Questions tagged [default-probability]

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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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201 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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2k views

A model to stochastic hazard rate and CDS spread term structure

I'm interested in the term structure of CDS spread. It's known that the Market CDS rate (fair CDS spread or T-maturity spread) of a CDS contract initiated at $s$, maturity $T$ and recovery function $...
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91 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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3answers
332 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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188 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: ...
2
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0answers
116 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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63 views

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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1answer
116 views

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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0answers
28 views

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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0answers
37 views

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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0answers
53 views

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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36 views

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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188 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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95 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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71 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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0answers
45 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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57 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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0answers
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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0answers
123 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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209 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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51 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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59 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 ...
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0answers
63 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 ...
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0answers
2k views

How to calculate Probability of Default from Survival Probability

I would calculate Probability of Default from Survival Probability. I want to know how they are related. This is how I think they are related: ...
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17 views

Variable transformation for probit regression model

I am trying to understand a credit rating model which is used in my company to assess company customers with large exposures. This model is provided by Moody's and assigns grades (similar to Aaa, Aa1, ...
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0answers
29 views

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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24 views

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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149 views

How to convert PIT PD to TTC PD

I am currently trying to estimate TTC PDs from PIT PDs and I am looking for methods of conversion. I have a data set containing loans that defaultet or not. For each loan there is an application FICO ...
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38 views

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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128 views

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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37 views

Concavity of Cumulative Accuracy Profile curve

I am writing my thesis for the default probability estimation in low default portfolios. One way to estimate the probability of default is from the Cumulative Accuracy Profile (CAP) curve (Marco Van ...
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21 views

Financial models under the defprobstrip() command in Matlab 2020a

what is the financial theoretical model below - defprobstrip() - hazardrates() - survprobs() contained in https://www.mathworks.com/help/fininst/examples/...
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37 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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64 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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840 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 ...