Credit Neural Network with Neural Designer

Credit Neural Network
with Neural Designer
This presentation file is prepared in accordance with
the text book
“Credit Neural Network with Neural Designer”
Website : https://sites.google.com/site/quanrisk
E-mail : quanrisk@gmail.com
Copyright © 2019 CapitaLogic Limited

Declaration
 Copyright © 2019 CapitaLogic Limited.
 All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
 Authored by Dr. LAM Yat-fai (林日辉),
Director, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.
2Copyright © 2019 CapitaLogic Limited

Outline
 Data preparation
 Classical regressions
 Monotonic neural network
 Continuous response network
 Credit neural network
 Shadow credit rating
 LGD of residential mortgages

What is research?
 There is a result
 Theory
 Which factors cause this result?
 How increases and/or decreases in these factors
impact the result?
 Testing
 Does the theory work in real life scenarios?

Financial research
 Response variable (y)
 To be explained and then estimated
 Explanatory variables (x1, x2, x3, … , xN)
 Independent
 Individually impacts the response variable
 Collectively sufficient to explain the response variable
 Random noise
 Impact but immaterial to the response variable
 1 2 3 Ny = f x ,x ,x , ... ,x + Random noise

Data preparation
 Outliers
 Relevancy
 Inter-dependency
 Randomization
 Consistency
 Sampling
Copyright © 2019 CapitaLogic Limited 6
Example 1.1

Outliers
 Smallest 1% value of the variables
 Largest 1% value of the variables
 To exclude outliers
Example 1.2

Relevancy
 Between the response variable and an
explanatory
 Quantified by the Spearman’s ρ
 Smaller t-statistic and larger p-value suggest
weaker relevancy
 To exclude irrelevant explanatory variables
Example 1.3

Inter-dependency
 Between any two explanatory variables
 Quantified by the Spearman’s ρ
 Larger Spearman’s ρ suggests stronger inter-
dependency between two explanatory variables
 To drop one of the inter-dependent
explanatory variables
Example 1.4

Randomization
 For a continuous response variable, order the
records randomly
 For a categorical response variable, order the
records randomly for each category of the
response variable
Example 1.5

Consistency
 Consistent variables
 Cover a similar range
 Increase in an explanatory variable
=> Increase in the response variable
while holding other explanatory variables fixed
 More effective and efficient for computer
implementation
Example 1.6

Consistent transformation
12
Consistent variable
Value of the variable - Average of the variable
=
Standard deviation of the variable
Spearman's ρ between the variable
× Sign
and the response variable
 
 
 

Inverse consistent transformation
13
Value of the variable
= Consistent variable
× Standard deviation of the variable
Spearman's ρ between the variable
× Sign
and the response variable
+ Average of the variable
 
 
 

Sampling
 For a continuous explanatory variable
 Training data set
 No. of explanatory variables × 15 or
 1% of all records, which ever is more
 0.5% of all records, which ever is more
 For each value of a categorical explanatory variable
 1% of all records, which ever is more
 0.5% of all records, which ever is more

Outline

Simple linear regression
 Explanatory variable (x)
 Sufficient to explain the response variable
 Random noise
 Linear relationship
 Increase in one unit of the explanatory variable always increases the
same level of response variable; or
 Increase in one unit of the explanatory variable always decreases the
same level of response variable
0 1y = a + a x + Random noise

Polynomial regression
 Explanatory variable (x)
 Sufficient to explain the response variable
 Random noise
 Advantage
 Increase in the order of polynomial will increase the fitness
 Disadvantage
 Increase in the order of polynomial may introduce over fitting
2 3 N
0 1 2 3 Ny = a + a x + a x + a x + ... + a x + Random noise
Example 2.1
Example 2.2

Multiple linear regression
 Independent
 Random noise
 Normally distributed with constant standard deviation
 Independent
 Linear relationship
 Holding other explanatory variables fixed
 Increase in one unit of an explanatory variable always increases the same level of response variable; or
 Increase in one unit of an explanatory variable always decreases the same level of response variable
0 1 1 2 2 3 3 N Ny = a + a x + a x + a x + ... + a x + Random noise
Example 2.3

