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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

I understand that Moody's uses an empirical distribution while KMV uses a normal distribution in order to calculate these probabilities KMV doesn't use a normal distribution to map distance to default to a probability of default (EDF in the KMV model). It uses a proprietary database. By a strict structural interpretation, $EDF$, the expected default ...


5

I'll assume $$ J_t = \sum_{i=1}^{N_t} Z_i$$ be a compound Poisson process, with $(T_n)_{n\geq 1}$ being the jump times for Poisson process $(N_t)_{t\geq 0}$ and $(Z_i)_{i\geq 1}$ sequence of i.i.d. variables independent of $(N_t)_{t\geq 0}$. For SDE $$ dP_t = P_{t^-} dJ_t $$ we notice that at jump times we have $$ dP_{T_i} = P_{T_i} - P_{T_i^-} = Z_{i} P_{...


5

The defaulted bond is a claim on the accelerated repayment of the remaining principal. The maturity date is a non-event for a defaulted bond. Its maturity date and the coupon rate are only useful for identifying the bond, but have no economic meaning and in general should not be used in any calculations. Some IT systems are buggy in that they assume that ...


4

The owner of the bond at the time of resolution of the default/bankruptcy is entitled to the recovery value. The bankruptcy proceedings may go well past the scheduled maturity of the debt obligations outstanding at the time of default. People that think the recovery value may be higher than the traded price of the bond may be looking for a gain. Also, ...


3

The formula for the accrual on default $$ S_n \sum_{i=1}^n \frac{\Delta_i}{2}(Ps(i-1)-Ps(i))DF_i $$ is just an approximation that says conditional on default occurring within period $i$ (probability of $Ps(i-1)-Ps(i)$), defaults occurs on average in the middle of the period, thus the $\frac{\Delta_i}{2}$ average accrual time from beginning of period to ...


3

The accrual on default is like the accrued interest on a bond. A credit default swap can be looked as a synthetic bond. As such, with each passing day, interest is earned to the seller of protection (similar to a holder of a bond). The accrual is due to the seller of protection (holder of the bond) but has not been paid since interest is paid on a ...


3

I have actually looked into this a lot and I don't have a full answer. You can (sort of) see what the market participants think by looking at the consensus "quanto factors" published monthly by IHS Markit Totem. They even have some term structure, although usually it's the same factor for all tenors. For some sovereigns, people sometimes trade a CDS ...


3

A methodology for estimating rating/ region/ sector proxies for ACVA calculations can be found here: http://www.nomura.com/resources/europe/pdfs/cva-cross-section.pdf Please let me know if you need anything to be clarified (caveat: I am one of the authors). The methodology assigns a CDS mark to counterparties that either have no CDS marks, or their marks are ...


3

Your reference says "This method derives implied CDS spreads for unobservable issuers through the interpolation or extrapolation of observable CDS. It is a factor model that constructs CDS spread surface as a function of credit rating and maturity." So this is for issuers which do not have any CDS contracts priced (there are no CDS spreads to bootstrap). I'...


3

There are quite a few methods to calculate default probabilities from CDS data. Simply you start at the shortest tenor, assume constant hazard rate. Then for the next tenor, you assume the previous hazard rate is still valid till the previous tenor, and the hazard rate between the previous tenor and new tenor is calibrated so that CDS PV matches the market ...


2

Yes, you can. Also, do not use Altman's Z. The extreme scores are predictive, but a load of empirical research shows the intermediate values are not predictive. The best solution is a Bayesian solution because you are gambling money. Bayesian methods are coherent. Coherence is the statistical property by which fair gambles can be placed. Frequentist ...


2

Merton model will be a bit more quantitiative. Z-Score is an option, as is Ohlson. In the end you are going to want some non-defaulted->defaulted transition mapping based on factors you identify as meaningful.


2

A CDS would not be a good instrument to hedge this kind of credit risk for the following reasons: 1 CDS is traded by two counterparites that have an ISDA agreement. Most participants in this space don't. 2 CDS are traded on a relatively small number of most liquid corporate reference entities. If you want to trade a CDS on an illiquid name, it would be ...


2

Maybe some do but I believe it’s rare because it’s not practical: CDS are traded for a limited amount of companies and CDS might not protect against late or non payment. What is more commonly done is that vendors buy trade credit insurance from insurance companies such as Euler Hermes, Coface or Atradius. Disclosure: I work for Atradius.


