Valuing Illiquid Mortgage Products
Valuing Illiquid Mortgage Products
March 9, 2011
Outline US mortgage market Prepayment modeling Inputs of market-implied prepayment model Parameters of prepayment model Methodology
Conventional U.S. Mortgages and MBS Mortgages offered in standardized structures Maturity: 30-year or 15-year Rate: Fixed, ARM, or hybrid ARM Principal payment: amortizing
Prepayable at any time, without penalty Refinancing entails transaction cost
Usually packaged as Agency MBS
3
By Fannie Mae, Freddie Mac, and Ginnie Mae Principal and specified interest passes through to MBS investors
Alternative Approaches to Prepayment Modeling Statistical Model parameters estimated from past experience
Market implied CLEAN™ model* (as below) Parameters are fitted from observed prices of liquid securities in the prevailing environment Illiquid securities are valued with fitted model With adjustment for illiquidity
* Coupled Lattice Efficiency Analysis
How MBS Analytics Got Off on the Wrong Track Early practitioners focused on trends and seasonal patterns of prepayments Statistical approach Effect of interest rates on refis an afterthought
Emphasis on cashflows, rather than on value Similar in spirit to today’s “econometric” models
But the ultimate goal is to determine value Rather than to explain history
Prepayment models should be only a means to an end
JPMorgan Report (2003): “It’s All About Economics” …prepayment models have strayed away from economics and have increasingly relied on fitting data with complicated ad hoc parameterizations… …prepayment behavior of large pools can be explained … through economic incentive …
Parameters of CLEAN™ Prepayment Model Refinancing-driven Transaction cost (% of original principal) Homeowner credit spread (relative to swap curve) Refinancing efficiency (based on option value)
Other prepayment Turnover speed vector Default speed vector
Recovery rate for defaulted mortgages For whole loans and non-Agency MBS
7
Data to Estimate Prepayment Parameters Interest rate environment: Swap curve Swaption implied volatilities Primary mortgage rates
Prices of relevant mortgage products TBA (to-be-announced) prices Including dealer consensus duration and convexity
Dealer specified pool pay-up grid for seasoned MBS For age and loan size
TBA Market Prices
9
Source: Bloomberg
Dealer Duration and Convexity for Fannie Mae 30-yr TBAs Duration
10
Convexity
Dealer model 1
Dealer model 2
Dealer model 3
Dealer model 1
Dealer model 2
Dealer model 3
FNCL 4
4.7
5.2
4.5
-2.1
-2.8
-3.0
FNCL 4.5
3.1
4.2
2.6
-3.3
-3.1
-3.9
FNCL 5
1.3
3.7
1.4
-2.7
-2.5
-2.8
FNCL 5.5
1.2
1.8
1.1
-1.7
-1.4
-2.0
FNCL 6
1.0
1.3
0.6
-0.1
-0.9
-1.3
FNCL 6.5
1.9
2.9
0.5
0.0
-0.4
-1.4
Dealer Specified Pool Pay-up Grid Relative To TBA Prices (7/30/2010) FNMA 30 Yr Coupon
Weighted Average Life (WALA) 20 Months
40 Months
60 Months
80 Months
4.5
2/32
12/32
23/32
36/32
5.0
0
2/32
6/32
16/32
5.5
0
0
11/32
19/32
6.0
1/32
7/32
28/32
44/32
6.5
1/32
0
28/32
46/32
Loan Balance FNMA 30 Yr Coupon
11
Low
Medium
High
4.5
17/32
13/32
7/32
5.0
27/32
18/32
10/32
5.5
46/32
30/32
14/32
6.0
54/32
42/32
20/32
6.5
58/32
46/32
20/32
Sample Prepayment Parameters For Fannie Mae 30-Year 4.50% MBS Transaction cost: 1% of original principal Homeowner credit spread relative to swap curve: 110 bps 30-yr mortgage rate – 10-yr swap – 40 bps call premium
Refinancing efficiency: default distribution (discussed below) Turnover/default speed vector: 9%
Different parameters are used for different MBS coupons 12
CLEAN™ Prepayment Model: Details Basic approach Turnover and defaults modeled using deterministic speeds Refinancings modeled using stochastic interest rate model
Modeling a mortgage As a callable amortizing bond Financial engineer will refinance optimally Others will refinance too late (“laggards”) “Leapers” are rare
Modeling heterogeneous refinancing behavior Divide mortgage pool into 10 buckets according to laggard parameter Use a standard laggard distribution for a new pool
Modeling seasoned pools 13
Fastest refinancing buckets disappear first Automatically accounts for ‘burnout’
CLEAN Uses Two Separate Credit Spreads Homeowner credit spread determines refis Refinance when refinancing option is worth more dead than alive
OAS determines discount factors used for discounting MBS cash flows Credit spread of guarantor Plus market discount for unhedged uncertainty in price
14
Calibration: Straightforward and Intuitive Rarely adjusted Refinancing cost Refinancing efficiency Turnover speed vector Default speed vector
Adjusted monthly Homeowner credit spread Can be refined for specific pools
15
Mortgage Refinancing Efficiency: Refi When Rates Decline by 40 to 70 bps 105
Refinancing Efficiency (%)
.
