Loss Given Default

Developing a Loss-Given-Default (LGD) model

Bela Koch

March 26, 2024

Table of contents

• Introduction
• The Dataset
• Modelling
• The Champion Model
• Alternative Models
• The Application
• Conclusion
• Questions?

Introduction

Theory

Definition of LGD:

• Loss Given Default (LGD): loss that arises in default event
• LGD commonly expressed as ratio of loss on exposure to the amount outstanding at default
• Basel Capital Accord: LGD should measure economic loss, i.e. include all potential costs and benefits of default event
  • example of costs: administrative costs, legal costs, time delays, …
  • example of benefits: interest/penalties for delay, commissions, …
  • all cash flows discounted at time of default event

• definition (slide)

• the ratio of the loss on the exposure to the amount of outstanding exposure at the time of default event

• we might think that we cannot loose more than we lose more than we have given as credit or event profit from the default, which is why the lgd should be between 0 and 1

• mention economic loss

Theory (cont.)

Definition of Default:

• use real default for modeling LGD: default due to financial problems or insolvency of obligor
• important: use same default definition for modeling LGD and PD
• after default event, various actions can take place:
  • cure: defaulter pays back all outstanding debt
  • restructuring: recovery plan, e.g. extension of loan maturity to reduce monthly payments
  • liquidation: bank takes possession of collateral assets and sells it

• alternatives: obligor might be late by accident or there could be technical issues in the transfer of the money

• default definition: use for example that the obligor is 60 days in delay of the payment for both LGD and PD

The Dataset

The Dataset

• synthetic data
• mortgage portfolio of one bank
• 1453 observations in total of defaulted customers
• each row in data set is one independent loan

variable	data type	description
customer	categorical	type of customer (private or corporate)
loan_amount	numerical	loan granted to customer in CHF
real_estate_type	categorical	type of mortgage (single family house, apartment, office building)
mortgage_collateral_mv	numerical	market value of mortgage collateral at time of origination
additional_collateral_type	categorical	type of additional collateral (retirement account, cash account, none)
additional_collateral_mv	numerical	market value of additional collateral at time of origination
lgd	numerical	(non-economic) loss given default in percent of loan granted

• synthetic data: Gabor and Paolo created the data set completely themselves and did not modify any real life data set

• we can think of the data set as all defaulted loans of one single bank

target variable

• lgd: (non-economic) Loss Given Default
• continuous variable from 0 to 0.69 (theoretically up to 1)
• 57.67% of defaulted position did not result in a loss

• right skewed variable with a lower bound of 0

• most default events did not end up in a loss

categorical predictors

• LHS: we have more private customers than corporate customers in the data set

• private customers had either a loan for an apartment or a house while corporate customers only had loans for office buildings

• around 2/3 of customers pledged additional collateral, which is a retirement account for private customers and a cash account for corporate customers

continuous predictors

• again the variables are right skewed

• for all loans, the sum of collateral was bigger than the loan amount

next as the only information we have about the loans are the nominal values and the customer and collateral type, we might want to subset our data set and look at different segments separately

compare segments: loss given default

• here we can see the estimated distribution of LGD if we consider the three real estate types separately

• it seems that for apartments, the loss given default is smaller and more centered near zero, while the LGD for single family houses and office buildings seems to be bigger and more widely distributed

compare segments: recovered value of mortgage collateral

• here I wanted to get a feeling on how much of the loan we can recover by selling the collateral

• therefore I first only considered loans with no additional collateral, therefore the only way to cover the loss is by selling the mortgage

• to do this, I calculated the difference between the loan amount and the loss in nominal value resulting in the amount we can recover in swiss francs

• then, I divided this amount by the market value of the collateral to get a ratio and estimated the density you see in the plot

• interpretation: percentage amount of value of collateral which can be used to cover the loss

• talk about mean and spread

compare segments: recovered value of additional collateral

• here I essentially did the same by looking at the percentage amount of value of the additional collateral which can be used to cover the loss after the mortgage collateral was sold

