Questions tagged [default-probability]
The default-probability tag has no usage guidance.
64
questions
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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):=\...
0
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41 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
82 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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0answers
42 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 ...
0
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1answer
42 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 ...
0
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2answers
154 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 firm’s default process follows a Bernoulli distribution with parameter $p = 0.01$. ...
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0answers
38 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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0answers
37 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 ...
3
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1answer
137 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' ...
1
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1answer
257 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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134 views
Probability of Default from Altman Z-score
I know how to calculate the PD using the Merton Model, Logit or Monte Carlo Simulation, but how do you go about calculating it from Altman's Z-score? I've read somewhere that it can be done by mapping ...
2
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3answers
124 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 ...
1
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1answer
199 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/...
2
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1answer
55 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 ...
3
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1answer
432 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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0answers
66 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 ...
2
votes
1answer
404 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
66 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
43 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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0answers
50 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 ...
0
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2answers
329 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 ...
0
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1answer
911 views
From quoted spread and coupon to ufront, and inversely : 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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0answers
76 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 ...
3
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1answer
110 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 ...
3
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1answer
106 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 :
$$ \mathbf{E}\left[ e^{\...
5
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1answer
622 views
Conversion between physical and risk-neutral default probabilities
In the simple Merton structural credit risk model, the physical default probability is given by:
$$
DD_p = \frac{\ln(A / D) + (\mu -0.5\sigma^2)T}{\sigma \sqrt{T}}
$$
$$
P=N(-DD_p)
$$
Assuming that ...
0
votes
1answer
61 views
What relevance might the Modigliani-Miller theorem have for weight of evidence?
Suppose in computing weight of evidence based on financial ratios of some bank, one finds that their debt ratio and equity ratio have largely (you pick how large I guess) differing weights of evidence....
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2answers
60 views
Problem of PD estimation [closed]
Why is small number of defaults is a problem in case of PD estimation? What are the consequences? Can you recommend notes, books, etc about the topic?
6
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0answers
171 views
What is the probability of ruin of a Geometric Ornstein-Uhlenbeck process?
I would like to calculate the probability of ruin (or, default), i.e.
$$\text{Pr}(\tau<T),$$
where $\tau$ is the default time and $X_t$ follows the Geometric Ornstein-Uhlenbeck (O-U) process
$$...
0
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0answers
493 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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0answers
173 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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0answers
318 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.
...
2
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0answers
148 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:
...
0
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1answer
397 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 ...
2
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0answers
83 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
172 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.
1
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2answers
405 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 ...
3
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1answer
3k views
Interest rate implied probability of default
Is there an equation or rule of thumb to determine the probility of default for a loan with a specific interest rate?
Let's say, a bank offers a company a loan with an interest rate of 6%, by which ...
2
votes
1answer
198 views
Girsanov theorem and default rates in bond credit rating
Default rates are kind of probabilities, right?
Is it possible to use the Girsanov theorem in that context? For example if we have a table of real world probabilities, could we use the Girsanov ...
1
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2answers
77 views
How exactly are correlated defaults used/analyzed?
I've read a lot about correlate defaults but I can't seem to understand how they're used practically in a portfolio theory setting. Suppose I have two (?) companies, X and Y, and historic default ...
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2answers
94 views
What is the probability of defaulting in year 2?
I was asked this question the other day, but it's been years since I've done this work.
If the probability of a company to default in a year is $8\%$, what is the probability that it will default in ...
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0answers
47 views
Using Put Volatilities to Estimate Firm Leverage/Credit Risk
This paper by Hull, Nelken and White uses implied volatilities in structural credit risk models to back out a market-implied leverage ratio. CreditGrades has a similar implementation using equity ...
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0answers
53 views
Valuation Models for Bank Credit Default
What approaches exist for calculating a fair price for a credit default swap for a bank? Most of the traditional valuation models are geared towards industrial firms. Are there any theoretical ...
2
votes
1answer
134 views
Pricing homogeneous Basket Default Swap
Consider a basket with $K=10$ names. Default times of the names,
$\tau_k$, are i.i.d. random variables with distribution $P(\tau_k \leq
t) = 1 - e^{-\lambda t}$. Suppose that each name in the basket ...
0
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2answers
103 views
Business cycles and missing data
For many probability of defaults models in credit risk it is needed to use data observed from a "full" business cycles. Usually a business cycle is defined as a recurring (not necessarily periodic) ...
5
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1answer
4k views
Is marginal probability of default the same as conditional probability of default?
I'm thrown off by the term marginal probability of default. I've seen it defined by some authors as synonymous term for conditional probability of default
conditional probability of default: ...
1
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1answer
14k views
Cumulative vs marginal probability of default
I understood the cumulative (aka unconditional) probability of default to be the probability of defaulting in a given period eg: between years 1 and 5. Further $\pi_{cumulative} = 1-e^{-\lambda*t}$ ...
3
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1answer
427 views
Calculating probability of default with no recovery
Given two methods to calculate the 1 year conditional probability of default of a zero coupon bond, I've come up with slightly different but close results.
From my approaches below, is it reasonable ...
3
votes
2answers
546 views
Extracting Default probability from a single CDS
I have to find the CDS's default probability using the simplest Poisson Process (intensity constant).
I'm wondering how to get this estimate if I have only a CDS with maturity 5years.
If I had ...
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0answers
57 views
Alternatives to CDSs for default term structure?
The CDS market seems to be drying up, funding&liquidity issues are now prevalent over credit, so other sources for default probabilities are needed.
What else is commonly used to obtain a ...
