Questions tagged [default-probability]

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14 views

How do I create Stress scenario to compute point int time Probability of Default using Vasicek Single Factor model? [closed]

I have GDP data as the single macroeconomic factor from 2009 to 2018 and have forecasted for 5 years till 2023. Using these forecasted GDP I can compute PIT PD using the equation: ๐‘ƒ๐ผ๐‘‡ ๐‘ƒ๐ท=๐‘((๐‘^(...
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1answer
20 views

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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18 views

Individual Credit Risk Data - Probability of Default

Given the current coronavirus-induced financial crisis and the possibility that it evolves in an economical crisis trough Companies (See: Credit Is the Scariest Market to Watch, Not the Dow or S&P)...
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31 views

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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1answer
57 views

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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1answer
92 views

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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1answer
83 views

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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2answers
76 views

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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1answer
145 views

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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69 views

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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1answer
176 views

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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17 views

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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56 views

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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73 views

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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60 views

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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51 views

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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2answers
140 views

CDS, default probability and bond price

When we calculate the implied default probabilities from CDS, can we use that information to price bonds? I am getting familiar with Fixed Income. I saw textbooks using implied default probabilities ...
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54 views

Extracting Risk Neutral Default Probabilities using Option Adjusted Bond Prices

I am currently in a project trying to quantify default risk premia for US Corporate Bonds. The data I have consists of bond prices, and other information (i.e. YTM, OAS, Effective Duration, Maturity ...
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1answer
94 views

PD for ECL modelling

I am trying to understand the interrelations between the marginal, cumulative and conditional PDs (Probabilities of Default) when modelling ECLs (Expected Credit Losses). My current understanding is ...
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2answers
216 views

Portfolio - Default Probability

Suppose we want to identify the frequency of default on a portfolio with a 1000 loans. In the independence case, each firmโ€™s default process follows a Bernoulli distribution with parameter $p = 0.01$. ...
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40 views

How to convert a vector of bonds ZC Spreads into default spreads

If we consider a set of bonds issued by a given entity that are quoted on the market, one can get for each of those bonds a ZC spread on top of reference swap curve (say the bonds are in USD and so we ...
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49 views

Gaussian copula: contract price

The hazard rates for A and B are 1% and 2% respectively. A contract pays you $1 if A defaults earlier than B. What is the correlation that minimizes the price of the contract? I have not studied the ...
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1answer
155 views

Risk-return ratio using ML default probability

I have access to a very large bond database (>20m rows) where 50% of the set are matured bonds for which a dummy variable identifies whether the bond defaulted or not. The remaining 50% are 'live' ...
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1answer
730 views

Deriving default probability from CDS spread via stripping

I am currently trying to derive the cumulative probability of default from a CDS spread where the LGD is 30% and there are quarterly premiums including the accrued premium. ...
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3answers
244 views

How to estimate market based PD and LGD for small enterprises?

I am estimating CVA/DVA for derivatives... How to estimate PD and LGD (or RR) based on market data for the small enterprises, if there is no external rating for them and they don't have bonds or ...
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1answer
459 views

Probability of default: issuer vs volume weighted

Some probability of default are issuer-weighted and some are volume-weighted. I don't understand what this means. I had a look into Moody's documentation available here: https://www.moodys.com/sites/...
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1answer
59 views

Forecasting default rates using a macroeconomic model

I am trying to forecast corporate default rates using macroeconomic data. I have a few explanatory variables (all the variables are explained in figure 2), which range from 2000 to 2017. On this ...
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1answer
726 views

CVA - Where does the default probability (PD) come from?

Some authors use CDS from the market to derive the implied default probability (from a risk-neutral point of view). I wonder: how exactly does a CDS reflect counterparty risk? Let me put an ...
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68 views

How to determine the default probability of a county in a bond that is not in its native currency?

Disclaimer: This post is cross posted in here also. Consider the following case: Country P uses the currency Euro and gives p percent interest on a one year bond issued in Euro. Country Q uses the ...
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1answer
583 views

credit risk - marginal default probability

I have been working on an assignment trying to calculate marginal/conditional probability of default. Using a logistic regression framework, I was able to compute the 12-month unconditional PD for ...
2
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1answer
82 views

Objective measure of highly leveraged firms using Debt-to-EBITDA ratio

I am looking for some kind of guidance what is generally considered a high or low ratio of Debt-to-Earnings before interest, tax, depreciations and amortisations (EBITDA). In a recent article by The ...
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1answer
46 views

Heuristic (or algorithm) for calculating a risk premium, given a probability of default and a “minimum” profit margin (expressed as a yield)

Assuming that I have means of determining and calculating the following metrics: Risk (i.e. probability*) of a default to a particular borrower as P Profit margin of X% The profit margin is taken to ...
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55 views

Quantitative and regulatory aspects of portfolio integration in IRB credit portfolios

Say bank A buys a credit portfolio "B" (e.g. corporate loans or retail mortgage, ...) from bank B. Bank A fulfills the the requirements of CRR (capital requirement regulation) for its existing ...
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2answers
444 views

Merton model for Probability of Default - What liabilities?