• here we can see an U shape which I will talk about more in a second

• talk about mean and spread

The true DGP

The loss given default data was modeled as follows:

\[ \text{lgd} = 1-\frac{\text{real estate coll. MV}}{\text{loan amount}} * \text{e}^{-a-bX} - \frac{\text{other coll. MV}}{\text{loan amount}} * y \]

whereby

\[ X \sim \text{N}(0,1)\quad\text{and}\quad y \sim \text{Ber}(p) \]

Parameters \(a\) and \(b\) are fixed but different for client types and real estate types (private apartment, private house, corporate office)

Parameter \(p\) can take one of three different values, depending on the customer type and collateral type (private retirement, private cash, corporate cash)

• at some point Gabor revealed the true data generating process they used to generate the data set

• rest look slides

The true DGP: intuition

\[ \color{grey}{\text{lgd} = 1-\frac{\text{real estate coll. MV}}{\text{loan amount}}} *\mathbf{\color{black}{\text{e}^{-a-bX}}} \color{grey}{- \frac{\text{other coll. MV}}{\text{loan amount}} * y } \]

• \(e^{-a-bX}\in(0, 1]\) reflects the amount of market value which is obtained when selling the collateral
• \(b\) in combination with \(X\sim N(0,1)\) introduces variability in the haircuts between different loans

• let’s gain some intuition on the true data generating process

• maybe think first in nominal terms: explain formula in nominal terms by multiplying loan amount

• look slides

• this is exactly what we can see in the estimated density on slide 12

The true DGP: intuition (cont.)

\[ \color{grey}{\text{lgd} = 1-\frac{\text{real estate coll. MV}}{\text{loan amount}} *\text{e}^{-a-bX} - \frac{\text{other coll. MV}}{\text{loan amount}}} \mathbf{* y} \]

\[ \text{Ber}(p) = y = \begin{cases} 1 & \text{with probability } p\\ 0 & \text{with probability } 1-p \end{cases} \Rightarrow y = \begin{cases} 1 & \text{if (whole) additional collateral can be liquidized}\\ 0 & \text{if none of additional collateral can be liquidized} \end{cases} \]

• here, the Bernoulli variable \(y\) can be either zero or one

• this should reflect that if we can sell the additional collateral, we get its whole market value. this with probability \(p\)

• but, there is a possibility that we get nothing from the additional collateral at all, for example if the customers manages to hide his money or disappears completely with probability \(1-p\)

• notice the distribution in the plots here where I simulated a Bernoulli variable

• we can see this pattern in the estimated density on slide 13

Modelling

What are we trying to model?

Scenario: A customer defaults

Question: How much do we loose due to this default?

\[ loss\,given\,default = \max\biggl(0,\;\frac{loan - Revenue\,from\,selling\,collateral}{loan\,amount}\biggr) \]

Problem: We are forced to sell (potentially) under market value

\[ Revenue\,from\,selling\,collateral = (1-haircut) * market\,value \]

whereby \(haircut\in[0,1]\) is unknown in advance

• loss (max) function: we only consider non-economic LGD, hence we do not consider additional cash flows which might arise in default event and could move LGD below 0 or above 1

What are we trying to model? (cont.)

Let’s define

\[ \beta_1 = (1-haircut_{mortgage}) \quad\text{and}\quad \beta_2 = (1-haircut_{additional\,collateral}) \]

Then, loss given default in our setting is given by

\[ nominal\,lgd_i = loan\,amount_i-\beta_1*mv\,mortgage_i-\beta_2*mv\,additional_i \]

resp.

\[ lgd_i = 1 - \beta_1 * \frac{mv\,mortgage_i}{loan\,amount}_i - \beta_2 * \frac{mv\,additional_i}{loan\,amount_i} \]

The haircuts might depend on the type of collateral

example: an apartment might be sold easier and therefore with less haircut compared to office building (risk driver: liquidity in corresponding market)

at the end: therefore we need a beta for each collateral type

The Champion Model

Two Step Simple Regression Model

Step 1:

Only consider loans of certain mortgage type without additional collateral. Estimate \(\beta_1\):

\[ lgd_i = 1 - \beta_1*\frac{mv\,mortgage_i}{loan\,amount}_i + \epsilon_i \]

Step 2:

