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Net Portfolio Value Model for Mortgage Prepayment

NPV Model for Mortgage Prepayment. Contents. OverviewDefinition of prepaymentPrepayment risk Calibration of NPV modelSeasonalitySeasoningInterest rate dependence Validation ConsistencyTest of predictive power. NPV Model for Mortgage Prepayment. Definition of Prepayment. What is mortg

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Net Portfolio Value Model for Mortgage Prepayment

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    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?

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