Modélisation Comportementale en ALM Bancaire

19 Pages·2009·0.19 MB·French

Modélisation comportementale en ALM
bbancaiire : applliicatiion aux ddéépôôts àà vue
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Finance comportementale et risques
29 avril 2009
Jean-Paul LAURENT
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Alexandre ADAM, BNP Paribas Asset and Liability Management
MMohhamedd HHOOUUKKAARRII, BBNNPP PPariibbas AALLMM andd IISSFFAA, UUniiversiittéé dde LLyon, UUniiversiittéé LLyon 11
Jean-Paul LAURENT, ISFA, Université de Lyon, Université Lyon 1
Presentation related to:
(cid:132)
Hedggingg Interest Rate Marggins on Demand Depposits
(cid:133)
Working paper available on SSRN (to be updated soon)
(cid:132)
PPrreesseennttaattiioonn OOuuttllooookk
(cid:132)(cid:132)
Modeling framework
(cid:133)
ccuussttoommeerr rraatteess
(cid:132)(cid:132)
deposit amounts
(cid:132)
IInntteerreesstt rraattee mmaarrggiinnss
(cid:132)
Optimal strategies
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TThhee bblliinnkkeerreedd iinnvveessttoorr
(cid:132)(cid:132)
Integrated risk management
(cid:132)
CCoonncclluussiioonn
(cid:133)(cid:133)
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PPrroolleeggoommeennaa
Demand Deposits involve huge amounts
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(cid:133) Bank of America Annual Report – Dec. 2007
Averagge Balance

(Dollars in millions) 2007 2006
Assets

Federal funds sold and securities purchased under agreements to resell $ 155,828 $ 175,334
TTraddiing accountt assetts 118877,228877 114455,332211

Debt securities 186,466 225,219

Loans and leases, net of allowance for loan and lease losses 766,329 643,259

All other assets 306,163 277,548

Total assets $$ 1,,602,,073 $$ 1,,466,,681
Liabilities

Deposits $ 717,182 $ 672,995

Federal funds purchased and securities sold under agreements to repurchase 253,481 286,903

