cmbs ppt.pdf
Transcript of cmbs ppt.pdf
-
7/27/2019 cmbs ppt.pdf
1/23
Mortgage Backed Securities
Jesse Laeuchli, Paul Romine, Katherine Reid, HuiFang
-
7/27/2019 cmbs ppt.pdf
2/23
Introduction to MBS Valuation
-
7/27/2019 cmbs ppt.pdf
3/23
Mortgage Backed Securities
A security backed by
monthly mortgage
payments Is an important sector
of the bond market $468.9 billion
Need to price security
18%
8%
36%
17%
16%
Municipal Sec.Treasury Sec.Fed. Agency DebtMBSAsset Backed Sec.Corporate Debt
Figure 1. Percentages of each security in the
Debt Market in 2006
http://www.bondmarkets.com/story.asp?id=98
-
7/27/2019 cmbs ppt.pdf
4/23
Basic MBS Cash Flow Homeowners make monthly
payments of principal and
interest at the mortgage rate.
The service retains a portion of
the interest components of each
monthly payments as the
Monthly servicing fee.
The pass-through rate is themortgage rate net of the
servicing rate.
Homeowners
Service
Investors
Mortgage Rate
Pass-through Rate
-
7/27/2019 cmbs ppt.pdf
5/23
MBS ValuationKey Idea:The price of any security can be written inThe price of any security can be written in
terms of the net present value (NPV) of its discountedterms of the net present value (NPV) of its discounted
cash flows under the risk neutral probability measure.cash flows under the risk neutral probability measure.
Where
d(t) : Discounting Factor, available from market.
C(t): Payment at time t.
Q: Risk-Neutral Measure.
0 0
( ) ( ) ( )M M
Q Q
t t
P E PV t E d t C t= =
! " ! "= =# $ # $
% & % &' '
-
7/27/2019 cmbs ppt.pdf
6/23
Interests
tax
property
Casualty
insurance
Principal
Prepayment
Monthly Payment
WhereWhere
SP(tSP(t): Scheduled Payments): Scheduled Payments
TPP(t): Total Principal PaymentsTPP(t): Total Principal Payments
INT(tINT(t): Interest Payments): Interest Payments
PRIN(tPRIN(t): Scheduled Principal Payment): Scheduled Principal Payment
PP(t): Principal PrepaymentsPP(t): Principal Prepayments
C(t) =C(t) =SP(tSP(t) +) +PP(tPP(t))
SP(tSP(t) =) =PRIN(tPRIN(t)) ++INT(tINT(t))
TPP(tTPP(t) =) =PP(tPP(t) +) +PRIN(tPRIN(t),),
-
7/27/2019 cmbs ppt.pdf
7/23
How to Value MBS?
Observation: Cashflow C(t) is interest-rate
path dependent.
Questions:
1. What is the Cashflows of MBS?
2. How to predictthe Interest Rate ?
Interest rate models!3. How to predictthe prepayment Behavior?
Prepayment models!
-
7/27/2019 cmbs ppt.pdf
8/23
Interest Rate Modeling
-
7/27/2019 cmbs ppt.pdf
9/23
Pricing Along One Path
Zero-Curve Interest Rate Models
Prepayment Model
Realized Forward-Rate
Predicted Cashflow
SMM(t)
0( ) ( ) ( )
N
i tPV t d t C t
=
=!C(t)
d(t)
-
7/27/2019 cmbs ppt.pdf
10/23
IR Model Hull-White ModelImplement Hull-White Model via Trees
( ) ( ( ) ( ) ( )) ( ) ( )dr t t t r t dt t dW t ! " #= $ +
-
7/27/2019 cmbs ppt.pdf
11/23
IR ModelLibor Market ModelArbitrage-Free Market Models
-
7/27/2019 cmbs ppt.pdf
12/23
Prepayment Model
-
7/27/2019 cmbs ppt.pdf
13/23
Prepayment Terminology
Where
Q(t): Fraction of Mortgage that has not been prepaid.
SMM(t): Fraction of pool prepaid during month t.
1
( 1) ( )( )( 1)
( ) (1 ( ))t
n
Q t Q t SMM tQ t
Q t SMM n=
! !=!
= !"
Key Idea:The survival factorQ(t) links MBS cash
flow
with prepayments models.
-
7/27/2019 cmbs ppt.pdf
14/23
Prepayment Model--Cox ModelPrepayment is governed by a hazard function h(t)
( )
0( ) ( )v t
h t h t e!
=
Where
h0(t): baseline hazard function.
v(t): is a vector of explanatory variable for prepayment.
Notice:
h(t) is calibrated by historical data.
v(t) is functional of interest rates.
SMM(t) = h(t) dt
-
7/27/2019 cmbs ppt.pdf
15/23
Probability of Prepayment
Figure 5. Example Prepayment Probability
Coxs proportional hazard specification
-
7/27/2019 cmbs ppt.pdf
16/23
Numerical Example and Results
-
7/27/2019 cmbs ppt.pdf
17/23
Numerical Examples
Mortgage Description:
1 Million 30y mortgage with 8.5% mortgage rate
and 7.25% coupon rate.
Model Input:Model Input:
1.1. Interest Rate Models (Libor Market Model)Interest Rate Models (Libor Market Model)
1.1 Zero Curve1.1 Zero Curve
1.2 Forward Rate Covariance Structure1.2 Forward Rate Covariance Structure
1.3 Instantaneous volatility function.1.3 Instantaneous volatility function.2.2. Prepayment Models.Prepayment Models.
3.3. OASOAS
-
7/27/2019 cmbs ppt.pdf
18/23
Scheduled PaymentsC(t) =PRIN(t)+INT(t)
-
7/27/2019 cmbs ppt.pdf
19/23
Cashflow with PrepaymentC(t) =PRIN(t)+INT(t)+PP(t)
-
7/27/2019 cmbs ppt.pdf
20/23
Monte Carlo Simulation Results The model
demonstrate good
converged rate.
Able to predict value
of security.
Figure 6. Histogram of MBS Net Present Value
-
7/27/2019 cmbs ppt.pdf
21/23
Questions?
-
7/27/2019 cmbs ppt.pdf
22/23
Cash Flow with Prepayments
'( ) ( ) ( 1)
'( ) ( ) ( 1)
'( ) ( ) ( 1)
'( ) ( '( ) '( )) ( )
'( ) ( ) ( )
SP t SP t Q t
PRIN t PRIN t Q t
INT t INT t Q t
PP t BAL t PRIN t SMM t
BAL t BAL t Q t
= ! "
= ! "
= ! "
= " !
= !
Let SP(t), PRIN(t), INT(t), BAL(t) be the corresponding
quantities with prepayments
Qestion: How to compute SMM(t)?
Answer: History repeats!
-
7/27/2019 cmbs ppt.pdf
23/23
CashFlow without Prepayment
( )
( ) 1
( ) 1
12
( )1
(1 )( )
1
( )1
R t
R t
N
R t
N
WACG
GSP t
U
G UINT t
U
GUPRIN t
U
+
+
=
=
!
!
=
!
=
!
Where,WAC: Wighted Average Coupon Rate
U =1/(1+G): Monthly Discouting Factor.
R(t) = N t: Remaining Loan Terms.