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Manuel L. Esquível
Departamento de Matemática
Faculdade de Ciências e Tecnologia (FCT)
Universidade Nova de Lisboa (UNL)
& C.M.A.F. - U.L.
e-mail: [email protected]
Alexandra D. Pinheiro
Departamento de Matemática
Faculdade de Ciências e Tecnologia (FCT)
Universidade Nova de Lisboa (UNL)
e-mail: [email protected]
Daily closing values of the PSI-20 index
0,00
2.000,00
4.000,00
6.000,00
8.000,00
10.000,00
12.000,00
14.000,00
16.000,00
31-12-199231-03-199330-06-199330-09-199331-12-199331-03-199430-06-199430-09-199431-12-199431-03-199530-06-199530-09-199531-12-199531-03-199630-06-199630-09-199631-12-199631-03-199730-06-199730-09-199731-12-199731-03-199830-06-199830-09-199831-12-199831-03-1999
Time
Values of PSI-20
Daily closing values of the PSI-20 index
Daily closing values returns of the PSI-20 index
-0,12
-0,1
-0,08
-0,06
-0,04
-0,02
0
0,02
0,04
0,06
0,08
31-12-199231-03-199330-06-199330-09-199331-12-199331-03-199430-06-199430-09-199431-12-199431-03-199530-06-199530-09-199531-12-199531-03-199630-06-199630-09-199631-12-199631-03-199730-06-199730-09-199731-12-199731-03-199830-06-199830-09-199831-12-199831-03-1999
Time
Returns
Daily returns from the closing values of PSI-20 index
Fitting of an EVD to the negative returns of PSI-20
0
1
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07
x
F(x)
Empirical distr.
Fitted distrib.
Fit of an EVD to the negative returns of PSI-20
Fiting of an EVD to the positive returns of PSI-20
0
1
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07
x
F(x)
Empirical distr.
Fitted distr.
Fit of an EVD to the positive returns of PSI-20
Fitting of a generalised Pareto to the excesses (x-u) of the negative returns
0
1
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08
x-u
Fu(x-u)
Empirical distrib.
Fitted distrib.
Fit of a generalised Pareto to the excesses (x-u) of the negative returns
Fit of a generalised Pareto to the excesses (x-u) of the positive returns
0
1
0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05
x-u
Fu(x-u)
Empirical distrib.
Fitted distrib.
Fit of a generalised Pareto to the excesses (x-u) of the positive returns
Fit of the unconditional distribution to the negative returns, F(z) for z > u, and quantile estimates (95% and 99%)
1-F (
z) (
o n l o
g sc
a le)
0.015 0.02 0.03 0.05 0.07
0.002
0.005
0.01
0.02
0.05
0.1
z (on log scale)
0 0.02 0.04 0.06 0.08 0.1
0.02
0.04
0.06
0.08
0.1
z
1-F(
z)
Fit of the unconditional distribution to the positive returns, F(z) for z > u, and quantile estimates (95% and 99%)
z
1-F(
z)
0.02 0.04 0.06 0.08 0.1
0.01
0.02
0.03
0.04
0.05
0.06
z (on log scale)
1-F(
z) (
o n l o
g sc
a le)
0.02 0.03 0.05
0.002
0.005
0.01
0.02
0.05