# Questions tagged [transition-matrix]

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### Through-the-cycle rating transition matrix

Suppose we know the observed transition matrix for annual migrations between credit ratings, $T_{ij,t}$, for $N$ years. How is the through-the-cycle (TTC) transition matrix defined? Sometimes the ...
146 views

### Long term average of transition matrix

Some companies publish historic yearly/quarterly transition metrics for credit rating transitions such as the "Credit Rating Transition and Default Study 2021" by Kula and Bourin from Scope ...
43 views

### Transition probabilities of a stochastic volatility model

I have a stochastic volatility model for commodity price which follows an AR(1) process: ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1) σt − μ = ρσ(...
83 views

### Strange calculation for Credit risk [closed]

One of the measures to quantify credit risk is to calculate the Expected loss, which is typically quantifies as $EL = EAD \times PD \times LGD$ However, I have come across a somewhat strange ...
148 views

### Transition Matrix Operation in Stoikov's Micro Price Paper

Sasha Stoikov's paper provides an interesting finite state approach to modeling the mid. It makes good sense to me except one property. On page 7 of the linked paper, G^1(x)=\left(\sum_s\mathbf{Q}^{...
1 vote
189 views

### Observed rating migration matrix to derive the generator matrix

I am doing some reading on the derivation of credit rating migration/transition matrices and probability of default term structures. I understand that a homogeneous Markov chain can be either discrete-...
3k views

### Calculation of the Transition matrix for Credit rating

Let say, I have Cumulative default rates for various credit rating as below - Given this, how can I calculate the typical ...
1 vote
322 views

### Mapping FICO score to PD or Moody's Rating

I need to analyze the risk of a fund with various types of credits, such as consumer, student, and real estate. These categories all have FICO credit scores. I need to assess the risk of the fund ...
161 views

### Developing Markov Transition Matrix

I’m working with historical credit performance data and would like to build a transition matrix to predict defaults and delinquencies. I can model the transition between states (ie current - ...
1 vote
126 views

### Evaluating Fama French 3 factor model Using Fama Macbeth

Hi Can someone please explain me how the cross sectional calculation can be done. For an example, I'm having a vector like this. Vector 1: This is the vector where all the excess returns for n ...
1 vote
228 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 ...
238 views

### Fitting transition matrices in R by solving for coefficient

I'm using various matrices to impute a fitted transition matrix for credit ratings by solving for a variable [S]. Essentially the idea is to determine a base matrix and stress matrix to compare to a ...
538 views

### Deriving credit spreads or migration matrices from prob of default

How do I derive credit migration/transition matrices or spreads from default probability? May you please provide references, or do you know what type of articles or authors to find?
770 views

Consider a credit rating system consisting of three credit states, A, B and D (default) with the following annual credit transition probability: T = [0.7 0.2 0.1;0.2 0.5 0.3; 0 0 1]. For a company ...
2k views

### Scaling of a transition matrix

I am working on a ratings transition matrix and I wondered how people scale it down to shorter time periods (although one should more or less stick to the estimation period i know). It is clear that ...