Probit transformation
19
   
   
2
Probit
-
-1
1 τ
Probistic = exp - dτ
22π
Probistic = Φ Probit 0,1
Probit = Φ Probistic - ,+

 
 
 
 


Probistic regression
 Either 0 or 1
 Independent
 Consistent
 Random noise
 
0 1 1 2 2 3 3 N NProbit = a + a x + a x + a x + ... + a x + Random noise
Probistic = Φ Probit
y = 0 if Probistic < 50%
= 1 if Probistic 50%
Example 2.4

Probit transformation

22
Maximum likelihood method
 
   
 
0 1 1 2 2 3 3 N N
1 1 1
1 2 3
1 0 0
U 1 2
0
3
Probit = a + a x + a x + a x + ... + a x
Probistic = Φ Probit
L = Probistic × Probistic × Probistic
× × Probistic × 1 - Probistic × 1 - Probistic
× 1 - Probistic × × 1 - Probisti 
     
     
   
0
V
1 1 1
1 2 3
1 0 0
U 1 2
0 0
3 V
c
Mazimize ln(L) = ln Probistic + ln Probistic + ln Probistic
+ + ln Probistic + ln 1 - Probistic + ln 1 - Probistic
+ ln 1 - Probistic + + ln 1 - Probistic

Outline

Monotonic neural network
 To release the limitations of multiple linear
regression
WITHOUT
 Introducing complex mathematics
 An extremely simplified version of neural
network
 The entry level of artificial intelligence, machine
learning and deep learning

Requirements of
monotonic neural network
 Consistent
 To be explained and estimated
 Consistent
 Random noise
 1 2 3 Ny = f x ,x ,x , ... ,x + Random noise

Monotonic: Black Scholes model
Explanatory variable Change Call option value
Stock price
↑
↑
Strike price ↓
Volatility ↑
Risk free rate ↑
Time to maturity ↑

Monotonic: Merton’s model
Explanatory variable Change Credit quality
Value of equity
↑
↑
Value of liabilities ↓
Volatility of equity ↑

Not monotonic
x1 x2 y
+
↑
↑
- ↓
1 2y = x x + Random noise

Implementation of a neural network
 Variables from theory and/or experience
 A response variable
 A set of explanatory variables
 Prepare samples
 Training : Testing = 3 : 1
 Set up the neural network
 Train the neural network with training data set
 Calculate values with the neural network
 Assess the in sample accuracy with the training data set
 Assess the out sample accuracy with the testing data set
 Use the neural network to conduct estimation
 Assess the monotonicity with scenario analysis to verify the theory

Network structure
Explanatory
variables
Response
variable
Neurons
30
y
Example 3.1

Optimization
 For each neuron k
 Response variable
 Sum of squared error
 Find a set of as and bs to minimize the SSE
31
 
 
 
k k k k k k
0 1 1 2 2 3 3 N N
k k k N
0 1 2 3 N
2
n =Φ a + a x + a x + a x + ... + a x
y est. = Φ b + b n + b n + b n + ... + b n
SSE = y - y est.

No. of as and bs
 No. of nodes
 N explanatory variables
 N neurons
 One response variables
 Each neuron
 N + 1 as
 N + 1 bs
 Total number
 (N + 1)2
 Including irrelevant or dependent explanatory variable will
waste a lot of computing power

Advantages of
 Higher predictive power
 Minimum structural assumption
 Consistency
 Simple network structure
 Single neuron layer
 No. of neurons = No. of explanatory variables
 Moderate computing power
 Robust to irrelevant and/or dependent explanatory variables at a cost
of computing power
 Can be easily applied to most financial analysis
 Particularly suitable for marginally decreasing response variable
 For example, PD

Disadvantages of
 Rely on theory and/or experience to identify
explanatory variables
 May incorporate the effect of random noise
during training
 No straight forward mathematical formulation
 More samples

Outline

Variables and samples
 y
 Explanatory variables
 x1, x2, x3
 Sufficient no. of samples
Example 4.1