In Merton structural model for credit risk (74), the company's Assets and Liabilities are used to imply the default probability of the firm. At the end, we don't need to know the assets value, and ...
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1answer
1k views

From quoted spread and coupon to upfront, and vice versa : which recovery rates and when?

Echoing the following question : Markit recovery rates : assumed vs real I would like to have a confirmation on my understanding on the matter. Markit provides data for CDS, namely, for tenors ...
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92 views

PD validation in the low/no default setting

The topic of this question is the validation as prescribed in the Basel N ($N \ge 2$) framework. The task is given the probability of default $p_k$ for $K$ rating classes at time $t$ and the outcome ...
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1answer
113 views

Is it possible to sell protection on own asset with CDS?

Is it possible for a company to sell protection on their own assets or own country bonds by CDS? The company can buy protection on those assets, but how about selling? I suppose it can not sell. Is ...
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1answer
114 views

Simplifying an expectation function of default time and rates

I have the following expectation to calculate : $$ \mathbf{E}\left[ e^{\int_{t_0}^{\tau} r_s ds} \mathbf{1}_{\{\tau < T\}}\right] $$ More precisely, I want to show that : $$ \mathbf{E}\left[ e^{\...
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1answer
809 views

Conversion between physical and risk-neutral default probabilities

In the simple Merton structural credit risk model, the physical default probability is given by: $$ DD_p = \frac{\ln(A / D) + (\mu -0.5\sigma^2)T}{\sigma \sqrt{T}} $$ $$ P=N(-DD_p) $$ Assuming that ...
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1answer
73 views

What relevance might the Modigliani-Miller theorem have for weight of evidence?

Suppose in computing weight of evidence based on financial ratios of some bank, one finds that their debt ratio and equity ratio have largely (you pick how large I guess) differing weights of evidence....
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2answers
74 views

Problem of PD estimation [closed]

Why is small number of defaults is a problem in case of PD estimation? What are the consequences? Can you recommend notes, books, etc about the topic?
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177 views

What is the probability of ruin of a Geometric Ornstein-Uhlenbeck process?

I would like to calculate the probability of ruin (or, default), i.e. $$\text{Pr}(\tau<T),$$ where $\tau$ is the default time and $X_t$ follows the Geometric Ornstein-Uhlenbeck (O-U) process $$...
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668 views

Survival Probability and Hazard Rate Function

I'm currently reading the article written by David X.Li "On Default Correlation: A copula Function Approach". I'm deepening my interest in subprime mortgage crisis. In the introduction of the paper ...
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194 views

Three-state Markov Chain: Credit rating question

Consider a credit-rating system, with two solvency states (A & B) and a default state (D), and assuming recovery rate and interest rate are 0%. The one year credit spread for an A-rated company ...
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459 views

Altman Z-Score model for PD calculation [duplicate]

I am approaching you with one important for me question. I have a task to calculate probability of default for our clients. I used an Altman Z-Score model to calculate the Z-Scores for each client. ...
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161 views

Price of a Bond-Call option in the defaultable framework

I would like to compute the price for a Call option written on a defaultable bond as underlying. Suppose you have the following dynamic under the risk free measure $\mathcal{Q}$ for the interest rate: ...
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1answer
435 views

Which interest rate to choose to estimate a CDS default probability?

As you know, with basic assumptions default probability could be calculated by $$\text{CDS Spread} = p \cdot \frac{1-RR}{1+r}$$ Does that make sense to use 5 Year CDS Spread with 5 year Generic ...
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0answers
96 views

Portfolio diversification on default risk

A portfolio of 13 different companies have loans. Company $i$ default on their loan with probability $p_i$ and survive with prob $q_i=1-p_i$. Let $Y_i=1$ denote default. Question: How could I get to a ...
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1answer
181 views

LGD/PD Databases

I am trying to compare LGD/PD for Banks and other financial institutions using different approach thank Merton. Are there any publicly available data on which I can build? Thanks.
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4answers
667 views

Is exposure at default the same thing as the limit amount on a loan?

In Credit Risk terminology, is the Exposure at Default(EAD) the same thing as the total Credit LIMIT amount on the Loan? Because if Bank gives a loan with a limit of 10,000$ and the borrower has a ...