Créer une présentation
Télécharger la présentation

Télécharger la présentation
## Net Portfolio Value Model for Mortgage Prepayment

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**2. **NPV Model for Mortgage Prepayment Contents Overview
Definition of prepayment
Prepayment risk
Calibration of NPV model
Seasonality
Seasoning
Interest rate dependence
Validation
Consistency
Test of predictive power

**3. **NPV Model for Mortgage Prepayment Definition of Prepayment
What is mortgage prepayment?
Early repayment of a mortgage by a customer
Types of prepayment
Cyclical prepayment : financial/rational
arbitrage for an economic interest
linked with the market rates levels
Structural prepayment : statistical/irrational
unavoidable phenomenon without economic interest
depends on customer behaviour

**4. **NPV Model for Mortgage Prepayment Causes of Prepayment
Structural payments:
geographic mobility (home, work, ...)
personal situation change (birth, decease, marriage, divorce, ...)
sale, cash out, inheritance, ...
Cyclical prepayment:
interest rate level
interest rate type (fixed-rate, adjustable-rate)
burnout, ...

**5. **NPV Model for Mortgage Prepayment Prepayment Risk A hidden option costly for the ALM
interest rate risk for a lender
liquidity risk
Prepayment penalty
legal constraints to limit prepayment penalties (e.g. Scrivener law in France)
lenders competition soft penalty

**6. **NPV Model for Mortgage Prepayment OTS and NPV Model Office of Thrift Supervision (OTS)
established in 1989 following American Savings & Loans debacle
agency of the United States Department of the Treasury
the primary regulator of federal savings associations
issuing ALM reports for the regulator
Net Portfolio Value Model
one of the rare existing regulatory models
explicitly cited in Basel II

**7. **NPV Model for Mortgage Prepayment NPV Model A reduced form model evaluates the probability of mortgage output ?(i,t) of each loan i at each date t
The prepayment rate txRA at date t :
CRD: outstanding balance of loan principle
The probability of mortgage output as the product of three variables :
Seasonality
Seasoning: the age of the loan
Interest rate level

**8. **NPV Model for Mortgage Prepayment Methodology Protocol of five steps:
Calculation of outstanding balance of loan principle
Calibration of the parameters of seasonality by stratification
Calibration of the parameters of seasoning by stratification
Calibration of the dependence of interest rate
Validation : consistency & predictive power

**9. **NPV Model for Mortgage Prepayment Seasonality(1) Sine function with seasonal coefficients :

**10. **NPV Model for Mortgage Prepayment Seasonality(2) Stratification :
To avoid rate effect on seasonal coefficients, we sort the couples (i,t) of loan i and date t in 10 divisions
Prepayment rate by division :
Minimize

**11. **NPV Model for Mortgage Prepayment Seasoning(1) Definition of the relative age variable
For a d-year loan, we normalize the first d-1 years as the first 9 years of a 10-year loan basis
Piecewise affine function with decline :

**12. **NPV Model for Mortgage Prepayment Seasoning(2) Stratification :
Unseasonalized Prepayment rate by division :
Minimize

**13. **NPV Model for Mortgage Prepayment Rate Dependence(1) Market rate perceived by the customer with a delay
choice of interest rate
choice of delay
utilization of moving average
Interest rate evolution

**14. **NPV Model for Mortgage Prepayment Rate Dependence(2) Arctangent function with rate dependent coefficients
Minimize

**15. **NPV Model for Mortgage Prepayment Model Fit

**16. **NPV Model for Mortgage Prepayment Consistency(1) Consistency:
reaction under the hypothesis of interest rate crisis
Scenario 1: interest rate hike before summer 2003

**17. **NPV Model for Mortgage Prepayment Consistency(2) Scenario 2: interest rate hike in 2004
In both cases, the prepayment rate falls sharply and then it stabilises as expected.

**18. **NPV Model for Mortgage Prepayment Predictive Ability(1) A classical method for testing the predictive power
determine parameters on an early period of historical data
observe whether they can describe properly the later data
Prevision on a low interest rate period: 01/2005-05/2006

**19. **NPV Model for Mortgage Prepayment Predictive Ability(2) Prevision on a interest rate rising period:
06/2006-07/2007

**20. **NPV Model for Mortgage Prepayment Conclusion This model describes a credible prepayment comportment with two sharp rate rises in 2003 and in 2005.
Moreover, it can predict the prepayment tendency on a up-rate period as well as a down-rate period.
Note that the NPV model gives the output probability of loan, instead of the prepayment rate directly.
That demands to have an idea of the distribution of the stock at future date t when we want to predict.
The amount of loan to be drawn out from the account from now on to date t may be determined by this model.
We also require to measure the loan flow which will be contracted between the actual date and the estimation date.

**21. **NPV Model for Mortgage Prepayment Thanks for your attention!
Questions?