Transcript The Microfinance Collateralized Debt Obligation: a Modern

The Age of Turbulence,
Credit Derivatives Style
Hans NE Byström
Lund University
The paper focuses on
•
the many extreme credit default swap spread movements
observed during the credit crisis 2007-08
• how the tails of the spread change distribution significantly
differ from those of the normal distribution.
• how not even extreme value theory methods are able to
satisfactorily capture the extreme behavior of the credit
derivatives market at the peak of the credit crisis.
• how the credit market of July 2007 is comparable only to that of
the equity market of October 1987.
Companion papers
• This paper, Byström (2008), “The Age of Turbulence,
Credit Derivatives Style”, 2008.
and
• Byström (2007), “Back to the Future: Futures
Margins in a Future Credit Default Swap Index
Futures Market”, The Journal of Futures Markets,
27(1), pp. 85-104.
Quote from Byström (2007)
“Although the General Motors episode [of 2005] might not
repeat itself, it should nonetheless be a lesson for the future;
whether or not the credit environment becomes riskier over the
next couple of years, similar sudden changes in CDS spreads
most likely will strike the CDS index market from time to time.”
This was written in 2006 (i.e. well before the credit crisis) and
today few would argue against the importance of an explicit
focus on low-probability tail events!
The market
•
The European credit default swap index market.
• More exactly, we look at the 5-year iTraxx Europe index. This is
an index of 125 European investment-grade credit default
swaps.
• This is the most widely used “animal” in the credit derivatives
world.
• The credit default swaps are selected based on their trading
volume over the last six months and every six months the index
is updated.
Data
• Daily 5-year iTraxx Europe CDS index spread over the time period
June 2004-March 2008.
• We divide the sample into a pre-crisis period and a crisis period. The
crisis period is the period July18, 2007 (the day Bear Stearns reported
large losses in two of its hedge funds) to March 18, 2008 (the day JP
Morgan bought Bear Stearns).
• In addition to these CDS spread changes we also study daily returns of
a typical stock market index (S&P500) over the same time period.
Some Descriptive Statistics
• the iTraxx Europe CDS index spread change distribution is not only
volatile but skewed and fat-tailed as well.
• the most striking deviation from normality, however, is the number
and magnitude of the largest (positive and negative) spread changes.
Extreme Spread Changes in the Credit
Default Swap Index Market
During the crisis, many CDS index spread changes
are larger than +/-10%:
During the 8-month crisis period there are 11 daily spread
changes that are larger than +10% and 6 daily spread
changes that are larger than -10%. Meanwhile, during the
four times longer pre-crisis period there are only 1 spread
change that is larger than +10% and 2 spread changes that
are larger than -10%.
Extreme Spread Changes in the Credit
Default Swap Index Market
During the crisis, many CDS index spread changes
are much larger than the largest spread changes ever
seen before the crisis.
During the 8-month short crisis period, a total of 3(6)
positive (negative) daily spread changes are larger than any
spread change seen during the 36-month long pre-crisis
period. Moreover, 18 (7) spread changes are larger than the
second-largest spread change ever observed before the
crisis.
Extreme Spread Changes in the Credit
Default Swap Index Market
During the crisis, the most extreme CDS index
spread changes are very large.
The most extreme daily spread changes during the crisis are
+/-26%.
Extreme Spread Changes in the Credit
Default Swap Index Market
A comparison of multi-sigma events in the credit
derivatives market and in the stock market reveals
large differences
The largest daily spread changes during the crisis represent
spread movements of more than 13 (pre-crisis) standard
deviations. If we had seen one or two daily S&P500 stock
returns of the same magnitude (i.e., 13-sigma events) during
the crisis months they would have been around +/-9%.
Extreme Spread Changes in the Credit
Default Swap Index Market
Out of the first 30 days of the credit crisis, every
second day sees a 5-sigma, or larger, CDS index
spread change
Over the first month (22 trading days) of the credit crisis 11
daily spread changes are larger than +/-5 standard
deviations. The corresponding return history in the US stock
market (S&P500) would be -9.1%, -6.5%, -4.1%,-3.9%, 3.4%, 3.4%, 3.6%, 4.3%, 5.5%, 7.4% and 8.6%. And that is
in July only!
Extreme Spread Changes in the Credit
Default Swap Index Market
The cost of insuring corporate debt against default in
the iTraxx Europe CDS index market has increased
eight-fold since the start of the crisis.
In mid-June 2007, the cost of insuring corporate debt in
Europe against default hit a low-point at about 20bp. Since
then, the cost has gone up eightfold to reach a high of
160bp in mid-March 2008 (never before in the history of the
iTraxx indexes has one observed costs above 60bp.)
Value At Risk Estimates in the Credit
Default Swap Index Market
• The extreme (non-normal) spread changes in the credit derivatives
market might be a problem in risk management of credit derivatives
portfolios and we therefore investigate the usefulness of the normal
distribution in Value at Risk (VaR) calculations of credit default
swap portfolios (proxied by the iTraxx Europe CDS index).
• Moreover, as an alternative to the normal distribution we suggest a
simple and easy-to-implement extreme value theory-based approach
as an alternative in VaR calculations of credit derivatives positions.
Extreme Value Theory
• Extreme value theory (EVT) focuses on the tails of a distribution.
• It has sound theoretical underpinnings (Fisher and Tippett [1928],
Gnedenko [1943], Gumbel [1958]), Embrechts, Kluppelberg and
Mikosh [1997], and Reiss and Thomas [1997]).
• EVT models can be divided into two broad groups; peaks-over
threshold (POT) methods, and block maxima methods.
• In this paper we use the POT method.
Extreme Value Theory
• POT methods focus solely on the observations that exceed a certain
high threshold, u, and Balkema and de Haan [1974] and Pickands
[1975] have shown that for a large class of distributions the excess
distribution of observations above the threshold can be approximated
by the so-called generalized Pareto distribution (GPD).
• This GPD distribution contains two parameters, the tail index ξ and
the scale parameter α, and by fitting it to historical observations
above the threshold u we try to infer the ”true” shape of the extreme
tail(s) of the CDS index spread change distribution.
Extreme Value Theory
• The parametrization of the tail is used to get an expression for the
EVT-based VaR estimate associated with a certain probability p:
VaRp = u +α/ξ[(n∙p/Nu)-ξ − 1]
where n is the total number of spread changes in the data set and
Nu is the number of spread changes above the threshold u.
Value At Risk Estimates in the Credit
Default Swap Index Market
• Our purpose is to compare the EVT-based VaR estimates to
corresponding VaR estimates implied by the normal and the
historical distributions.
• Our hypothetical investor holds a well-diversified portfolio of credit
default swaps (as a protection buyer or protection seller) and we
define the VaR estimate/forecast as the potential percentage daily
change in a long or short position in the iTraxx Europe index (i.e., the
quantile at a certain small probability ranging from 0.01% to 5%).
• A good VaR estimator produces accurate estimates in tranquil as well
as in turbulent times. We acknowledge this by looking both at the
pre-crisis period (in-sample) and the crisis period (out-of-sample).
Conclusion
• Compared to, for instance, the S&P500 stock index the number and
magnitude of extreme observations in the credit derivatives
market is striking.
• Extreme value theory (EVT) based VaR estimates are much more
accurate, in the European CDS market, than those based on the
normal or historical distribution. The difference is particularly
significant at more conservative VaR levels.
• However, not even EVT is able to satisfactorily capture the extreme
behavior of the credit derivatives market at the peak of the credit
crisis. Not even at the aggregated (index) level.