In the consumer lending space, fintech companies have innovated many aspects of the consumer experience. One of the biggest innovations has been the real-time approval of consumers for installment loans with borrowed cash hitting consumer bank accounts in an expedited and highly satisfying way.

1. Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost
Created by: Salvatore Tirabassi
Document Copyright 2023

2. Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost
In the consumer lending space, fintech companies have innovated many aspects
of the consumer experience. One of the biggest innovations has been the real-
time approval of consumers for installment loans with borrowed cash hitting
consumer bank accounts in an expedited and highly satisfying way.
For those of you not in the business, the loan origination system, as we
often call it, provides all of the capabilities to take a credit shopper and
turn them into a borrower. To drive this positive consumer experience,
fintech lenders rely heavily on real-time credit-scoring processes built into
the loan origination system.
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3. Many fintech lenders have advanced innovations using machine learning and
data science to develop algorithms that provide a consumer risk score
(probability of default) and loan price (interest rate and APR) to the
consumer. These algorithms generally ingest consumer credit and financial
data to discern the risk of a consumer and provide an appropriately priced
installment loan, if possible, given the risk profile.
At the heart of many of these algorithms lies tree-based classification
algorithms such as the XGBoost machine learning model, which seeks to classify
consumers into risk categories based on their credit and financial profiles.
Loan pricing is subsequently determined to generate a profitable loan.
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Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

4. We used this approach in the past, but in a new effort, we decided to
calculate risk and pricing in a manner that aligns more closely to typical
fixed income cash flows. In other words, if a consumer installment loan is a
series of cash flows, why not calculate the probability of default for each
payment and then do a risk adjusted discounted cash flow valuation of the
loan that generates a specified profit regardless of risk?
• In this manner, the loan pricing accounts for the risk of each cash flow and
all loans could be targeted to achieve our profit target with interest rates
increasing as risk increases.
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Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

5. This approach evolved from research that one of our data scientists did when
examining credit risk pricing models and discovered previous academic
research using a survival regression algorithm to predict the payment-by-
payment probabilities of default for the duration of the loan. A survival
regression model is a technique that models the time until an “event” occurs.
This family of models is often used in health-care related analysis, where
“survival” means exactly that – did the subject survive to the next period. In
our case, survival means “no default on payment” in this period, or that the
loan value survives to the next payment.
Document Copyright 2023
Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

6. By taking into account credit and financial factors of the individual
influencing a potential event of default and a probability of the event of
default occurring at payment of the loan, a projected series of default
probabilities is generated for the entire loan duration. This series is
called the “hazard function curve”.
Here, for three applicants, are the hazard function curves (showing the
probability of default at each loan payment) and the survival function curves
(showing the probability of no-default up to each loan payment) for a 36-month
installment loan.
Document Copyright 2023
Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

7. Document Copyright 2023
Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

8. Document Copyright 2023
Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

9. The two figures display the same three applicants: A, B and C, in two ways,
using the cumulative hazard function and the survival function. The higher
the forecasted cumulative hazard curve throughout the months, the lower the
ending survival probability of the applicant.
The Cox Proportional Hazards algorithm is the specific survival regression
method we improved upon to forecast this series of default probabilities
throughout the loan term, as shown in the Hazard Function Curve above. Each
point on this hazard curve represents the likelihood that the borrower will
default on the loan in a specific month, given no default has occurred up to
that point. Similar to other supervised machine learning algorithms, we trained
the Cox Proportional Hazards model on a dataset comprising historical loan
originations, which includes the borrower's financial attributes, loan default
status, and time-to-default labels.
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Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

10. The remaining loan origination process requires only fundamental financial
analysis to price the loan based on the modeled risks. By applying this
resulting default curve to a series of loan payments, we construct a risk
weighted cash flow series for the consumer loan. With that series of expected
value cash flows, we apply interest rate expenses using a forward curve:
In our case, we use the SOFR 1-month forward curve plus our cost of capital
spread. We leave a target variable to flex for our interest margin, which
iteratively solves (we use an optimization function) to reach the targeted Net
Present Value of the loan, which also factors in all origination costs,
servicing costs and capital lent to the borrower.
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Using a Survival Model for Credit
Risk Scoring and Loan Pricing
Instead of XGBoost

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