a. Describe thefeature setFICO score, LTV at origination and vintage (FICO_orig_time, LTV_orig_time, and orig_time) and outcome variable mortgage lo

1. Data-description

a. Describe thefeature setFICO score, LTV at origination and vintage (FICO_orig_time, LTV_orig_time, and orig_time) and outcome variable mortgage loan rate (Interest_Rate_orig_time)

b. Form ten classes using deciles or self-defined boundaries for the feature set and visualize the average mortgage loan rate (Interest_Rate_orig_time) per class. You may consider using the 'if...then...' statement and make assumptions if you can not form ten distinct classes. Interpret your findings.

2. PD modelling

a. Estimate a basic credit risk model for mortgage default probabilities (PD) (you may choose a logit or a probit model). Include the feature set. Compute the estimated PD for all mortgage loans and periods. Plot and compare the average probability of default and default rate over time and over each feature (four charts). Provide your code, output for the model and interpret the output.

b. Estimate the PD model again by including a transformation for every variable of the feature set that results in a better model accuracy. You may use splines, polynomial terms or other transformations (chapter 6 of textbook may help). Compute the estimated PD for all mortgage loans and periods. Plot and compare the average probability of default and default rate over time and over each feature (four charts). Provide your code, an output for the model, the plots and interpret the output. Explain the reason for your transformation

b. Compare the accuracy of two models from sub-questions 2A and 2B. Present and explain your findings with regard to model accuracy?

3. Mortgage rate modelling

a. Estimate a linear regression model to predict loan rate. Include the feature set from 2A. Plot and compare the average model implied and observed loan rate over time and over each feature category (four charts). Provide your code, output for the model and interpret the output. [6 marks]

b. Suggest two additional features that you think can explain for mortgage loan rate. Explain the rationale (relation to LGD).

c. What should be the appropriate interest rate charged for a borrower with the following features LTV_orig_time=80, orig_time=20, FICO_orig_time=570? Include all your assumptions. [5 marks]

4. Bank capital allocation

Compute the Basel capital ratio for all mortgage loans and periods using the internal ratings based approach. Assume correlation at 15%. PDs should be inferred from question 2A and LGDs are 90%. The exposures at default is standardised to one unit. Plot the average capital ratio by time in one chart. Provide your code, plots and analyse the output.

5. Loan Pricing Interface

Draft a dashboard application for loan pricing and loan payments for interest and principal over time: define inputs (e.g., feature, loan amount), calculations and outputs: mortgage loan rate and payments over loan lifetime (interest, principal and total payments) in a single output chart