Joint Estimation of Parameters of Mortgage Portfolio Joint Estimation of Parameters of Mortgage...

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  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Joint Estimation of Parameters of Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Czech Academy of Sciences

    CMS 2017 Bergamo, 1.6.2017

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    1 Data

    2 Factors

    3 Statistics

    4 Estimation of σ

    5 Likelihood

    6 Asymptotics

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Data

    Detailed loan data are usually (more than) confidential

    Thus, we took the US nationwide data

    mortgage delinquency (= PD) charge-off (= PD × LGD)

    for

    residential mortgages commercial mortgages

    Thus, we in fact examined a hypothetical nationwide US portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    The Data - Losses

    0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

    0.1 0.11 0.12

    1992 1998 2004 2010 2016

    Qr

    0 0.02 0.04 0.06 0.08

    0.1 0.12 0.14

    1992 1998 2004 2010 2016

    Qc

    0 0.05

    0.1 0.15

    0.2 0.25

    0.3 0.35

    1992 1998 2004 2010 2016

    LGDr

    0 0.05

    0.1 0.15

    0.2 0.25

    0.3 0.35

    0.4 0.45

    1992 1998 2004 2010 2016

    LGDc

    Qr, LGDr - residential, Qc, LGDc - commercial

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    The Data - Factors (Naive Dynamics)

    1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

    2 2.1 2.2 2.3

    1992 1998 2004 2010 2016

    Yr

    -0.4 -0.35

    -0.3 -0.25

    -0.2 -0.15

    -0.1 -0.05

    0 0.05

    1992 1998 2004 2010 2016

    Ir

    1 1.2 1.4 1.6 1.8

    2 2.2 2.4

    1992 1998 2004 2010 2016

    Yc

    -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

    0 0.1 0.2

    1992 1998 2004 2010 2016

    Ic

    Yr, Ir - residential, Yc, Ic - commercial

    σ speculatively determined from volatility of HPIr , HPIc respectively, as σr = 0.05, σc = 0.13.

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Y Explanation Candidates

    Y roughly identified with disposable wealth of household/company macro candidate variables

    GDP (both residential and commercial) PI - personal income (residential) IP - industrial production (commercial)

    vars suggested by literature HPI - house price index (Case et. al. 1995)

    Y residential Y commercial

    9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

    1992 1998 2004 2010 2016

    GDP

    9.1 9.2 9.3 9.4 9.5 9.6 9.7

    1992 1998 2004 2010 2016

    PI

    4.8 4.9

    5 5.1 5.2 5.3 5.4 5.5

    1992 1998 2004 2010 2016

    HPIr

    1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

    2 2.1 2.2 2.3

    1992 1998 2004 2010 2016

    Yr

    9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

    1992 1998 2004 2010 2016

    GDP

    4.55 4.6

    4.65 4.7

    4.75 4.8

    4.85 4.9

    1992 1998 2004 2010 2016

    IP

    4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

    1992 1998 2004 2010 2016

    HPIc

    1 1.2 1.4 1.6 1.8

    2 2.2 2.4

    1992 1998 2004 2010 2016

    Yc

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    I Explanation Candidates

    I roughly identified with house price index (HPI)

    macro candidate variables

    HPIr / HPIc - residential / commercial price indices

    vars suggested by literature

    U - unemployment, GDP growth (Qi at. al. 2009)

    I residential I commercial

    4.8 4.9

    5 5.1 5.2 5.3 5.4 5.5

    1992 1998 2004 2010 2016

    HPIr

    1.3 1.4 1.5 1.6 1.7 1.8 1.9

    2 2.1 2.2 2.3

    1992 1998 2004 2010 2016

    U

    -0.025 -0.02

    -0.015 -0.01

    -0.005 0

    0.005 0.01

    0.015 0.02

    1992 1998 2004 2010 2016

    d_GDP

    -0.4 -0.35

    -0.3 -0.25

    -0.2 -0.15

    -0.1 -0.05

    0 0.05

    1992 1998 2004 2010 2016

    Ir

    4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

    1992 1998 2004 2010 2016

    HPIc

    4.55 4.6

    4.65 4.7

    4.75 4.8

    4.85 4.9

    1992 1998 2004 2010 2016

    IP

    -0.025 -0.02

    -0.015 -0.01

    -0.005 0

    0.005 0.01

    0.015 0.02

    1992 1998 2004 2010 2016

    d_GDP

    -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

    0 0.1 0.2

    1992 1998 2004 2010 2016

    Ic

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Statistical Analysis

    According to ADF test, none of

    Yr , Ir ,Yc , Ic ,GDP,PI , IP,U,HPIr

    is either stationary or trend stationary (HPIc was not treated because its series is shorter and explanation power poor)

    Dynamics of the first differences could be studied

    However, we also tested for cointegration (long term dynamics).

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Statistical Analysis - Cointegration

    Engle-Granger tests

    F. Significant regressors Unit root of residuals Lags Ic U PI IP GDP HPIr rejected 0 Ir PI IP GDP HPIr rejected 0

    Yc U PI IP HPIr not rejected 4 Yc U PI IP HPIr not rejected 4

    ⇒ only Ix found cointegrated with macro vars Tests remain positive after removal of PI and U.

    Johansen test VAR involving

    VAR involving Ic Ir Yc Yr IP GDP HPIr

    Lag selection - HQC: 2, BIC: 1, AIC: max, LR: max - 2 chosen

    Johansen test (with exogenous FEDRate, ∆U and ∆PI - Trace: 3, LMax: 2 - 3 chosen

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    VECM model

    Partial VECM model estimated (Johansen 1992) with lag 2:

    ∆Ft = αβ ′(Ft−1,Mt−1)+Φ∆Ft−1+ΨEt−1+Et , rank(β) = 3

    Ft = (Ict , Irt ,Yct ,Yrt), Mt = (IPt ,GDPt ,HPIrt), Et = (FEDRatet ,∆Ut ,∆PIt ,∆IPt ,∆GDPt ,∆HPIrt)

    Insignificant regressors removed

    Resulting model ∆Ict−1 ∆Yct−1 ∆Irt−1 ∆Yrt−1 α1 α2 α3 FEDRt−1 ∆GDPt−1 ∆HPIrt−1

    ∆Ic x x x x x x x ∆Yc x x x x x ∆Ir x x x x x ∆Yr x x x x x

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko Joint Estimation of Parameters of Mortgage Portfolio

  • Joint Estimation of Parameters of

    Mortgage Portfolio

    Jaroslav Dufek, Martin Šḿıd, Petr Gapko

    Data

    Factors

    Statistics

    Estimation of σ

    Likelihood

    Asymptotics

    Estimation of σ

    So far, σ (standard deviation of individual “collateral price” factor) was set speculatively and θ (VECM parameters) were estimated

    We want to estimate θ and σ jointly

    Obvious candidate: MLE