 28 blog.

Stress Testing and ICAAP

One of the most important aspects of the internal capital adequacy assessment process is stress testing, a discipline with very long history in interest rate risk management.  Over the last three decades, both bankers and regulators have relied heavily on parallel shifts of the yield curve itself and ignored the implications of the yield curve shift for interest rate volatility. Ignoring the impact of interest rate volatility shifts in the ICAAP process when yield curves move is a serious error.  The data from the U.S. Treasury market from 1962 to 2011 shows that interest rate volatility depends on the level of various points on the yield curve in a complex but intuitively attractive way.  When these volatility shifts are correctly taken into account, one can see that the projected levels of interest rates have a much wider potential dispersion than a similar projection from a lower starting yield curve level.

This narrated video from Kamakura shows the stress testing of the U.S. Treasury yield curve of March 31, 2011 in combination with the 3 U.S. Treasury risk factors identified in the March 28, 2012 blog.  The volatility of these 3 risk factors generally (but not always) rises with the level of interest rates.  The volatilities both rise and fall with the maturity of the forward rate being analyzed.  The result, as shown in this video, is a change in the level of future interest rate dispersion projected by a multi-factor interest rate model:


The video shows 1250 parallel shifts, in one basis point increments, of the Heath Jarrow Morton “bushy tree” for the one year U.S. Treasury spot rate based on the shifted initial yield curve and the volatilities of the three driving risk factors that are appropriate at starting interest rate risk levels.  A video of Monte Carlo scenarios using the same Heath Jarrow Morton no arbitrage restrictions would give similar results.

Common practice ALM systems which do not have this multi-factor interest rate risk capability and the related ability to pick up multi-factor volatilities will produce incorrect risk assessments and under-estimate capital needs for most typical interest rate risk positions seen in practice.  This is well-known to sophisticated financial institutions regulators and it is likely that a firm using such common practice techniques will be under increasingly tough regulatory scrutiny with respect to ICAAP.  This is particularly true in the current interest rate environment in many countries, where interest rates have little potential to fall and a much higher potential for sharp increases.

Benchmarking Interest Rate Forecasts for Realism Under ICAAP

Another important failure of common practice in interest rate risk management and ALM analytics involves the consistency of the interest rate forecast assumptions with both history and market prices.  As explained above and in many recent blogs, one factor term structure models assume away yield curve twists even though a twist is in fact what took place on 94% of the business days studied for the U.S. Treasury market. 

More generally, the ICAAP process should ensure that the projected volatility of rates and the collective set of interest rate paths that is assumed was, after the fact, realistic.  The best way to check the realism of interest rate assumptions is to apply them to historical data and measure whether the projected dispersion of interest rates is consistent with the actual paths of interest rates that came about.  The video below does exactly that.  In doing this analysis, an interest rate assumption would be rejected at the desired level of statistical significance N (say the 99th or 95th percentile) if actual rates are either too high or too low relative to the set of assumed interest rate paths. A more subtle interest rate forecasting error comes about if the actual movement of rates is much less volatile (varying, say, between the 53rd and 47th percentile 100% of the time) than the set of alternative scenarios used for modeling.

The video below could be done either using Monte Carlo simulation or a bushy tree using the Heath Jarrow and Morton approach.  For ease of exposition, we again take the bushy tree approach.  We assume that there are three factors driving interest rates and that these three factors have volatilities that vary with the level of rates.  We use the actual volatilities that prevailed from 1962 to 2011 and hold them constant.  We ask the question, “Are these assumptions consistent with the ultimate movement in rates that actually occurred?”  We show that by comparing a projection of 1 year U.S Treasury rates in a bushy tree with the actual 1 year U.S. Treasury rates that actually came about 1 year, 2 years and 3 years later.  The actual rates are depicted by the heavy red line for 12,395 business days in this video:


The video shows that the volatility assumptions were generally accurate over the entire 50 year period with the exception of the extremely high interest rates in the late 1970s and early 1980s and the extremely low interest rates that have prevailed in the aftermath of the 2006-2010 credit crisis.  Given this, updating interest rate volatility assumptions frequently, rather than holding them constant for 50 years as we have done here, is the obvious way to increase the accuracy of the ICAAP analytics.

Stepping Away from Common Practice to Best Practice

A wide array of financial institutions are committed to moving away from common practice to best practice in reaction to the large number of firms who failed using legacy risk systems in the credit crisis.  Kamakura advises clients on how to do this in a progressive, scalable step by step process that ultimately leads to a sophisticated multi-factor interest rate modeling environment for the full range of enterprise risks.  For information on this process, please contact us at info@kamakuraco.com.

Donald R. van Deventer
Kamakura Corporation
Honolulu, April 17, 2012

© Copyright 2012 by Donald R. van Deventer. All rights reserved.