Now consider loans of same mortgage type but with additional collateral. Estimate \(\beta_2\):

\[ 1 - lgd_i - \hat{\beta}_1*\frac{mv\,mortgage_i}{loan\,amount}_i = \beta_2*\frac{mv\,additional_i}{loan\,amount_i} + \epsilon_i \]

assumption: \(\beta_1\frac{mv\,mortgage_i}{loan\,amount_i}\) and \(\beta_2\frac{mv\,additional_i}{loan\,amount_i}\) independent

• notice that I do want an intercept in my linear model but it should be fixed to one

• this, because if we do not have any collateral at all, we should loose the whole loan amount and therefore we should have a LGD of 1 or 100%

• and we do this two step process for all real estate types

Step 1: estimate \(\beta_1\) (example for apartment)

\[ 1-lgd_i = \beta_1 * \frac{mortgage\,collateral\,mv_i}{loan\,amount_i} \]

Call:
lm(formula = y ~ 0 + x)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.140193 -0.023305  0.006439  0.028488  0.094793 

Coefficients:
  Estimate Std. Error t value            Pr(>|t|)    
x 0.767774   0.002265     339 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04399 on 226 degrees of freedom
Multiple R-squared:  0.998, Adjusted R-squared:  0.998 
F-statistic: 1.149e+05 on 1 and 226 DF,  p-value: < 0.00000000000000022

• here we can see the regression we run in the first step with apartment as an example

• we get an estimate for beta 1 of about 0.77, which means that we expect to get 77% of the market value when selling the apartment due to a default event

• framed differently, the estimated haircut for apartments is about 23%

Step 2: estimate \(\beta_2\) (example for retirement account)

\[ 1 - lgd_i-\hat{\beta}_1*\frac{mortgage\,collateral\,mv_i}{loan\,amount_i} = \beta_2*\frac{additional\,collateral\,mv_i}{loan\,amount_i} \]

Call:
lm(formula = y ~ 0 + x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.23179 -0.01373  0.01717  0.04128  0.09469 

Coefficients:
  Estimate Std. Error t value            Pr(>|t|)    
x  0.81690    0.02313   35.31 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04532 on 395 degrees of freedom
Multiple R-squared:  0.7594,    Adjusted R-squared:  0.7588 
F-statistic:  1247 on 1 and 395 DF,  p-value: < 0.00000000000000022

• now, let’s look at the second step regression

• we now get a coefficient of around 0.82

• while we can use this coefficient similarly as the coefficient estimated beforehand, the interpretation is now slightly different

• now, we can say that in around 82% of defaulted apartment loans, we get the whole additional collateral to cover the loss and in 18%, this money is not around anymore

Results

percentage from MV	private apartments	private houses	corporate offices
mortgage	0.77 (apartment)	0.73 (single family house)	0.66 (office building)
additional collateral	0.82 (retirement account)	0.87 (retirement account)	0.94 (cash account)

• Interpretation: on average 77% of the market value of the apartment measured at time of origination of the loan can be recovered if the apartment must be sold due to a default

• Differences between the real estate types could be explained by liquidity in corresponding markets (assumption)

• Differences between the additional collateral types could be explained by characteristics of the account used and characteristics of the corresponding obligor

Predict

• predict LGD using \(\hat{\beta}_1\) and \(\hat{\beta}_2\):

\[ \widetilde{lgd}_i = 1 - \hat{\beta}_1*\frac{mortgage\,collateral\,mv_i}{loan\,amount_i} - \hat{\beta}_2 * \frac{additional\,collateral\,mv_i}{loan\,amount_i} \]

• to ensure that the predicted LGD is between 0 and 1, following transformation is done after prediction:

\[ \widehat{lgd}_i = \min(\max(\widetilde{lgd}_i, 0), 1) \]

Evaluation: Portfolio Level

• here we can see the difference between the observed and the estimated LGD over all loans in the sample

• if this difference is negative, we overestimate the true LGD, else we underestimate it

• this plot suggest that we tend to overestimate LGD rather than underestimate it

• but notice that in some cases we drastically underestimated the LGD, in some cases up to 50 percentage points

Evaluation: per real estate type

The realised LGD in CHF for our portfolio was 1174.87 million CHF while we would have estimated a LGD of 1187.62 million CHF for the portfolio using our model, hence we overestimated LGD by 12.75 million CHF.

