# Tag Info

15

The limitations of the Gaussian copula were well-known among the quantitative finance practitioners before the crisis. See this paper by D. Brigo. To answer the question: no "fat tails" unable to fit the market prices without tweaks (base correlation) which make the model arbitrageable it's a static model (e.g. forward-starting tranches are impossible to ...

10

There is a fairly recent (2010) monograph by Martin Hibbeln entirely devoted to this very question. He starts with the standard Asymptotic Single Risk Factor model and shows how it can be modified in order to be consistent with the Basel II framework. He also compares the accuracy and runtime of several modern models which have been developed to measure ...

9

Distance to default $DD$ should be measured in standard deviations. You convert this into a probability $p_{default}$ using the normal CDF: $p_{default} = N(-DD)$. So if $DD = 2.978$ then the firm is about 3 standard deviations from default and has a $\frac{1 - 0.997}{2} = 0.0015 = 0.15 \%$ chance of defaulting in the next period. I divided by two because ...

9

If you want a 'pop science' account for it, the Wired article by Felix Salmon is a pretty good start. If you want harder technical stuff, well then you can start at the Wikipedia article and its section on Applications and follow the references: [...] Some believe the methodology of applying the Gaussian copula to credit derivatives to be one of ...

6

In practice, I would begin with the recovery assumption. In the case of Greece, dealers are probably already quoting recovery swaps, allowing you to set this parameter directly. In general, you have to be willing to make assumptions based on history or on conversations with bankruptcy experts. Once I have the recovery assumption, I can take any instrument,...

5

The standard reference is Anderson and Sidenius Extensions to the Gaussian Copula: Random recovery and random factor loadings. Random recovery proved necessary in 2007/2008 when you couldn't calibration standard one factor base correlation models. This paper discusses this, and might be an easier starting point than the Anderson and Sidenius paper.

5

I could not find any such detailed documentation after some weeks of looking (not non-stop obviously). It is appallingly documented. I do understand fully what it does though so am happy to field some questions on it if you like. In a nutshell, I can tell you it is a standard reduced-form credit model under a constant hazard rate (i.e. homogeneous Poisson ...

4

Most of the credit risk models are some derivative of survival models. Cox Proportional Hazard is one of the early and more popular models, Kaplan-Meier and Logrank tests are others you may have heard of. There are a few ways to go from here. The simplest is to model the sample as binomial with one population as current and the other as in default. A ...

4

Via Liquidity Horizons $LH$ (which have to be taken into consideration anyway when modelling for $Basel_3$) as function of the specific concentrations $c$'s. Increasing the effective maturity of the contract, $M_0+LH_0$, by a quantity proportional to its concentrations with respect to different slicings magnifies the credit risk. $M_0$ is the maturity ...

4

there is no standard approach to model quanto CDS. In practice, people look at the dynamic hedging costs over time as well as the expected loss from an fx gap in the event of a default of the ref entity. the former is modelled by some correlated brownian (for FX) and mean-reverting processes (for credit - could be Ornstein Uhlenbeck for example). In addition,...

4

Actuarial science traditionally focuses on estimation of joint probabilities using real data where math finance is on valuation of contracts under an arbitrary distribution. It means the first one deals with methods of estimation of future distributions (the number of accidents of a given kind, the probability of someone with a given profile to have a ...

4

You could read it like this: The typical change in equity value is equal to the typical change in asset value, adjusted for the probability of the assets surviving. Note that the formula is not specific to Merton models, it's also true for regular options and their underlyings. It's just that volatility of option prices isn't typically a concern in "...

4

If you don't have a significant amount of losses in your portfolio to validate the model, you should be able to obtain external loss data and adjust it where necessary to better fit your organization. This is very common with operational loss models where operational losses are quite scarce.

3

Yes, you can have two different ratings. The issuer has one credit rating, but the individual issues, even if they are both senior unsecured/secured with the same maturity, coupon, etc. can have different ratings. The key factor is going to be the structure/provisions of the issue itself. For example, an issue with a sinking fund is going to be viewed as ...