Trading account liabilities 82,721 64,689

Commercial paper and other short-term borrowings 171,333 124,229

Long-term debt 169,855 130,124

All other liabilities 70,839 57,278
Total liabilities 1,465,411 1,336,218

Shareholders’ equity 136,662 130,463

Total liabilities and shareholders’ equity $ 1,602,073 $ 1,466,681

Demand deposits involve both interest rate and liquidity risks
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Modelingg Depposit Rate – Exampples
We assume the customer rate to be a function of the market rate.
(cid:132)
(cid:133) Affine in general (US) / Sometimes more complex (Japan)
(( )) (( )) {{ }}
( ) g L = α+ β⋅ L ⋅1 L ≥ R
g L =α+ β⋅ L
T T T
T T
United States Japan
3.00% 0,9
M2 Own Rate
JPY Libor 3M
0,8
2.50% Japanese M2 Own Rate
0,7
0,6
2.00% Affine Dependance
0,5
1.50% 0,4
00,33
Quasi Zero Rates !
1.00%
0,2
0.50% 0,1
USD 3M Libor Rate 0
00.0000%% 99 99 00 00 1 1 22 22 33 33 44 44 55 55 66 66 77
9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% ars- ept- ars- ept- ars- ept- ars- ept- ars- ept- ars- ept- ars- ept- ars- ept- ars-
m s m s m s m s m s m s m s m s m
44
LL
Dynamics for Market Rate : forward Libor rate
t
MMaarrkkeett MMooddeell ffoorr ffoorrwwaarrdd LLiibboorr rraattee((ss))
(cid:132)(cid:132)
dL
t = μμ ddtt ++σσ ddWW ((tt))
L L L
L
t
μμ ≠≠ 00
LLoonngg--TTeerrmm IInnvveessttmmeenntt RRiisskk PPrreemmiiuumm
L
Coefficient specification assumptions:
(cid:132)
μ ,σ
Our model: constant
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L L
Assumptions can be relaxed:
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Time dependent coefficients
(cid:133)
CEV type Libor models
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55
DDeeppoossiitt AAmmoouunntt DDyynnaammiiccss
Diffusion process for Deposit Amount
(cid:132)
dK = K ⎡⎡μ dt +σ dW (t)⎤⎤
⎣ ⎦
t t K K K
(US marketplace)
SSensiittiiviitty off ddeposiitt amountt tto
(cid:133) 668800 44
market rates 660 3,5
640
3
(cid:132) Moneyy transfers between depposits 620
22,,55
and other accounts 600
2
580
Interest Rate partial contingence. 1,5
(cid:133)
560
1
554400
Business risk, …
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520 US Demand Deposit Amount 0,5
US M2 Own Rate
Incomplete market framework
(cid:132) 500 0
0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
oct- anv- avr- juil- oct- anv- avr- juil- oct- anv- avr- juil- oct- anv- avr- juil- oct- anv- avr- juil- oct- anv- avr- juil- oct- anv- avr- juil-
j j j j j j j
dW (t) = ρdW (t) + 1− ρ2 dW (t)
−1< ρ< 0
K L K
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Depposit Amount Dyynamics – Exampples
( )
( )
dK = K μ dt +σ dW t
t t K K K
US and Euro Zone Emerging Markets
33550000 880000
30000 400
700
3000
350
25000
600
2500 300
500 20000
250
UR bln. 2000 400 SD bln. Y Bln.15000 200 H Bln.
E 1500 U R A
T U
300
150
10000
1000
200
100
500 5000
100
50
00 00 0 0
1997-109998-109198-109598-109999-109199-109599-200900-200100-200500-200901-200101-200501-200902-200102-200502-200903-200103-200503-200904-200104-200504-200905-200105-200505-200906-200106-200506-200907-200107-200507-09 sept-97 janv-98mai-98 sept-98janv-99 mai-99 sept-99 janv-00mai-00 sept-00janv-01 mai-01 sept-01 janv-02mai-02 sept-02janv-03mai-03 sept-03 janv-04 mai-04sept-04 janv-05mai-05 sept-05 janv-06 mai-06sept-06 janv-07mai-07 sept-07
Euro Overnight Deposits US Demand Deposits
Turkey - M1-M0 Ukraine - M1-M0
EuroZone − μˆ =10.19%,σˆ = 6.56%
Turkey − μˆ = 51.74%,σˆ = 37.38%
K K
K K
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Demand Deposit Interest Rate Margin
(cid:132)
For a given quarter T
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Income generated by:
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Investing Demand Deposit Amount on interbank markets
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while paying a deposit rate to customers
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( ) ( ( ))
Interest Rate Margin IRM K , L = K L − g L ⋅ ΔT
g T T T T T
Deposit Amount at T
Investment Market Rate duringg
time interval [T,T+ΔT]
Customer rate at T
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WWee nneeeedd ttoo ffooccuuss oonn IInntteerreesstt RRaattee MMaarrggiinnss
( ) ( ( ))
IRM K , L = K L − g L ⋅ ΔT
gg T T T T T
According to the IFRS (International accounting standards) :
(cid:132)
The IFRS recommend the accounting of non maturing assets and
(cid:133)
lliiaabbiilliittiieess aatt AAmmoorrttiizzeedd CCoosstt // HHiissttoorriiccaall CCoosstt
Recognition of related hedging strategies from the accounting
(cid:132)
viewpoint
IInntteerreesstt MMaarrggiinn HHeeddggee ((IIMMHH))..
(cid:133)(cid:133)
The fair value approach does not apply to demand deposits
(cid:132)
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(( )) (( (( ))))
Risks in interest rate margins IRM K , L = K L − g L ⋅ ΔT
(cid:132)
g T T T T T
IInntteerreesstt rraattee rriisskk
(cid:132)
( )
L − g L
Direct interest rate risk on unit margins
(cid:133)
T T
KK LL
Indirect interest rate risk due to correlation between and
(cid:133)
T T
Business risk
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Deposit amounts are not fully correlated to interest rates
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Hedging tools
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Interest rate swaps (FRA’s)
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L
three months forward Libor at date t for quarter T
(cid:133)
t
ddLL
:: iinnccrreemmeennttaall ccaasshh-ffllooww aatt ttiimmee TT aassssoocciiaatteedd wwiitthh aa uunniitt FFRRAA
(cid:133)(cid:133)
t
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