100
95
90
85
80
1% Cost 2% Cost
75
95% Efficiency 70
65 70
65
60
55
50
45
40
Old Rate - Refi Rate (bps)
35
30
25
20
Option-Based Mortgage Technology Available to Homeowners
Patented option-based Mortgage Refinancing Calculator at www.kalotay.com/calculators 17
17
Why CLEAN™? Realistic, transparent behavior Based on well established financial and economic principles Instead of mysterious mathematical formulas and parameters
Consistent with valuation models for callable bonds and cancelable swaps Calibration is straightforward and intuitive And ridiculously fast Critical for simulation 18
Benchmark Speeds for CLEAN™
19
References Andrew Kalotay & Qi Fu (June 2009), A Financial Analysis of Consumer Mortgage Decisions, Mortgage Bankers Association. Andrew Kalotay & Qi Fu (May 2008), Mortgage servicing rights and interest rate volatility, Mortgage Risk. Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 1, 2008), Optimum refinancing: bringing professional discipline to household finance, Applied Financial Economics Letters. Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 3, 2007), Refunding efficiency: a generalized approach, Applied Financial Economics Letters. Andrew Kalotay, Deane Yang, & Frank Fabozzi (December 2004), An option-theoretic prepayment model for mortgages and mortgage-backed securities, International Journal of Theoretical and Applied Finance. Available from http://www.kalotay.com/research 20
March 9, 2011
Outline US mortgage market Prepayment modeling Inputs of market-implied prepayment model Parameters of prepayment model Methodology
Conventional U.S. Mortgages and MBS Mortgages offered in standardized structures Maturity: 30-year or 15-year Rate: Fixed, ARM, or hybrid ARM Principal payment: amortizing
Prepayable at any time, without penalty Refinancing entails transaction cost
Usually packaged as Agency MBS
3
By Fannie Mae, Freddie Mac, and Ginnie Mae Principal and specified interest passes through to MBS investors
Alternative Approaches to Prepayment Modeling Statistical Model parameters estimated from past experience
Market implied CLEAN™ model* (as below) Parameters are fitted from observed prices of liquid securities in the prevailing environment Illiquid securities are valued with fitted model With adjustment for illiquidity
* Coupled Lattice Efficiency Analysis
How MBS Analytics Got Off on the Wrong Track Early practitioners focused on trends and seasonal patterns of prepayments Statistical approach Effect of interest rates on refis an afterthought
Emphasis on cashflows, rather than on value Similar in spirit to today’s “econometric” models
But the ultimate goal is to determine value Rather than to explain history
Prepayment models should be only a means to an end
JPMorgan Report (2003): “It’s All About Economics” …prepayment models have strayed away from economics and have increasingly relied on fitting data with complicated ad hoc parameterizations… …prepayment behavior of large pools can be explained … through economic incentive …
Parameters of CLEAN™ Prepayment Model Refinancing-driven Transaction cost (% of original principal) Homeowner credit spread (relative to swap curve) Refinancing efficiency (based on option value)
Other prepayment Turnover speed vector Default speed vector
Recovery rate for defaulted mortgages For whole loans and non-Agency MBS
7
Data to Estimate Prepayment Parameters Interest rate environment: Swap curve Swaption implied volatilities Primary mortgage rates
Prices of relevant mortgage products TBA (to-be-announced) prices Including dealer consensus duration and convexity
Dealer specified pool pay-up grid for seasoned MBS For age and loan size
TBA Market Prices
9
Source: Bloomberg
Dealer Duration and Convexity for Fannie Mae 30-yr TBAs Duration