Create a neural network

Import training data
Example 4.1

Train the neural network
Example 4.2

Conduct estimation
Example 4.3

Testing
 Estimate y with the training and testing data
sets
 Compare with the historical response variable
 Calculate the error
41
y est.
Absoulte percentage error = - 1 × 100%
y

Accuracy matrix
42
% error < Count Percentage
50% 184 92%
30% 176 88%
10% 126 63%
5% 58 29%
3% 36 18%
1% 10 5%
Total 200 The larger the better

Estimation
 Given a set of explanatory variables without
response variable
 Use the neural network to estimate the ys
Example 4.4

Monotonicity analysis
 Baseline scenarios
 All explanatory variables set to
 The medians
 The averages
 The maximums
 The minimums
 While fixing other explanatory variables
 Vary one explanatory variable from the minimum to the
maximum
 Conduct estimation
 Plot response variable vs explanatory variable
 Repeat for other explanatory variables
Example 4.6

Example 4.7

Exception
 Violation of monotonicity
 The theory and/or experience need to be reviewed
 Inter-dependency among explanatory variables
 Too much random noise
 Response variable insensitive to an
explanatory variable
 The explanatory variable may be irrelevant
 Remove the explanatory and re-build the neural
network

Outline

Merton’s corporate default model
 Market’s view of credit quality can be derived
from observable
 x1 = Market value of equity
 x2 = Book value of liabilities
 x3 = Volatility of equity

Example 5.1
Example 5.2
Example 5.3

 Coded PD of the listed companies
 0 for survival and 1 for default
 x1, x2, x3

Testing
 Conduct estimation with the training and
testing data sets on the coded PD
 Use the neural network to estimate a PD
 If PD < 50%, then a bad borrower
 If PD > 50%, then a good borrower

Accuracy matrix
52
Match ? Count Percentage
Yes 180 90%
No 20 10%
Total 200
The more Yes
the better

Estimation
the coded PD
 Use the neural network to estimate the PDs
 If PD < 50%, then a bad borrower
 If PD > 50%, then a good borrower
Example 5.4

Outline

Merton’s corporate default model
 Market’s view of credit quality can be derived
from observable
 x1 = Market value of equity
 x2 = Book value of liabilities
 x3 = Volatility of equity

Example 6.1
Example 6.2
Example 6.3

Shadow credit rating
 The idea of using credit ratings from major
credit agencies to derive a relationship
between credit rating and explanatory
variables
 Assume that the credit ratings are largely
accurate

 Credit rating
 x1, x2, x3

Testing
 Estimate the probabilities of credit ratings with
the training and testing data sets
 Select the credit rating with the highest
probability
 Map the credit rating to the rank

Accuracy matrix
60
Variation Count Percentage
0 152 76%
1 42 21%
2 4 2%
3 2 1%
Total 200
The more 0 variation
the better

Estimation
credit rating
 Use the neural network to estimate the
probabilities of credit ratings
 Select the credit rating with the highest
probability
Example 6.4

Outline

LGD of collateralized lending
 Factor impacting the LGD
 Outstanding loan amount
 Current value of collateral
 Drift of collateral value
 Volatility of collateral value
 x1 = Loan to value ratio
 x2 = Drift of collateral value
 x3 = Volatility of collateral value

Example 7.1
Example 7.2
Example 7.3

 Credit rating
 x1, x2, x3

Testing
 Estimate the LGD with the training and testing
data sets

Estimation
LGD
 Use the neural network to estimate the LGDs
Example 7.4

Deep learning
 Many explanatory variables
 Many layers of neurons
 Several response variables
 Can handle very complex relationships
 Non-monotonic relationships
 Periodic relationships
 Require huge computing power

Deep learning neural network
Explanatory
variables
Response
variables
Layers of
neurons
69
y

Credit Neural Network with Neural Designer

Recommended

Recommended

More Related Content

Similar to Credit Neural Network with Neural Designer

Similar to Credit Neural Network with Neural Designer (20)

More from crmbasel

More from crmbasel (20)

Recently uploaded

Recently uploaded (20)

Credit Neural Network with Neural Designer