Matematik simulation and monte carlo with applications in finance and mcmc phần 2 pdf
Matematik simulation and monte carlo with applications in finance and mcmc phần 1 pps
... 16, 20 , 20 , 18, 22 ,
23 , 26 , 25 , 29 , 27 , 26 , 30, 27 , 29 , 27 , 25 , 26 , 30, 30, 27 , 28 , 23 , 25 , 21 , 24 , 22 , 23 , 22 ,
25 , 22 , 22 , 25 , 25 , 23 , 19, 19, 19, 21 , 23 , 25 , 24 , 26 , 24 , 27 , 24 , 27 , 29 , 29 , 29 , ... (op (2, res[i]), i=11 100);
data = 29 , 30, 30, 28 , 25 , 30, 26 , 30, 26 , 23 , 25 , 25 , 28 , 30, 24...
Matematik simulation and monte carlo with applications in finance and mcmc phần 2 pdf
... 1 29 130
2
31
−1 630360016 0 1 29 2 92 164
2
16
29 3 Odd 1 20 107 145
2
31
−1 950,706,376 0
2
31
−1 7 42, 938 ,28 5 0
2
31
−1 1 ,22 6,874,159 0
2
31
−1 62, 089,911 0
2
31
−1 1,343,714,438 0
U0 1 ... stdnormal:=proc() local r1,r2,r3,E1,E2;
do;
r1:=evalf(rand()/10ˆ 12) ;
r2:=evalf(rand()/10ˆ 12) ;
E1:=-ln(r1);
E2:=-ln(r2);
if E2 > 05
∗
E1-1 2 then break end if;
en...
Matematik simulation and monte carlo with applications in finance and mcmc phần 3 ppsx
... =
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
1/
√
2 e
√
2x+1
1/
√
2 +2 1/
√
2 +1/
√
2
=
1
4
e
√
2x+1
x<−
√
2
2
1/
√
2 +x +1/
√
2
1/
√
2 +2 1/
√
2 +1/
√
2
=
√
2x +2
4
x≤
√
2
2
4/
√
2 −1/
√
2 e
−
√
2x+1
1/
√
2 +2 1/
√
2 ... e.s.e.
vrr
1 52 5 12 6 .2 0013 82 0000 92 3 001399 000031 29
1 52 5 12 6.5 000474 0000 32 9 000498...
Matematik simulation and monte carlo with applications in finance and mcmc phần 4 pptx
...
2
G/X
2
=−1/X
2
, and G/t =0. Using Itô’s lemma,
dG =
G
X
dX +
G
t
dt +
1
2
b
2
2
G
X
2
dt
=
dX
X
−
2
X
2
dt
2X
2
=
Xdt +XdB
X
−
2
dt
2
=
−
2
2
dt +dB
Comparing this with Equation (6.3), ... R
2
,
W
1
=
−ln R
1
2/ 3
W
2
=
−ln R
2
2/ 3
122 Simulation and finance
simulation. Then for a path in the jth stratum,...
Matematik simulation and monte carlo with applications in finance and mcmc phần 5 ppsx
... 23 49 0514 24 04 0 028 2 (171,544)
2
600 7168 0390 72 25 00390 (51,164)
2
660 22 74 0 28 3 23 09 00096 (447,1 420 )
2
720 2 74 0100 2 87 00 029 7 (585,1869)
a
10 000 paths.
b
25 replications, ... 2. 803064014]
[1.5968 724 39, 2. 03 624 3709, 2. 0 429 995 52, 2. 341445360, 2. 513656874, 2. 9879858 32,
3.185 727 007, 3.370 120 4 32]
[0.9566889486, 1.35 824...
Matematik simulation and monte carlo with applications in finance and mcmc phần 6 doc
... is
−
f
x
2
+y
2
/ 2
x
2
+y
2
dy =
0
f
x
2
+y
2
/
x
2
+y
2
dy and similarly for Y .
(a) Here, f
XY
x y
=
1/ 2
exp
−x
2
/2 −y
2
/2
, which is separable in x and y,
showing that X and ... number
in [0,1) insert R= x/61. Answers: (a) = 60, (b) = 30.
Simulation and Monte Carlo: With applications in fi...
Matematik simulation and monte carlo with applications in finance and mcmc phần 7 ppt
... j,x1,x2,y1,y2,d;
for j from 1 to n do;
x1:=
rand()/10^ 12;
y1:=rand()/10^ 12;
x2:=rand()/10^ 12;
y2:=rand()/10^ 12;
d
[
j
]
:=sqrt((x1-x2) ^2+ (y1-y2) ^2) ;
end do;
seq(d
[
j
]
,j=1 n);
end proc:
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
> ... random number generator
‘schrage’. The final execution group sets an (initial) seed and calls ‘expon’
three times.
2
6
6
6
6
6
6
6
4
Simulation...
Matematik simulation and monte carlo with applications in finance and mcmc phần 8 pot
... ¼ 1 52. 688
‘seed’ ¼ 639156
‘mean’ ¼ 2. 1670967 62, ‘standard error’ ¼ 0.0 025 07078 421
t4: ¼ 21 .531
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
> estimated_vrr:=( .25 07078 421 e -2/ .9 127 721 506e -2) ^( -2) ;
estimated_efficiency:=t3*estimated_vrr/t4;
estima
ted_vrr:=13 .25 528 056
estimated_efficiency:= 12. 620 55880
2
6
6
6
6
6
6
6
4
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6...
Matematik simulation and monte carlo with applications in finance and mcmc phần 9 ppt
... 4:mu:=0.15:beta: =2. 5:
n: =25 :
beta1:=1/beta:
bet
a2:=evalf(GAMMA(beta1+1)):
beta3:=evalf(GAMMA (2/ beta+1)):
t0:=
[
3.3,1.4,5.7,3.3,0.1,1 .2, 2.1,5.6,3 .2, 2,6,7.1,3.3,
4.5,5.3, 2. 5,4.4 ,2. 5,4.8,3.5,infinity,infinity,infinit
y,
infinity,infinity
]
:
print("_______________________INPUT
DATA____________________");
seeda:=87341:seedb:=6 428 7:
print("Arriv
al ... seed:=rando...
Matematik simulation and monte carlo with applications in finance and mcmc phần 10 potx
... ‘is’, 1.9584973 32
1.
0.
3 .2. 1.
1.
0.
4 .2.
5.
0.
4 .2.
5.
0.
4 .2.
2.
0.
1.
2.
0.
2. 1.
.1e2
0.
.2. 1
.1e2
0.
.2. 1
.2e2
0.
.6.4 .2
.1e2
0.
.2. 1
prior and posterior densities
lambda[10]
prior and posterior ... values against iteration number
320 0
3000
28 00
26 00
24 00
22 00
0
1000
20 00 3000 4000 5000
0
20 00 22 00 24 00 26 00 28 00 3000 320 0
0.0015
0.001
0.0...