Questions tagged [default-probability]
The default-probability tag has no usage guidance.
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Help with simple derivation of probability of credit default
I'm going over a chapter in Hull's Options, Futures, and Other Derivatives and am stuck on how the probability of default is derived. Here's the image of the derivation.
I can follow all of it except ...
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Square root specification of parameters in factor models
The following formulation is from Vasicek and refers to the cond. probability of the loss of a loan (equ. 3 in the reference):
$$p(Y)=\Phi\left(\frac{\Phi^{-1}(p)-\sqrt{\rho}\,Y}{\sqrt{1-\rho}}\right)....
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Estimating default probability if no default in history
I would like to estimate a given country's default probability with a logit regression from macro variables but there was no default in it's history. I was able to calculate the probabilities of ...
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Debt seniority and probability of default
I would like to ask if different debt seniorities ( like senior unsecured bonds and subordinated bonds) have different probability of default?
(Before edited I used debt tiers instead of seniority but ...
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PD estimation methods
Could someone explain me or suggest a good reference how to categorize the PD calculation methods without going to deep in the details?
I learned on riskmanagement lecture, that there are three major ...
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Time series data for probability of default (or credit ratings)
I'm currently investigating potential correlations among ESG ratings and credit ratings; more in particular, i'm trying to understand whether such correlation evolved during the last 20 (?) years, and ...
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Calculation of Total Credit Risk Capital % but seeing lower capital percentage for higher risk band. Is there any correction required?
I am trying to calculate the Total Credit Risk capital % for my learning purpose as given below. Assuming adding 1 single loan with different pds.
i have noticed one point in the table and have two ...
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Quarterly Survival rate given there is a Quarterly Probability of Default
I am trying to calculate the Quarterly Marginal PD. I have calculated it as given in the below image but I am thinking about whether the Survival rate calculation is making sense or not.
The ...
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Mapping bank credit score to PD
I currently work in a bank so I do have some of the required information that is my bank (internal) assigned credit score and the calculated probability of default for every company.
My question is ...
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Default rate short majurity
What is the best way of measuring default rates for a portfolio which contains mostly loans which are either 30, 60 or 90 days term?
Normally I use the following methodology
Look at all loans which ...
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Why does Basel require Pooled PDs?
Since Basel II requires banks to utilize pooled PDs per rating grade / segment, I wonder why exactly. Via a logistic regression you can directly estimate an obligors PD, why the extra step to pool ...
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Beginner's resources on copulas and impact of correlation on loan defaults?
I'm hoping this question is not too banal or off-topic for this forum.
Could you please help me understand / point me towards some resources on the impact of correlation on loan defaults?
First ...
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Generalized Linear Mixed Model (GLMM) for the probability of default of corporates
I work in the financial industry and we want to implement an internal rating model for our clients (think corporates large or mid , banks etc. some listed on an exchange some others not).
We want to ...
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Survival probabilities starting from CDS spreads
How is that possible to get survival probabilities starting from CDS spread?
Could you please provide me with a demonstration?
What is more, is that true that CDS Zero type is necessary so as to get ...
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Marginal default distribution when default intensity is log-normal
I'm interested in the stochastic process followed by the marginal default density $e^{-\int_0^th(s)ds}h(t)$ in the case where the default intensity $h(t)$ follows a log-normal process.
Assuming
$$\...
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Where can I find recent tables with the average cumulative default rates?
I'm mostly interested in Moody's average corporate cumulative default rates, possibly in 2020 or the latest version. I tried to take a look at Moody's website but I am still in trouble. The latest ...
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Measurability of contingent claim in State-variable approach
I'd like to know, if we have the filtrations $\mathbb{F}$ and $\mathbb{G}$ with $\mathcal{F}_t\subset\mathcal{G}_t\subset \mathcal{F}_t\vee \sigma(\eta)$, for $\eta$ being independent of $\mathcal{F}_\...
