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I'm searching for information on the best way to generate scenarios to be used in VaR or ES calculations, for CDS spreads.

Given that we need significant historical data in order to achieve a decent empirical probability distribution, I wonder what problems could exist.

For single name entities.

  1. Is it a problem if the company profile has changed a lot during the past 5-10 years?
  2. Do we somehow need to care about the underlying reference obligations? (Is this connected to 1) ?)
  3. Would it be proper to apply a PCA technique to reduce dimensionality, given that we probably want to take into consideration the entire term structure?

For indices.

  1. For, say, iTraxx, we get new constituents every 6 months (from Markit homepage), however. I imagine this may cause something of a bump in prices. How can we handle this?

Lastly, is it even possible to use historical simulation for CDS spreads, or is better to apply some Monte Carlo simulation?

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    $\begingroup$ For (1) I am sure the answer is yes (but don't have evidence to back that claim right now) and your model would be better including such events explicitly, even if just in a naive way. Or try to remove such companies' data. $\endgroup$ – P.Windridge May 10 '16 at 19:11
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    $\begingroup$ Here are some notes about effecgt of M&A activity on CDS spreads web.stanford.edu/class/msande444/2011/… $\endgroup$ – P.Windridge May 10 '16 at 19:17
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I used to help manage a large CDS portfolio, and (along with the folks at RiskMetrics) we settled on an approach I reckon was pretty decent.

First, let me say that market-data only simulations are the wrong way to go. Credit risk is sticky at various levels and then jumps like mad, so any given company's history tends to contain a highly unrealistic representation of the risk.

Let's think in terms of Monte Carlo simulation. Sometimes you can solve these things analytically, but in practice analytic solutions quickly become brittle.

First off your simulation must include jumps to default. They, after all, are the reason CDS have any value at all!

For the benefit of readers who don't know the market that well, since the CDS Big Bang CDS are nearly always priced in terms of an upfront payment, and coupons then are paid at standard rates. However these upfront prices may be positive or negative and ultimately depend on default probabilities. Thus it is much easier to do the simulations if you convert CDS upfront to default probability curves, which then have the property of not dipping below zero.

For simulating the curve changes, you can start stealing ideas from the interest rates literature. For expected shortfall, it is usually good enough to just treat a few points on any individual curve as log normally distributed, with high positive correlations.

I like treating all the curves with a 1-factor model, actually, on a single principal factor consisting of either the HY or IG CDX curve. Links with the equity or interest rate market can then be captured with correlation just through the CDX curve, leaving the individual curves to have their CDX component plus entirely idiosyncratic terms (of jump-to-default and default probability variation).

If you like, you can add simulations for recovery rates, though in practice I found those tended to just integrate out, so I ended up removing recovery rate simulation.

Once you have your curve simulations worked out, it is easy enough to convert back to upfront prices as necessary for scenario pricing.

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  1. Market Risk VaR takes one year of history. Thus you wouldn't look 5-10 years of history.
  2. If you are using CDS prices only for pricing CDSs you don't need to, but if you have another model that takes CDS prices and links them to bonds, yes
  3. You don't need PCA. You can take quotes on CDSs closest to each term node, but you need to roll them to adjust for fixed term nodes.

iTraxx, you need to give more information about the exposure you have related to iTraxx

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    $\begingroup$ "Market Risk VaR takes one year of history. Thus you wouldn't look 5-10 years of history." This statement I don't find credible at all. From a practical perspective, regulations require multiple years of data. $\endgroup$ – UmaN Feb 10 '16 at 12:32
  • $\begingroup$ Please give reference of the regulation which requires for Market Risk VaR more than 252 data points $\endgroup$ – adam Feb 10 '16 at 17:50
  • $\begingroup$ Actually EMIR/ESMA and FRTB seems to indicate "at least" 1 year. But it's irrelevant either way; historical simulation with 1 year of data is useless. You can't get a good empirical distribution from that. Anything below 750 observations is questionable. $\endgroup$ – UmaN Feb 11 '16 at 12:23
  • $\begingroup$ Your 750 is completely arbitrary :) Banks prefer using recent data for VaR, thus it is based on latest 252 days. Stressed VaR will use 252 days of a stressed period. 10 day returns are the standard. There are 1000s of factors in a typical VaR portfolio, usually if one factor is regime switching its affects will be ignored. $\endgroup$ – adam Feb 11 '16 at 23:35
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    $\begingroup$ Well ideally you'd have data throughout the economic cycle, regardless of minimum regulatory requirement. Take a look at spreads during 2007-2009 to see that any model missing this period is doomed.... $\endgroup$ – P.Windridge May 10 '16 at 19:04

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