• let’s take a closer look and analyze if we performed differently for the different real estate types

• it seems that we tend to overestimate LGD for all types but less so for houses and offices as for apartments

• read sentence on slide

• 12 million CHF is about 1% of total LGD in swiss francs

Tweek model coefficients

As a bank we might decide that we prefer to overestimate rather than underestimate the LGD. To check whether we over- or underestimate LGD on average, let’s define \(x\) as the difference between the observed and estimated LGD for given real estate type:

\[ \mu(x) \begin{cases} > 0 & \text{if we underestimate LGD on average}\\ < 0 & \text{if we overestimate LGD on average}\\ = 0 & \text{if we neither under- nor overestimate LGD on average} \end{cases} \] Therefore, let’s test:

\[ H_0: \mu(x) \geq 0 \quad vs \quad H_A: \mu(x)<0 \]

With a p-value of 0.00 we can reject \(H_0\) for apartments, with p-values of 0.06 for single family houses and 0.21 for office buildings, we cannot reject \(H_0\).

• say that mu is the mean of x

• say that we want to reject the null hypothesis

Tweek model coefficients (cont.)

ad hoc modification: decrease the coefficients for single family house and office building by one percentage point each:

percentage from MV	private apartments	private houses	corporate offices
mortgage	0.77 (apartment)	0.72 (single family house)	0.65 (office building)
additional collateral	0.82 (retirement account)	0.86 (retirement account)	0.93 (cash account)

After decreasing the coefficients for single family houses and office buildings and their corresponding additional collateral by one percentage point each, we can reject \(H_0\) for each segment with a p-value of 0.00.

• since we cannot reject the null hypothesis for single family houses and office buldings, I decreased their coefficients by one percentage point

• read sentence below table

Evaluation: ad hoc coefficients

The realised LGD in CHF for our portfolio was 1174.87 million CHF while we would have estimated a LGD of 1293.19 million CHF for the portfolio using our model, hence we overestimated LGD by 118.32 million CHF.

• don’t read sentence

• now we overestimate LGD by around 120 million CHF or by around 10%

Alternative Models

Single Step Simple Regression Model

• First, create single variable for each collateral type with properties

\[ mv\,collateral_i = \begin{cases} mv\,collateral_i & \text{if collateral used for loan of type }i\\ 0 & \text{otherwise} \end{cases} \]

• Then, run following regression:

\[ lgd_i = 1 - \sum_i\beta_i*\frac{mv\,collateral_i}{loan\,amount_i} + \epsilon_i \] - Idea: we get all coefficients of interest in one regression

• read first bullet

• so i have one column for each collateral type which contains the market value of the corresponding collateral if this type of collateral is relevant for the given loan or zero otherwise

• rest of bullets

Single Step Simple Regression Model (cont.)

Call:
lm(formula = I(lgd - 1) ~ 0 + house_collateral + appartment_collateral + 
    office_collateral + retirement_collateral + cash_collateral, 
    data = df)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.20987 -0.06016 -0.01270  0.04014  0.48781 

Coefficients:
                       Estimate Std. Error t value            Pr(>|t|)    
house_collateral      -0.742875   0.006215 -119.54 <0.0000000000000002 ***
appartment_collateral -0.775577   0.004157 -186.57 <0.0000000000000002 ***
office_collateral     -0.665729   0.004440 -149.93 <0.0000000000000002 ***
retirement_collateral -0.751765   0.059018  -12.74 <0.0000000000000002 ***
cash_collateral       -0.883656   0.067523  -13.09 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1053 on 1448 degrees of freedom
Multiple R-squared:  0.9874,    Adjusted R-squared:  0.9873 
F-statistic: 2.268e+04 on 5 and 1448 DF,  p-value: < 0.00000000000000022

• notice that we have now negative coefficients which is only because I set up the regression a bit differently

Single Step Simple Regression Model (cont.)

single step regression:

percentage from MV	private apartments	private houses	corporate offices
mortgage	0.78	0.74	0.67
additional collateral	0.75	0.75	0.88

two step regression:

percentage from MV	private apartments	private houses	corporate offices
mortgage	0.77	0.72	0.65
additional collateral	0.82	0.86	0.93