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Implied funding/repo rates from Credit Default Swaps
One of the differences between a CDS and a bond is the funded vs unfounded nature of the two. Given that is the case, at least some portion of the CDS-Bond basis should be driven by an implied repo/...
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How to compute a zero spread for unexpected loss
I have to discount a cash flows of mezzanine and junior note of NPL's securization, so the discount curve have to include a zero spread for unexpected loss, could you suggest me a proxy to estimate ...
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Calculation of the Probability of Default
I am reading a book from Tiziano Bellini namely IFRS 9 and CECL Credit Risk Modelling and Validation, to understand the default probability calculation (link : https://www.sciencedirect.com/science/...
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Measuring stressed credit risk
What are good ways of measuring stressed credit risk specifically?
I know usually we just "stress" all market conditions, but are there credit-risk specific things we can do?
Or is it just a ...
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Default Probability estimation
Can you please provide some workout references on how to estimate the Default probability for Wholesale portfolio?
How does it defer from Retail portfolio case?
I ...
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Estimation of the probability of default for the expected loss model (IFRS9)
Hey guys I have to do a calculation for my BA. More precisely, I have to determine the expected loss of a company.
For this I need the probability of default.
What options do I have to determine this ...
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IFRS9 - Lifetime Expected Credit Losses (ECL) Probability of Default (PD) - how do they get distributed in quarters?
Let's assume we calculate a Lifetime ECL of 5 years. How do we then distribute the expected losses in each of the following 20 quarters? Do we just divide the lifetime ECL by 20 and calculate the ...
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Probability of Default calculation
I am looking for some good resources with handful of workout examples, on the modelling of the Probability of Default under IFRS9...
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Estimation of Default Probability using Merton's model
There is an explanation of Risk Neutral Default Probability using a Firm's Equity price here - https://www.mathworks.com/help/risk/default-probability-using-the-...
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Estimation of Default Probability from Bond
Typically the formula to calculate the default probability from corporate Bond looks like
$\frac{S}{1-R}$
where $S$ is the ...
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How to apply Kalman Filter to GDP data?
Once reverted the Merton/Vasicek formula I could compute the $PD^{PIT}$ for IFRS9 as
$PD^{PIT}_i(z) = \Phi \left( \phi^{-1}(PD^{TTC}_i) \sqrt{1-\rho_i} + \sqrt{\rho_i}z\right)$
The main issue is to ...
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Bond prices and probability of default
We learn in Finance 101 that the price of a bond is the present value of future cash flows. There is no mention of default risk. Still, bond prices move each day, without a change in the payment ...
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Longer / Shorter period loss
I am struggling on I think a quite simple issue.
Let's take a portfolio of 100 loans.
If we assume they are independent, each loan’s default is a Bernoulli with parameter $p=0.01$ over a certain time ...
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Use of PIT vs TTC PD in a Merton one-factor model
Under one-factor Merton framework, like Basel, you use unconditional PDs as input of the portfolio model and this "unconditional" means it is a TTC-PD.
Given a i-th borrower, the default ...
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CVA Probability of default
I have to estimate CVA for an exotic option. I used Monte Carlo method to price the option with 1000 number of simulation, maturity = 1 year, and 360 time steps. So I have two questions:
I've read in ...
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Definition of defaults via unobserved assets
Sorry if my question is a bit basic. I am considering the default model as used eg in Vasicek (I think this goes back at least to Merton, though) that looks at an unobserved quantity modeling the ...
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A model for probability of credit rating change for a single issuer
I am looking to model the probability of a single issuer upgrading or downgrading it's credit rating at some time using historical data. I have done research and everything I have found so far are for ...
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Credit Migration: Risk [duplicate]
Hi I am given two tables of two tables showing data about fictional corporate business partners and relevant credit risk data – ID, rating, probability of default (PD, defined by rating), loss given ...
