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Markov switching and financial watersheds

Posted by Sam Jones on Apr 21 13:15.

Not so long ago there was a small debate here on FT Alphaville about the consequences of the Lehman collapse back in September 2008, and whether it really did constitute – for lack of a less hackneyed phrase – a paradigm shift.

Anecdotally, we thought it did.

Now though, Vox EU contributors Brenda González-Hermosillo   and Heiko Hesse, both of the IMF, have authored a far more authoritative quantitative analysis that seems to support that view.

The authors perform a Markov-switch analysis to various financial market metrics – Vix, TED spread, dollar-euro FX etc.

- a Markov-switch model being one that contains an ability to switch between different statistical “regimes” when running a typical Markov probability model – for example, between a ‘normal’ markets regime and a ‘stressed markets’ regime.  Such switch models were relatively early developments in quantitative finance that were aimed at overcoming some of the problems in relying on regular “random-walk”-type modelling of datasets: normal distributions ineffectively capture extreme events.

Back to Vox EU though and González-Hermosillo and Hesse apply the 1994 Hamilton and Susmel “SWARCH” Markov Switch model backwards as a simple but effective method to identify, over different time series, between different volatility “regimes” in datasets from the current crisis. (Unfortunately we can’t locate the Hamilton and Susmel paper for free anywhere, but the SWARCH model itself is available from James Hamilton’s webpage at the University of California here.)

Here it is applied to VIX:

vix volatility states modelled using swarch

The higher the pink line (right hand scale) the more likely the model determines events to be occurring under a “high volatility” – stressed -  regime.

Figure 2 shows a daily SWARCH model of the VIX from 1998 to the end of 2008. The model has the highest probability of being in the high volatility state during the Russian Crisis and LTCM default in 1998, the period surrounding the WorldCom scandal and Brazil’s election in 2002, as well as the beginning of the subprime crisis in the fall of 2007 and the period following the Lehman collapse. The model also enters the high volatility state briefly at the time of the Shanghai stock market crash and the first abrupt ABX (BBB) price decline of investment grade subprime mortgage-backed securities in late February 2007. During the Bear Stearns rescue, the VIX was more likely to be in the high rather than medium-volatility state. The Lehman failure then triggered a very fast movement of the VIX into the high-volatility regime, where it remained until the sample period ended on 31 December 2008. After the start of the subprime crisis, the VIX oscillated exclusively between the medium- and high-volatility regimes, in contrast to the predominantly low-volatility regime during 2003-2007.

Although Lehman, conclude the authors, was a watershed event, what’s interesting is the way the model responded to other, less salient, events – or at least, events which received far less coverage in the media: the ABX (BBB) crash, for example, which scores higher on the SWARCH high-volatility state probability scale than the Bear bankruptcy.

Related link:
Vix challenger – FT Alphaville

This entry was posted by Sam Jones on Tuesday, April 21st, 2009 at 13:15 and is filed under Capital markets. Tagged with , . Edit this entry.

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