• running the linear model on different subsamples or with feature engineering (for example by adding polynomials, using (log of) nominal values, dummies, new features such as \(\frac{\text{loan amount}}{\sum\text{collateral mv}}\), …) did not really change the results

• it seems that some of the recovered amount from additional collateral gets attributed to the recovered value of mortgage collateral

• (the errors won’t follow a normal distribution so assumption of linear regression is not satisfied)

• (if we estimate in two steps we disentangle the two dynamics from one another)

Tobit Regression

• assumption: there is an underlying linear model:

\[ loss\,given\,default = \frac{loan - revenue\,from\,selling\,collateral}{loan} \]

• technically, if the revenue from selling collateral exceeds loan amount (which can be the case), loss given default would be negative

• however, the bank won’t receive more than the loan in this scenario (remember: non-economic LGD), hence:

\[ loss\,given\,default = \max\biggl(0, \frac{loan - revenue\,from\,selling\,collateral}{loan}\biggr) \]

• additionally, the bank cannot loose more than it lent to the customer (remember: non-economic LGD)

Tobit Regression (cont.)

• result: LGD is censored with a lower limit of 0 and an upper limit of 1

• Lets define \(y\) as the loss given default without the censoring process

\[ lgd_i = \min(\max(0, y_i), 1) \]

• the tobit regression model accounts for this censoring

• so \(y\) is the output from the true linear model but we only observe the censored LGD

Tobit Regression: Results

Call:
AER::tobit(formula = lgd ~ appartment_collateral + house_collateral + 
    retirement_collateral, left = 0, right = 1, dist = "logistic", 
    data = df[df$customer == "private", ])

Observations:
         Total  Left-censored     Uncensored Right-censored 
           842            617            225              0 

Coefficients:
                      Estimate Std. Error z value             Pr(>|z|)    
(Intercept)            0.93431    0.14793   6.316     0.00000000026894 ***
appartment_collateral -0.81429    0.11954  -6.812     0.00000000000962 ***
house_collateral      -0.72907    0.11746  -6.207     0.00000000053971 ***
retirement_collateral -0.78708    0.14184  -5.549     0.00000002873278 ***
Log(scale)            -2.74016    0.06004 -45.639 < 0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Scale: 0.06456 

Logistic distribution
Number of Newton-Raphson Iterations: 4 
Log-likelihood: -85.26 on 5 Df
Wald-statistic: 100.8 on 3 Df, p-value: < 0.000000000000000222 

• here we can see the output of the tobit regression using a sub sample for private customers

• again the coefficients have a negative sign due to the specification of the regression but they seem to be sort of in the right magnitude

Tobit Regression: Evaluation

Note: on LHS of vertical line are differences for apartments, on RHS for single family houses

• here I plotted the difference between observed and estimated lgd, whereby each point represents the difference of one loan in our portfolio

• if the value on the y axis is positive, we underestimate LGD, else we overestimate LGD

• LHS of the vertical line: apartments, RHS: houses

• more spread in this plots for other models

• when I compared this type of plot for the tobit model and other models, I though i have a great increase in accuracy

• problem: improvement is one sided as we eliminated overestimation -> dangerous

• we could for example change floor to negative value instead of 0 but unintuitive and feels like overfitting

Maximum Likelihood Estimation

• if we have a strong belief in true DGP (or in this project even know it) one might use maximum likelihood estimation (MLE)

• remember the true DGP:

\[ \text{lgd} = 1-\frac{\text{real estate coll. MV}}{\text{loan amount}} * \text{e}^{-a-bX} - \frac{\text{other coll. MV}}{\text{loan amount}} * y \\ \phantom{a} \\ \text{whereby } X \sim \text{N}(0,1)\quad\text{and}\quad y \sim \text{Ber}(p) \]

• using MLE, we would estimate the parameters \(a\), \(b\) and \(p\) of the DGP given the observed data

• using the synthetic data, MLE (should) deliver the best estimation and hence would be a great benchmark

at the end

unfortunately I did not do it

overview of possible models

Source: H. Scheule, D. Rösch, and B. Baesens (2016). Credit Risk Analytics (Measurement Techniques, Applications, and Examples in SAS). Chapter 10.