3

I just reviewed the paper Corporate Bond Liquidity Before and After the Onset of the Subprime Crisis by Dick-Nielsen, Feldhütter and Lando. They define a liquidity measure $\lambda$ as a conglomerate of price impact (Amihud) and its variability spread covariance (Roll) and its variability turnover imputed roundtrip cost (Feldhütter) zero trading days I ...

3

Well, the main intuition of the Merton model is that a company's equity can be treated as a call option on its assets, thus allowing for the application of Black-Scholes option pricing methods. Let's consider a company that has assets $A_{t}$ financed by equity $E_{t}$ and a zero-coupon debt $B_{t}$ with face value K, and maturity T. At time of maturity T, ...

3

Here is a link to a very interesting paper about the subject. The model assumes lognormal intensities (I think to ensure non-arbitrage as default probability must always be between 0 and 1, which is not the case if we assume Gaussian process for the intensity) deterministic FX volatility correlation between FX and the intensity a jump in the FX spot in the ...

3

Here are some practical tips for selecting stochastic processes for spread curves, for example, in Monte Carlo simulation. Typically you formulate a joint stochastic model for yields at key maturities due to data limitations. The corporate yield curves generally maintain order with the AAA yield below AA yield, AA yield below A yield, etc. If, for ...

3

well you can use CDS spreads to strip out implied default probabilities for default before time $T.$ These had better be increasing as a function of $T$ or you have an arbitrage opportunity. However, there is an assumption here that there is no default risk on the CDS swap itself once you take that into account there may be a good chance of profit but no ...

2

The consensus seems to be is using jump diffusion process (affine), and then using copula's and/or correlated brownian motions to handle the correlation structure. Here's a link to a recent paper that discusses these models in great detail, and includes application of these models for modeling quanto cds: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=...

2

CreditMetrics uses monte carlo simulation assuming a beta-distribution fitted to historical recovery rates.

2

Claudio Albanese has a paper on the topic of GPUs and CVA computations. Here is one of his papers: link to paper

2

Here is another Credit Default Swap database which is rather extensive, daily spreads of roughly 700 entities starting in 2006.

2

Markit is a pretty good source for CDS information, and their prices are pretty much the standard the industry goes by. Your best bet for finding large spreads would be to look at some of the European Banks or possibly TEPCO after the Japan Tsunami. Derivatives by default aren't "standard," the instruments are designed to be flexible, but the closest ...

2

The equation stated in the question is not at the core of Merton's credit model, (Not saying you claimed it is) but is a simple device in helping to solve the system of linear equations. The equation given simply establishes a relationship between the volatility of equity and the volatility of the assets and it follows from the application of Black Scholes ...

2

All else being equal, buying back stock would cause a company's credit spread to widen (increase). This is because a share buyback involves shrinking the firm's assets (spending cash to buy back the stock) and shrinking equity/retained earnings, while leaving the liabilities unchanged (or increasing them in the case of a leveraged buy back). This is an ...

2

The classical connection is the http://en.m.wikipedia.org/wiki/Esscher_transform developed for actuaries in 1932 which essentially transforms the objective probability measure into the risk neutral one used in quant finance.

2

Most, but far from all, companies maintain a relatively steady debt load. When a bond matures, they fund its principal payout with a new bond. Sometimes companies do take on more and more debt, meaning that CDS protection sold during earlier times of small debt loads becomes more valuable (and underpriced, from the point of view of the protection seller). ...

2

It depends on how one is thinking about the hedge. One might be thinking of it as A hedge against catastrophic risk (default of the issuer), or A hedge against changes in (market-implied) default intensity or hazard rate In the former case, which seems to be how you are considering it, the hedge is a static hedge, kept for up to 5 years, and insulates ...

2

When you long a 5y CDS and the spreads <5y increase and the 5y spread remains constant, the premium leg value is decreased. It appears that the CDS value should increase, and you should have a positive sensitivity. However, depending on the shape of the survival probability curve, the protection leg value may also decreased, and then the CDS value, which ...

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