10
Convexity
Dealer model 1
Dealer model 2
Dealer model 3
Dealer model 1
Dealer model 2
Dealer model 3
FNCL 4
4.7
5.2
4.5
-2.1
-2.8
-3.0
FNCL 4.5
3.1
4.2
2.6
-3.3
-3.1
-3.9
FNCL 5
1.3
3.7
1.4
-2.7
-2.5
-2.8
FNCL 5.5
1.2
1.8
1.1
-1.7
-1.4
-2.0
FNCL 6
1.0
1.3
0.6
-0.1
-0.9
-1.3
FNCL 6.5
1.9
2.9
0.5
0.0
-0.4
-1.4
Dealer Specified Pool Pay-up Grid Relative To TBA Prices (7/30/2010) FNMA 30 Yr Coupon
Weighted Average Life (WALA) 20 Months
40 Months
60 Months
80 Months
4.5
2/32
12/32
23/32
36/32
5.0
0
2/32
6/32
16/32
5.5
0
0
11/32
19/32
6.0
1/32
7/32
28/32
44/32
6.5
1/32
0
28/32
46/32
Loan Balance FNMA 30 Yr Coupon
11
Low
Medium
High
4.5
17/32
13/32
7/32
5.0
27/32
18/32
10/32
5.5
46/32
30/32
14/32
6.0
54/32
42/32
20/32
6.5
58/32
46/32
20/32
Sample Prepayment Parameters For Fannie Mae 30-Year 4.50% MBS Transaction cost: 1% of original principal Homeowner credit spread relative to swap curve: 110 bps 30-yr mortgage rate – 10-yr swap – 40 bps call premium
Refinancing efficiency: default distribution (discussed below) Turnover/default speed vector: 9%
Different parameters are used for different MBS coupons 12
CLEAN™ Prepayment Model: Details Basic approach Turnover and defaults modeled using deterministic speeds Refinancings modeled using stochastic interest rate model
Modeling a mortgage As a callable amortizing bond Financial engineer will refinance optimally Others will refinance too late (“laggards”) “Leapers” are rare
Modeling heterogeneous refinancing behavior Divide mortgage pool into 10 buckets according to laggard parameter Use a standard laggard distribution for a new pool
Modeling seasoned pools 13
Fastest refinancing buckets disappear first Automatically accounts for ‘burnout’
CLEAN Uses Two Separate Credit Spreads Homeowner credit spread determines refis Refinance when refinancing option is worth more dead than alive
OAS determines discount factors used for discounting MBS cash flows Credit spread of guarantor Plus market discount for unhedged uncertainty in price
14
Calibration: Straightforward and Intuitive Rarely adjusted Refinancing cost Refinancing efficiency Turnover speed vector Default speed vector
Adjusted monthly Homeowner credit spread Can be refined for specific pools
15
Mortgage Refinancing Efficiency: Refi When Rates Decline by 40 to 70 bps 105
Refinancing Efficiency (%)
.
100
95
90
85
80
1% Cost 2% Cost
75
95% Efficiency 70
65 70
65
60
55
50
45
40
Old Rate - Refi Rate (bps)
35
30
25
20
Option-Based Mortgage Technology Available to Homeowners
Patented option-based Mortgage Refinancing Calculator at www.kalotay.com/calculators 17
17
Why CLEAN™? Realistic, transparent behavior Based on well established financial and economic principles Instead of mysterious mathematical formulas and parameters
Consistent with valuation models for callable bonds and cancelable swaps Calibration is straightforward and intuitive And ridiculously fast Critical for simulation 18
Benchmark Speeds for CLEAN™
19
References Andrew Kalotay & Qi Fu (June 2009), A Financial Analysis of Consumer Mortgage Decisions, Mortgage Bankers Association. Andrew Kalotay & Qi Fu (May 2008), Mortgage servicing rights and interest rate volatility, Mortgage Risk. Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 1, 2008), Optimum refinancing: bringing professional discipline to household finance, Applied Financial Economics Letters. Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 3, 2007), Refunding efficiency: a generalized approach, Applied Financial Economics Letters. Andrew Kalotay, Deane Yang, & Frank Fabozzi (December 2004), An option-theoretic prepayment model for mortgages and mortgage-backed securities, International Journal of Theoretical and Applied Finance. Available from http://www.kalotay.com/research 20