• here you can see some possible models which can be used for loss given default modeling in general

if enough time (<17:30) maybe ask gabor and simone if they can give some input on what is used in practice

The Application

Demo

Deployed version accessible via:

https://betiko.shinyapps.io/acrm/

Source code available on GitHub:

https://github.com/bt-koch/acrm

Functionalities

Estimation of LGD on single loan level

potential use case: loan officers can estimate LGD for given loan and might only give out loan if LGD is below certain threshold (and might request higher additional collateral from client that LGD falls below the threshold)

Estimation of LGD on simulated portfolio

potential use case: managers can get a feeling on how high expected LGD resp. expected loss might be for \(n\) new loans to decide on how many loans of each type they want to approve

Implementation

.
├── R
│   ├── datahandling.R
│   ├── input_validation.R
│   ├── models.R
│   ├── simulation.R
│   └── utils.R
├── README.md
├── acrm.Rproj
├── calibrated_models
│   ├── corporate_office_building.rds
│   ├── linear_regression.rds
│   ├── private_appartment.rds
│   └── private_single_family_house.rds
├── data
│   └── lgd_dataset.csv
├── server.R
├── test
│   └── test_workflow.R
└── ui.R

most important files are

server.R which handles all the backend logic of this app

ui.R which defines the front end of this app

most of the actual coding is in the R folder which contains functions for handling data, estimate models, and so on

Server Logic

server <- function(input, output) {
  
  observeEvent(input$estimate, {
    ...
  })
}

• in the following few slides I will go through the server logic of the tab were we estimate the LGD on a single loan level

• this observe event function just checks wheter the button to estimate LGD is pressed

Server Logic: get user input

server <- function(input, output) {
  observeEvent(input$estimate, {
    model_input <- input |>
      read_input() |>
      preprocess_data()
    ...
  })
}

• then if the button is pressed, we read the user input and preprocess it

Server Logic: validate user input

server <- function(input, output) {
  observeEvent(input$estimate, {
    ...
    validation_result <- validate_input(model_input)
    
    if (any(lapply(validation_result, function(x) x[["type"]]) == "warning")) {
      ... display warnings in box
    }
    
    if (any(lapply(validation_result, function(x) x[["type"]]) == "error")) {
      ... display errors in box
    }
    ...
  })
}

• using the validate_input function, we can run some checks on whether the input of the user is valid and then can display messages of type warning or errors to the user

Server Logic: hanlde error

server <- function(input, output) {
  observeEvent(input$estimate, {
    ...
    if (any(lapply(validation_result, function(x) x[["type"]]) == "error")) {
      
      output$lgd_estimation <- renderInfoBox({
        valueBox(
          "Calculation not possible",
          "please see error message",
          icon = icon("bug"),
          color = "red"
        )
      })
      
    } else {
      ... predict LGD
    }
  })
}

• if there are errors, we won’t estimate the loss given default and just display an error box

Server Logic: predict LGD

server <- function(input, output) {
  observeEvent(input$estimate, {
    ...
    if (any(lapply(validation_result, function(x) x[["type"]]) == "error")) {
      ... handle error
    } else {
      estimated_lgd <- two_step_estimation_estimate(input) |> 
        cap_prediction()
      estimated_lgd_nom <- estimated_lgd * model_input$loan_amount
      
      output$lgd_estimation <- renderValueBox({
        ... display predicted LGD
      })
    }
  })
}

• if there are no errors, we estimate the loss givend default with the user input

Conclusion

Critical Review

Limitations:

• very simple model (but therefore to interpret)
• for some loans, we underestimate the LGD drastically (up to 0.5)
• tweeking the coefficients could have been optimized (minimize shrinking of coefficients to fall below desired p-value)
• only liquidation event considered, cures or recoveries not included in modeling process
• other sources obligor might use to cover the obligations in default event are ignored
• only non-economic LGD is modeled
• synthetic data (probably) does not reflect all real world dynamics

Critical Review (cont.)

Possible extensions:

• with more information about corresponding mortgage, maybe a more precise estimator for its haircut can be estimated (e.g. region, size, year of construction, etc.)
• with more information about corresponding counterparty, maybe a more precise estimator for the haircut on retirement resp. cash account can be estimated (e.g. age of private client, business model of corporate client, etc.)

Questions?

Thank you for your attention!