2

Simply speaking, as mentioned by Antoine, the accrual arises because default may happen between two payment dates and the accrued payment should be paid. $\Delta_i$ is the year fraction. Since $S_n$ is quoted as an annual rate, $S_n\Delta_i$ is the payment amount per $1 notional. However, in the formula you mentioned, default is modeled at the same frequency ...


2

To Recap: Your "Note" is a pool a of loans of which are expected to pay Yield Ydf. You want to estimate the mean and variance of the Loss in yield of non payment. First and foremost you need to get a historical YL or at least a Data Generating Process for YL. Some approaches A) Historical Calculate historically implied loss in yield and then use that ...


2

I have an Idea perhaps it helps you a bit (even though it deviates somewhat from your original setup). Let's assume you know the "anaffected" default probabilities for each bank $P(X_1<=C_1), \dots, P(X_n<=C_n)$. (Here I assumed that bank $i$ defaults when it's value falls below a certain value $C_i$) Now e.g. for bank $n$ you can calulate $P(X_1<=...


2

As a complement to @ir7’s comprehensive derivation, in the case of Burgard and Kjaer’s the jump process $J_t$ models the default of the issuer. You specialize the process by setting $Z_1=-1$, while the values of $\{Z_i:i\geq2\}$ are irrelevant. You then notice that as soon as the process jumps once, the product of jump sizes becomes null. We therefore have: $...


2

If I understand correctly, you don't have access to IHS Markit historical consensus CDS spreads, but you do have access to CMAN (CMA North America) historical CDS spreads on Bloomberg terminal. While IHS Markit would be a little better data, I think CMAN should be good enough for the study you're describing. Don't look at any tenors other than 5Y. Looking ...


2

(I didn't quite understand where exactly you are going with your questions, but I inserted a few statements below that might be useful.) Jorion's table shows: $$ \begin{bmatrix} P(A\cap B) & P(A\cap B^c) & : & P(A)\\ P(A^c\cap B) & P(A^c\cap B^c) & : & P(A^c)\\ .. & .. & & \\ P(B) & P(B^c) & & \end{bmatrix} $$ ...


2

Similar to above, I’ve wargamed this one in the past and come to the the simple conclusion that the currency and local equity return are informative about the probability of default. Defaults are not typically informative about currency risk, because the currency typically jumps (on the USDCCY basis in EM) in the “crisis”, well before any default actually ...


1

Let us denote with $r_f$ the yield of the 10 U.S.Treasury strip and $r_{A}$ the yield of the risky bond issued by XYZ Inc. We denote with $p$ the cumulative default probability, with $P$ the bond face value, with $R$ the recovery rate and with $T$ the bond maturity. In the absence of arbitrage, we have $$ \dfrac{(1-p)\times FV+p \times R \times FV}{ \left(1+...


1

For an in-homogeneous Poisson process, the intensity process $\lambda_t$ is assumed to be deterministic. More generally, we can define $\tau$ to be the first jump time of a Cox process, or a conditional Poisson process (see Chapter 6 of the book Credit Risk). We assume that $t_0=0$ is the valuation date. Then the intensity process $\lambda_t$ can be ...


1

Take a look at the Altman Z Score, sounds like it is what you are looking for - https://en.wikipedia.org/wiki/Altman_Z-score


1

Collateral imperfections: the CVA cover the expected exposure in the event that the counterparty defaults. When the trade is collateralized and subject to variation margin. This exposure will come only from the imperfection of the collateral. Because posting and receiving collateral actually has a cost, usually the collateral agreement will be a threshold ...


1

No, you cannot. If you had a pre-existing model that had been validated and used these variables, then yes you could, but you cannot calculate a probability from one data point and no other source of information. Subjectively, the short run probability is small as there is massive coverage of short term debt. Unless there is a hidden liability, it is ...


1

Note that Altman Z-Scoring model is calibrated on a sample many years ago. Therefore, a discrimination with these specific values for the coefficients is quite arbitrary. In that situation I think there are 2 options Option 1: Use the Altman's calibrated Z-Score as an indicator Suppose that you have a sample of $N$ private companies, where $D$ of them have ...


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