4

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 repaid. Economically speaking, equity is a call option on the asset value $A$ with strike price equal to the liability $L$, the formula for which is $$ E=AN(d_1)-...


4

It is actually that you forgot your $1 - R$ in formula (2) :) The index survival curve is defined similarly to the tranche's : $Q\left(t\right) = 1 - \mathbb{E} \left[L\left(t\right)\right] = 1 - \left(1 - R\right)\mathbb{P}\left(\tau < t\right)$. Hence, your formula for the 0-100 tranche survival curve does coincide with the index'. That history of loss ...


3

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. If you look at the 10y yield of the German bunds, these are negative 60 bps as of this morning. The ECB deposit rate is negative 50 bps: from the fact that the ...


3

I assume that you calculate ECL in the context of IFRS9 -correct? market practice often follows the following appraoch: estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your lifetime estimate (e.g. one marginal PD value for each year of the life of your exposure) in the average of the economic cycle. But for IFRS9 provisioning you have ...


2

To answer your question in the commentary above: IFRS 9 requires each financial instrument to be measured individually


2

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 can ask the question "is it really necessary"? If the accuracy greatly improves then whether the extension is considered complex or not I suspect that for ...


2

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 difficult to estimate. (2) A multi-period model is required for z so that you can use the PIT PDs in IFRS9. Using Kalman filter and Basel estimates of asset ...


2

what happens if such probability differs from those implied by CDS spreads? I would imagine there is an arbitrage opportunity there but don’t know what it would look like in practice Bonds vs. CDS is known as 'basis'. If you think it's an arbitrage, I suggest you look at what happened to basis during the GFC. C.f. https://chairegestiondesrisques.hec.ca/wp-...


2

In accordance with IFRS 9, risk provisions must be recognised immediately and are booked immediately.It can then be reversed later if necessary.


1

There are many ways to get physical PD, some much simpler and less data-intensive than others. If you are really required to jump through all the hoops in IFRS 9, then the books The New Impairment Model Under IFRS 9 and CECL by Jing Zhang (Moody's) and IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS ...


1

IFRS 9 requires a bank to have a probability of defaut (PD) and a loss given defaut (LGD) and other models. I looked at Tiziano Bellini IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS and it helped me understand what's being done. I also plan to look at Jing Zhang The New Impairment Model Under IFRS 9 ...


1

Simplistically, CDS = implied probability of default * loss given default. For one year maturity, you can assume flat CDS term-structure, therefore constant PD. Choose LGD (usually 50%), and you can back out the implied PD: PD = CDS / LGD. You could use Poisson process to model the PD, but I think the simple model above is a sufficient approximation. If you ...


1

That is really extensive question. I am no longer part of CVA desk, but I'll answer on this question, based on my experience. So, let's take a look at your first question. The CDS is a credit derivative, which price demonstrates a spread (sometimes with a multiplier) between bond/debt/protected asset buyer and seller, and it can be interpreted as a ...


1

traditional credit rating uses a set of macro and micro factors (country of incorporation political stability, economy, etc. ) and assigns subratings via a set a scorecards, based on the company's specifics, the final rating being an analyst consensus and essentially an aggregation of the subratings. this is updated when some inputs change (e.g. new annual ...


1

I think what you are calling marginal PD is simply the intra year PD. PD usually refers to the 1-year default probability, so if the default time is denoted by $\tau$ then $$ PD = \Bbb P (\tau \leq 1 \ \text{year}). $$ What you are refering to as marginal PD is the probability that you default within a shorter period of time, e.g. one month ($n = 12$) or ...


1

Failing an analytic answer I would use Newton's method as a quick and dirty numerical iterator: You can rearrange to: $$ (1-\rho) \left (\Phi^{-1}(LGD.DR) - \Phi^{-1}(DR) \right ) + \Phi^{-1}(PD) - \Phi^{-1}(PD.LGD) = 0$$ which given you have fixed DR, LGD and $\rho$ is essentially: $$K + \Phi^{-1}(PD) - \Phi^{-1}(PD.LGD) = f(PD) = 0$$ Newton's ...


1

There is a bit of stuff here so I will incrementally add details if there are any questions. The analysis is pretty much done as in Appendix K from Hull, J. (2012). Risk management and financial institutions,+ Web Site (Vol. 733). John Wiley & Sons. Python imports: import numpy as np import pandas as pd from scipy.optimize import brentq TABLE ...


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