16
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How to compute the implied probability of default from a CDS spread?
Risk-neutral default probability implied from CDS is approximately $P=1-e^\frac{-S * t}{1-R}$, where $S$ is the flat CDS spread and $R$ is the recovery rate.
The CDS Spread can be solved using the ...
14
votes
How to compute the implied probability of default from a CDS spread?
I believe the answer can be further improved for all those being directed here by google after 3 years.
A common way to model the default probability is by the hazard rate. As @Bob correctly mentions, ...
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10
votes
Accepted
Interest rate implied probability of default
You can use the "credit triangle" which states that the (annualised) credit spread $S$ equals the annualised probability of default $p$ times the loss given default LGD which equals par minus the ...
- 2,137
8
votes
Accepted
Recovery Rates in CDS valuation
Apparently, you refer to this passage from Prof John C. Hull (11th edition, 2021):
It's confusing because Hull is referring to the market conventions before the "Big Bang". This is no ...
- 12k
5
votes
CVA - Where does the default probability (PD) come from?
"Debt issuer default risk" and "counterparty risk" are very similar. From Risk magazine:
Counterparty Risk
The risk that a counterparty to a transaction or contract will default (...
- 7,999
5
votes
Accepted
Debt seniority and probability of default
A CDS contract has a "reference entity" (obligor, bond issuer) and a "reference obligation" (the specific bond that needs to default, rather than a tier). Read https://www.isda.org/...
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4
votes
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Calculating probability of default with no recovery
Let $\tau$ be the default time, $\lambda$ be the constant hazard rate, and $T=1.0$ be the bond maturity. The value of the defaultable zero-coupon bond is given by
\begin{align*}
D(0, T) &= e^{-rT}...
- 21k
4
votes
Accepted
Pricing homogeneous Basket Default Swap
Let $\tau_{(1)} = \min(\tau_1, \ldots, \tau_K)$ be the first-to-default time. Moreover, for $1< m \le K$, let
\begin{align*}
\tau_{(m)} = \min\left(\tau_k: k=1, \ldots, K, \tau_{k} > \tau_{(m-1)}...
- 21k
4
votes
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Is marginal probability of default the same as conditional probability of default?
Based on your definition, they are certainly not the same. Generally, the marginal default probability is the probability that the default happens in a given time period, such as $[t, t+\Delta]$, that ...
- 21k
4
votes
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Reproduce CDS Index Default Probability via Tranche [0,100] Probability
It is actually that you forgot your $1 - R$ in formula (2) :) The index survival curve is defined similarly to the tranche's : $Q\left(t\right) = 1 - \mathbb{E} \left[L\left(t\right)\right] = 1 - \...
- 2,570
4
votes
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Estimation of Default Probability using Merton's model
As you see in the third equation on that Mathworks page, the Merton model postulates that the value of equity equals the value on a residual claim on a company's assets after the creditor has been ...
- 6,425
4
votes
Survival probabilities starting from CDS spreads
OK, here is a simplified demonstration:
Before we consider swaps, let us consider very simple bonds. Suppose that you have a choice of two zero-coupon bonds. A riskless one costs 95 and is certain to ...
- 12k
4
votes
Quarterly Survival rate given there is a Quarterly Probability of Default
It helps to get some intuition on all the terms.
Point-in-Time (PiT) Probability of Default (PD) is a probability that the counterparty will default in a specific time-interval.
I will denote the ...
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3
votes
Accepted
Conversion between physical and risk-neutral default probabilities
I'm no expert on this topic but here's my two cents. Hopefully if I'm wrong someone will correct me.
From the 2 relations you wrote, we see that
$$ DD_q = -N^{-1}(P) - \lambda R \sqrt{T} $$
or ...
- 14.5k
3
votes
Accepted
Cumulative vs marginal probability of default
The question sounds like a conditional probability problem. However, note that, for conditional probability, people will generally say if survived to or conditional on. Here it says that survived in ...
- 21k
3
votes
PD and LGD for ECL calculations needs to be time dependent?
I assume that you calculate ECL in the context of IFRS9 -correct?
market practice often follows the following approach:
estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your ...
- 13.6k
3
votes
Bond prices and probability of default
Let's start with the "safest" bonds in the world, and work our way down the credit quality curve. In Europe, the safest and virtually "credit-risk free" bonds are the German Bunds. ...
- 5,998
3
votes
Beginner's resources on copulas and impact of correlation on loan defaults?
At the risk of arming you to create the next quant-apocalypse...
The statement that the expected loss does not depend on correlation is typically the result of modelling a portfolio as a sum of ...
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3
votes
Quarterly Survival rate given there is a Quarterly Probability of Default
Just to add to the above answer, if $\tau$ is the default time of an entity, we have
$$P(\tau>t-1) =: SP_{t-1}$$
as the definition of survival probability beyond time $t-1$ (where $t$ and $t-1$ are ...
- 5,008
3
votes
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Assessing Credit Rating Agencies
There are many papers.
Here are some random examples:
Many of the papers under https://www.michaeljacobsjr.com/research-papers/
http://dx.doi.org/10.2139/ssrn.1466710 Ralf Elsas, Sabine Mielert. ...
- 12k
2
votes
Girsanov theorem and default rates in bond credit rating
Suppose I give you objective probabilities $\mathbb{P}(S_T \geq K)$ of an equity finishing above a certain level $K$ at a future time $T$ (or in your case a survival probability in the form of default ...
- 14.5k
2
votes
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LGD/PD Databases
Re LGD: you can look at Mark-iT for ISDA Credit Event Auction settlements, here's a link actually
http://www.creditfixings.com/CreditEventAuctions/fixings.jsp
Obviously these will give recoveries as ...
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2
votes
Accepted
What relevance might the Modigliani-Miller theorem have for weight of evidence?
I understand your question to be, "Does the Modigliani-Miller theorem have any relevance for forecasting the probability of default based upon debt to equity ratios?"
Not really.
The Modigliani-...
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2
votes
Is it possible to sell protection on own asset with CDS?
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 ...
- 16.6k
2
votes
Objective measure of highly leveraged firms using Debt-to-EBITDA ratio
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 ...
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2
votes
Accepted
Probability of default: issuer vs volume weighted
If there are 10 issuers and one defaults this year, the issuer weighted probability of default is 0.1. But if the one issuer that defaults is one with a larger than average amount of debt outstanding,...
- 10.9k
2
votes
PD and LGD for ECL calculations needs to be time dependent?
You are building a model - the question you are asking is a trade off between accuracy and complexity.
If the accuracy only improves in a minor capacity and the extension is considered complex you ...
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2
votes
CreditRisk+ spreadsheet implementation
you can try this on waybackmachine:
https://web.archive.org/web/20000817021426/http://www.csfb.com/creditrisk/
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2
votes
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Use of PIT vs TTC PD in a Merton one-factor model
The first equation is already a PIT PD if $\displaystyle PD_{i}$
is substituted by TTC PD. The challenges of using this model are:
(1) $\displaystyle \rho _{i}$, the asset correlation, is very ...
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