Euro LIBOR rates: technical predictability overview

The motivation for the technical, mostly correlation-based study of LIBORs was outlined in the USD LIBOR article. Forex correlation analysis made me believe that LIBORs are important for speculative forex forecasting. From a more academic standpoint, it is interesting to hone one’s analytic skills by expanding the range of application of the correlation techniques which yield intriguing results in forex to what’s behind the forex movements, namely to the interest rates. I’ve structured this document to begin with historical LIBOR charts for Euro, continue with volatility analysis, culminate with LIBOR autocorrelations which is my prime tool of predictability analysis and conclude with cross-correlations among Euro LIBORs of different maturity terms.

As far as the overnight LIBOR is concerned, the money markets jump the gun trying to anticipate the course of events almost regularly, to the extent this nervousness must represent a regular and significant arbitrage opportunity, if the market instruments tied to the LIBOR rates have the same features. The overnight LIBOR chart is full of arbupt jumps up and down; the upward trend which began in 2005 looks like a staircase with distinct steps; these sharp features are gone in 3-month data. Curiously, the 12-month chart has “extra” oscillations which do not correspond to the clear-cut treds in the shorter term LIBOR data. Apparently these represent (often mistaken) attempts of bankers to price in their anticipation of LIBOR evolution. For example, the anticipated interest rates drop in early 2008 never materialized for EUR. As a result of this and other similar episodes, 12-month LIBOR is more volatile than many shorter maturities; the edges of the maturity gamut are more volatile than the middle. This will be seen also from Table 1 in the Volatility section.

LIBOR volatility

I use RMS of the logarithmic return distribution as a quantitative measure of volatility in LIBOR interest rates.

Table 1: Day-by-day volatilities (RMS) for the time series of logarithmic returns in EUR LIBOR in 2002-2008, various maturities

durationtime scalevolatility (RMS)
s/n-o/nday3.8×10-2
weekday1.1×10-2
monthday0.56×10-2
3 monthsday0.37×10-2
12 monthsday0.88×10-2

Distribution of logarithmic returns in s/n-o/n and 1-week EUR LIBOR rates Distribution of logarithmic returns in 1-month, 3-month and 12-month EUR LIBOR rates

Fig.2: Distributions of logarithmic returns in EUR LIBOR rates, top: s/n-o/n and 1-week, bottom: 1-month, 3-month and 12-month maturity. Volatility is a measure of the width of the return distribution.

As with US Dollar LIBOR, the distributions of logarithmic returns on the day time scale are not lognormal. The s/n-o/n distribution looks broader than power-law (remember that with returns already containing logarithm and with the vertical axis explicitly logarithmic, we are looking at what is effectively a log-log plot, where any power law dependence would have looked linear, with different power law exponents resulting in different slopes).

LIBOR autocorrelations

Fig.4 shows the autocorrelations of logarithmic returns in the historical LIBOR time series for the Euro.

Autocorrelation in the logarithmic returns of s/n-o/n EUR LIBOR. Day time scale. Autocorrelation in the logarithmic returns of 1-week EUR LIBOR. Day time scale. Autocorrelation in the logarithmic returns of 1-month EUR LIBOR. Day time scale. Autocorrelation in the logarithmic returns of 3-month EUR LIBOR. Day time scale. Autocorrelation in the logarithmic returns of 6-month EUR LIBOR. Day time scale. Autocorrelation in the logarithmic returns of 12-month EUR LIBOR. Day time scale.

Fig.4: Autocorrelations in the historical EUR LIBOR is shown against the backdrop of statistical “noise”. The noise is obtained from martingale simulations based on the historical volatilities of LIBOR for the period under study. The noise is presented as mean plus-minus 1 RMS, where the RMS characterizes distribution of the correlation value obtained for each particular time lag bin by analyzing 20 independent simulated pairs of uncorrelated time series. The RMS is a measure of accuracy in the determination of the correlation values, an irreducible uncertainty dependent on the amount of data and the time scale. Top to bottom: s/n-o/n, 1-week, 1-month, 3-month, 6-month, and 12-month data.

As with the US Dollar LIBOR and with some of the most volatile forex exchange rates, the most prominent feature of these Euro autocorrelations is the “bipolar disorder” pattern seen from the bins with large negative signal surrounding the zero-time lag bin. (The expression “bipolar disorder” in relation to the market is credited to Benjamin Graham). Continuing with the psychiatric analogy, these indicate rapid (next day in case of the s/n-o/n LIBOR) changes in the mood of the patient (Mr Market), a price action followed by a correction. The correction comes next-day for s/n-o/n and on the fourth day for the 1-week term, and may last up to three days. Significance of this and other features is seen from comparison with random walk or martingale simulations respecting the volatility distributions of real LIBOR markets. 1-week LIBOR data show definite periodicity, the period being about 20 days. In 1-month and 3-month data, there is a change in the picture: the correlation is purely positive; there is still an oscillation, but with a longer period of perhaps 50 days. The pattern weakens in the 6-month term data and is practically gone in the 12-month.

Cross-correlations of LIBOR terms

Next, I am going to look at correlation between LIBOR rates of different maturities for various time lags.

Correlation between logarithmic returns in s/n-o/n and 1-week EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 1-month EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 3-month EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 12-month EUR LIBOR rates as a function of time lag, days

Fig.5: Correlation between logarithmic returns in s/n-o/n and, top to bottom: 1-week, 1-month, 3-month and 12-month EUR LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

Correlation between logarithmic returns in 1-week and 1-month EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 3-month EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 12-month EUR LIBOR rates as a function of time lag, days

Fig.6: Correlation between logarithmic returns in 1-week and, top to bottom: 1-month, 3-month and 12-month EUR LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

Correlation between logarithmic returns in 1-month and 3-month EUR LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 12-month EUR LIBOR rates as a function of time lag, days

Fig.7: Correlation between logarithmic returns in 1-month and, top to bottom: 3-month and 12-month EUR LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

Naturally, individual LIBOR maturities are generally positively correlated with one another. Terms of similar duration show more correlation.