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5

Yes your formula seems correct under the simplifying assumptions as you can easily verify: Assume annual default rate is d, and the portfolio size is N. In the first year, we will have Nd defaults. In second year, the number of obligors would have declined by the number of default in the previous year to N-Nd=N(1-d), so the number of defaults in the second ...


5

You cannot do it. It is an under-determined problem. That is to say, a whole multitude (subspace of $\mathbb{R}^{N\times N}$) of migration matrices will agree with any given table of default probabilities. Say you want to find a transition matrix for 2 states (IG, HY) plus default $$\left(\begin{matrix} p_{11} & p_{12} & p_{1D} \\ p_{21} &...


5

Firstly, the use of the logit models to estimate the PDs is particularly appreciated in some credit industries, as, for instance, the credit retail one. The logit model predicts pretty well the PD on loans, consumer credit, credit cards, ... and all concerns the retail consumer world. Mainly, those listed are the principal sub-industries in the credit ...


4

Firstly it's good to straighten out our goal. You correctly say, that IFRS9 requires analysis of expected losses. There are two components of expected losses. 1) Expected probability of a default event 2) Expected recovery rate So, not only do we need the probability but also the recovery rate. Luckily, both are approximated by the credit spread, which ...


4

Actually, there is a practical way to do it. You can use you PoD estimates to assign a credit rating to your securities and then use a published transition matrix for your purposes. Or you can estimate transition probabilities by linear interpolation based on the PoD values that you have. Here is a publication containing transition matrices from Moody'...


2

This does not sum to 1 because you have forgotten to add the 6th scenario, the NonDefault (ND). If Ps is the probability of survival and Pd the probability of default, the ND has the probability Ps^5. This makes: Pd+ Ps*Pd+ ... Ps^4*Pd+ Ps^5= Pd*(1+Ps+...+Ps^4)+Ps^5= Pd*(1-Ps^5)/(1-Ps)+Ps^5= (1-Ps)**(1-Ps^5)/(1-Ps)+Ps^5=1.


2

(Although the question was asked long time ago it may be of help for others as well) You may want to have a look at Nagel and Purnanandam (2015) Bank Risk Dynamics and Distance to Default (https://www.bundesbank.de/Redaktion/EN/Downloads/Bundesbank/Research_Centre/Conferences/2016/2016_06_10_eltville_08_paper_nagel.pdf?__blob=publicationFile) The authors ...


2

First, I would emphasize that default protection is bought and sold on debt securities , not on assets. To answer your question, you cannot sell protection on your own debt. You can sell protection on sovereign debt, including the sovereign where your company is based. However, the buyer of this protection understands that there may be a high correlation ...


2

It is mainly subjective, depends on country and sector. E.g. when I worked in private equity in a distressed fund a highly levered company was a company with a net-debt to EBITDA ratio > 7.0. Those are back of the envelope numbers. They actually do not tell you much about the health of the company nor its risk. A company with 7.0x net-debt to EBITDA ratio ...


1

I don't know the answer to this and am responding purely out of interest and idea sharing, since I like the question. Could this work as a Parametric intensive computational statistical approach; 1) Define a universe of positions the portfolio can feasibly hold, and model each with some assumption about default over a given time period (statically at first ...


1

I was indeed wrong : only the assumed recovery rate is used. This is for instance confirmed by the QCDS Bloomberg screen that shows only one recovery rate to do the (quoted spread,coupon) --> upfront and (upfront,coupon) --> quoted spread conversions. To sum up : the assumed recovery rate is only used for a quotation purpose : to do the (quoted spread,...


1

In theory, it should indeed be equal as holding a bond $B_t$ from some company $X$ as well as paying on a CDS written on the bond should earn you the risk-free rate, given the CDS hedges the default risk of your bond. In practice, there is a CDS-bond basis, which is equal to: $$ \text{Basis}_{\text{ CDS-Bond}} = \text{Premium}_{\text{ CDS}} - \text{Spread}...


1

The capital structure of financial firms, especially one like Bank of Montreal, is indeed quite unlike the simple debts-and-assets model of CreditGrades. For context, the model is basically one that says there are some assets $A$ subject to a stochastic process, and a debt level $L$ (unknown at the present time). If ever $A<L$ the company defaults. ...


1

Although I, admittedly, did not go hunting through your code for an error, I have seen this phenomenon before using this model. This model (like all other models) isn't perfect. This is especially true when you can only observe those parameters that come from the balance sheet quarterly. There are scenarios where no asset vol can imply the current market ...


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