3. Prepayment Modeling
• Prepayment can happen due to several
reasons
– Low Interest rate , default, selling home to buy a
bigger or smaller one, divorce, natural disasters
that destroys the property
• A prepayment model uses loan charateristics
and economic environment to predict
prepayments
4. • Refinancing, turnover, defaults , curtailment
are four components of prepayment modeling
• These components are modeled separately
and their parameters are calibrated such as to
approximate historical data
5. S curve prepayments
• Modeling the refinancing component of
prepayments starts withan incentive function for
pool or group of loans
• It defines refinancing as a nondecreasing function
of that incentive
• Example of incentive :
• I = (WAC-R) times WALS*A-K
• Where R is the current mortgage rate, WALS =
weighted average of loans size, A = annuity and K
is cost of financing
6. • The logic of the incentive function is to
estimate the PV of dollars gains to the
borrower from re-financing
• CPR modeled as an S function of that
incentive
CPR(I) = T +1/(a+e^-bI)
T = turnover; a and b are the parameters that
are approximated to match the empirical
prepayment behaviour
7. • Good credit, large loan balance, home that
appreciated in price are more likely to
refinance
• Parameters a and b are chosen such that the
all the prepayment behaviour can be captured
8. • Turnover happens when borrowers sell their
home to move to a smaller or big homes,
divorce, or in response to other personal
circumstances
• Defaults
• Curtailment : are partial prepayments
9. MBS Valuation and Trading
• Monte Carlo Simulation
• Tree implementation model assumes cash
flows are path independent whereas cashflow
from burn out model are path dependent
• (the phenomenon of CPR being less
responsive to incentive as pool prepays is
known as burn out)
10. Valuation Models
• Need Interest rate model
• Housing prices model
• Mortgage rate model
• Scheduled cashflows model
• Prepayment model
11. OAS
• Measure of relative value for MBS
• OAS is particularly useful in the valuation of mortgage-
backed securities. In this sense, the prepayment risk is the
risk that the property owner may pay back the value of the
mortgage before it is due. This risk increases as interest
rates fall. A larger OAS implies a greater return for greater
risks.
In the context of an MBS, the embedded option relates
primarily to the borrower's right to refinance the debt at a
lower interest rate. These securities must therefore pay
higher yields than noncallable debt, and their values are
more fairly compared by OAS than by yield. OAS is usually
measured in basis points (bp, or 0.01%).
12. Price Rate Behavior of MBS
• Negatively convex in low rate environment
just like a callable bond
• When rates are high and prepayment is low,
PO is like a zero coupon bond which pays
nothing until maturity and when rates fall, its
value rises dramatically.
• For IO, when rates are high, its like any other
fixed security with fixed cashflows. When
rates fall, interest lives off principal