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CreditRisk+ spreadsheet implementation
I'm looking for an Excel spreadsheet where the CreditRisk+ model is implemented by means of a simple toy example, like the one the linked paper is referring to. If that spreadsheet is unavailable, I ...
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MATLAB - Probability Default with CDS Bootstrapping
I have not understood which "zerorati" I must use for the bootstrap of the PD from the curve of the CDS spreads. Can you help me please? I consulted O'Kane (2008) and Brigo and Mercurio (2006), but I'...
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Derivation of the 99.9% CI to a 1 in a 1000 year event
Keen to understand how BASEL derived the 1 in a 1000 year event from the CI 99.9%:
The confidence level is fixed at 99.9% (0.999) (i.e. a bank is expected to suffer losses that exceeds its capital ...
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Marginal Probability of Default for Credit Risk
I am working on a model to predict credit defaults. We have worked out PD's of clients using logistic regression.
When calculating the default amount, we have to convert PDs to marginal PDs. The ...
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PDs for negative credit spreads
My question is about credit spreads and the corresponding probability of default (PD).
One of the most simple relations between credit spreads and PDs is (see e.g. ch7 in Malz(2011))
$$
PD \approx \...
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Linking PD and LGD
I am trying to solve the equation for PD but struggling to bring it to the LHS. Any ideas as to how I can do that?
$$ LGD = \frac{\Phi \left [ \Phi^{-1}(DR) - \frac{\Phi^{-1}(PD)-\Phi^{-1}(PD\cdot ...
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PD and LGD for ECL calculations needs to be time dependent?
I'm studying the implementation of an expected credit loss (ECL) model. I have encountered a complication. Do I need to calculate a probability of default (PD) and loss given default (LGD) with a time ...
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Implied probability of default (CDS spread)
After some googling, I have made some progress but not enough to come to a conclusion, so here we go:
Given that the CDS spread of a counterparty is 100bp (flat across time) and that the risk free ...
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PD calibration using Bayes formula
When calculating ECLs for loans under IFRS 9, one of the requirements is that the PD estimates have to be Point-in-time ($PD_{PIT}$) rather than through-the-cycle ($PD_{TTC}$).The setting is as ...
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Reproduce CDS Index Default Probability via Tranche [0,100] Probability
The tranche survival probability up to time $t$ between attachment $K_1$ and detachment $K_2$ is defined as
$$Q(t,K_1,K_2) \quad=\quad 1 - \mathbb{E}[L(t,K_1,K_2)]$$
with tranche loss function
$$L(...
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Are Muni REVENUE bonds secured or can the local gov. use the revenues for other purposes not paying the bond holders if its going bankrupt? [closed]
Municipal bonds are of two kinds: GO (General Obligation) Bonds or Revenue Bonds. My question on Revenue Bonds is: are the revenues from the specific project secured or can the local government use ...
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Using transaction data to predict default of the customer
I am trying to build a prediction model that utilize the huge transaction database of all the customers of a bank. My dataset currently looks like this:
...
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Normal default probability vs forward default probability/conditional default
is the diagram correct in calculating foward PD(conditional default) ? Or should the formula be
Probability of default = probability of survival x forward PD
Which of this is equal to marginal PD(...
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Credit spread model
Let $c(t,T):=-\frac{1}{T-t}[\mathrm{ln}(P_1(t,T))-\mathrm{ln}(P_0(t,T))]$, with:
$c$ measure of how a company is prone to fail;
$P_0(t,T):=e^{-r(T-t)}$ price of no-defaultable bond.
$P_1(t,T):=\...
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Poisson distribution and counting process
Let $\begin{Bmatrix}
N_t
\end{Bmatrix}_{(t\in[0,T])}:=\mathbb{I}_{(\tau \leq T)}:=k, \forall t \in [\tau_{k}\leq \tau_{k+1})\sim \mathrm{Po}(\lambda_{t}:=\int_{0}^{t}\lambda_{s}ds<+\infty)$ a ...
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