Monday, January 21, 2013

Univariate statistics penalize multivariate filters

A while ago I wrote about simple accuracy statistics that, when applied to commercial pricing services, appear to be more than sufficient to delineate the good from the not so great. But I also mentioned that univariate statistics are somewhat simplistic, especially for assessing multivariate de-noising of market data. That comment was based on my numerical experiments, though it was somewhat underdeveloped.

This writeup (thanks to Nick West and George Papanicolaou) is a clean exposition of the point and is based on an independent numerical study. Here is the abstract:
In this report a simple piecewise constant curve based model is used to analyze the ability of various assimilation methods to be calibrated to observed market yields. To simplify the analysis, we make the following assumptions: (i) the yield of a bond (the observed quantity) is simply the integral of the hazard function through the maturity of the bond; (ii) the levels of the hazard function follow independent random walks; (iii) different bonds on the curve (with di erent maturities) trade with different frequencies, some of them continuously and others in bursts; (iv) observations that occur near (in time) to other observations have correlated observation errors. Assumptions (i) and (ii) allows usto easily apply the the Kalman Filter to obtain the optimal estimates of price; (iii) and (iv) are derived from our observations and experience with bond data. It is shown that a multivariate Kalman Filter's estimate of the current yield is both more accurate and precise when compared to the true, unknown yield. Furthermore, it is demonstrated that when the "next trade" is chosen as a target, serial correlation in observation errors cause the last trade to be chosen as the most accurate predictor of next trade; however, it is much less accurate at estimating the true yield; this bias is most notable is actively traded bonds.

To be clear, the report is not advocating reliance on a Kalman Filter per se. Rather, it is using a simplified model where the true prices are known to illustrate that simple univariate tests give misleading results (unfairly penalizing multivariate filters).

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