Estimating Corporate Bond VaR with Spread and CDS Data
Summary
The document discusses ways to estimate portfolio Value at Risk when corporate bond price histories are short or sparse. One proposed approach models changes in each bond’s credit spread, using option-adjusted spreads when feasible or simpler Z-spreads, then translates simulated spread scenarios back into bond prices. The discussion also recommends including default risk because it can materially reduce portfolio value.
Where bond observations are limited, CDS spread changes can serve as a proxy for credit-price volatility, with adjustments based on CDS and bond DV01s. The response cautions that cash bonds may behave differently from CDS, especially in stressed markets, and suggests increasing the proxy volatility to account for that basis risk. The document gives practical modeling suggestions rather than a validated VaR specification: it does not provide a calibration, portfolio example, or universal adjustment factor. It also notes that Expected Shortfall is often preferred because VaR lacks coherence.
Key ideas
- Modeling corporate bond spreads can be more practical than using sparse bond price changes.
- Simulated spread moves can be translated into bond prices, with option-adjusted spreads or Z-spreads as possible inputs.
- Default scenarios should be included because they can cause large portfolio losses.
- CDS spread changes can proxy for bond risk after accounting for DV01 differences and cash-CDS basis risk.
- Expected Shortfall is presented as an alternative to VaR because VaR is not a coherent risk measure.
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# VaR for corporate bonds # VaR for corporate bonds I am trying to create a simple risk calculation for the portfolio (ignoring correlations for the moment). I have some corporate bonds with limited daily price changes. Any one have ideas how I can get a VaR (95%) for these assets given their limited pricing history? Is there any easy way to use CDS for the name instead of corporate bond prices (if i can find a long enough history) ## Answer by Brian B (score 7) https://quant.stackexchange.com/a/4400 It's very common to work in spreads rather than price for this calculation. The simplest approach would be to get an implied spread for each bond, and then allow the spreads to vary in simulation according to an equity-style factor model. Each spread simulation can then be mapped back to bond prices by reversing the formula. A few points: - If you can, you should use option adjusted spreads, but that involves somewhat complicated interest rate models. Z spreads are a simpler choice. - Be sure to allow for default in your simulations, since a default will have a large negative effect on portfolio value. - Importance sampling will get better resolution. - Many people prefer Expected Shortfall to VaR because VaR is not a coherent risk measure. ## Answer by Wade Bratz (score 0) https://quant.stackexchange.com/a/14086 If you have CDS data, take ( cds spread changes * the dv01 of the cds / cds notional ) to get a percent change in cds. you can use that as a proxy for bond price volatility. Note that in bad times, cash tends to underperform cds so you need to increase the volatility of your bond relative to the cds. if your cds volatility is 3%, multiple that by say 1.5 to be conservative. additionally, you will need to adjust by the ratio of the cds dv01 to the bond dv01.
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