# Questions tagged [default-probability]

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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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### 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 ...
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}_\... • 141 1 vote 1 answer 159 views ### 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/... 0 votes 0 answers 28 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 ... • 1 1 vote 1 answer 264 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/... • 347 1 vote 0 answers 34 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 ... • 11 0 votes 0 answers 45 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 ... • 211 1 vote 1 answer 106 views ### 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 ... 1 vote 1 answer 138 views ### 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 ... • 275 1 vote 1 answer 277 views ### 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... • 347 1 vote 1 answer 220 views ### 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-... • 211 1 vote 0 answers 51 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$is the ... • 211 0 votes 0 answers 142 views ### How to apply Kalman Filter to GDP data? Once reverted the Merton/Vasicek formula I could compute the$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)$The main issue is to ... 3 votes 3 answers 399 views ### Bond prices and probability of default We learn in Finance 101 that the price of a bond is the present value of future cash flows. There is no mention of default risk. Still, bond prices move each day, without a change in the payment ... • 555 1 vote 0 answers 55 views ### Longer / Shorter period loss I am struggling on I think a quite simple issue. Let's take a portfolio of 100 loans. If we assume they are independent, each loan’s default is a Bernoulli with parameter$p=0.01$over a certain time ... 4 votes 1 answer 749 views ### 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 ... 3 votes 2 answers 361 views ### 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 ... 1 vote 0 answers 37 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 ... 2 votes 1 answer 82 views ### 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 ... • 21 0 votes 0 answers 65 views ### 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 ... 2 votes 1 answer 200 views ### 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 ... • 2,046 0 votes 1 answer 141 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'... 0 votes 0 answers 128 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 ... 2 votes 1 answer 407 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 ... 1 vote 1 answer 216 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)) $$PD \approx \... • 1,386 1 vote 1 answer 159 views ### Linking PD and LGD I am trying to solve the equation for PD but struggling to bring it to the LHS. Any ideas as to how I can do that?$$ LGD = \frac{\Phi \left [ \Phi^{-1}(DR) - \frac{\Phi^{-1}(PD)-\Phi^{-1}(PD\cdot ... • 11 2 votes 3 answers 204 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 ... • 21 1 vote 1 answer 1k 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 ... 2 votes 1 answer 963 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 ... 2 votes 1 answer 219 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(... • 1,132 1 vote 0 answers 27 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 ... • 183 3 votes 0 answers 120 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: ... • 57 1 vote 0 answers 254 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(... • 11 1 vote 0 answers 118 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):=\...
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 ...