Matematik simulation and monte carlo with applications in finance and mcmc phần 1 pps

... =1 2 (2 .1) Choose X 0 ∈0 15 , say X 0 =3. Then X 1 =30 mod 2 4 =14 X 2 =12 9 mod 2 4 =1 . The following sequence for  R i  is obtained: 3 16  14 16  1 16  12 16  15 16  10 16  13 16  8 16  11 16  6 16  9 16  4 16  7 16  2 16  5 16  0 16  3 16  ... appear random. Simulation and Monte Carlo: With appli...

Ngày tải lên: 09/08/2014, 16:21

... Odd 1 06 1 29 1 30 2 31 1 630360 016 0 1 29 292 1 64 2 16 293 Odd 1 20 1 07 1 45 2 31 1 950,706,376 0 2 31 1 742,938,285 0 2 31 1 1,226,874 ,15 9 0 2 31 1 62,089, 911 0 2 31 1 1,343, 714 ,438 ... aX i 1 +c. For example, in the generator (2 .1) X 7 = 9 13 +3mod 16  In binary arithmetic, X 7 =  10 01  × 11 01  + 11   mod 10 000. . Now 10 01  ×...

Ngày tải lên: 09/08/2014, 16:21

... e.s.e.      vrr 1 525 12 6.2 0 013 82 000092 3 0 013 99 0000 31 29 1 525 12 6.5 000474 000032 9 000498 000 012 70 2 51 512 9 0 019 37 000057 12 0 018 72 000039 24 2 51 52 418 00 017 6 000008 50 00 015 6 ... +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/ √...

Ngày tải lên: 09/08/2014, 16:21

... (£)  13 34 0 0 12 7 13  41 0 15 1 45 13 14 00 005 475 515 30 009 867 317 27 0 13 13 2 2 21 54 022 22 18 11 8 Simulation and finance 6.4 Asian options 6.4 .1 Naive simulation Result (6 .15 ) showed ... call asiannaive a asianimppoststrat b K  c 1   Var   c 1   c 2   Var   c 2  v.r.r. c 03552 214 9 00300 2 211 6 0000 313 (6 81, 119 2) 03504 16...

Ngày tải lên: 09/08/2014, 16:21

... 1 054 2 3 3 015 0 3 20302 1 9524 1 9 913 2 1 903 2 15 7 1 839 2066 10 11 11 449 11 10 3273 10 15 97 10 2435 10 9087 11 5688897 11 422 numbers. For best effect a given random number and its ... 0.8584469999, 1. 32484 819 5, 1. 564463956, 2.34 210 3589, 2.753604757, 3 .16 1 013 255, 3.355203 918 ] [0. 310 5425825, 0.68 519 1 014 2, 1. 02550 615 2, 1. 0363...

Ngày tải lên: 09/08/2014, 16:21

... 2303 317 10 66 11 81 923 7756 2656 879 12 32 697 3368 486 6767 484 438 18 60 11 3 6062 590 16 33 2425 367 712 953 19 89 768 600 30 41 1 814 14 1 10 511 7796 14 62 Single component MH and Gibbs sampling 16 7 a ... of (8.22),  10 + 1 ≥u 11 leads to  10 + 1 ≥ R 11  10 + 1 0 , that is  ≥  0 R 1/ 10 + 1 11  Finally, e − ≥ u 12 leads to e − ≥ R 12...

Ngày tải lên: 09/08/2014, 16:21

... distance:=proc(n) local 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 > ... 0.64, 1. 39, 0.62, 0.22, 0 .15 , 2. 21, 0.76, 0.80, 0.97, 1. 06, 0.26, 0.47, 0 .13 , 0.28, 0 .18 , 0.57, 1. 35, 0. 61,...

Ngày tải lên: 09/08/2014, 16:21

... j,r1,r2,w,v,y,m,sum1,sum2,k1,s1, mean; sum1:=0;sum2:=0; for k1 from 1 to k do; s1:=0; for j f rom 1 to n do; for m from 1 to n do; r1:=(j -1+ evalf(rand() /10 ^12 ))/n; r2:=(m -1+ evalf(rand() /10 ^12 ))/n; w:=(-ln(r2)) ^(2/3); v:=(-ln(r1))^(2/3); y:=(v+w)^(5/4); s1:=s1+y; end ... with( finance) : h > B:=blackscholes (10 0, 97, 0.05, 10 3/252, 0.2); evalf(B); B : ¼50 erf 0:0242 71...

Ngày tải lên: 09/08/2014, 16:21

... then; na:=na +1; randomize(seed1); seed1:=rand(); r1:=evalf(seed1 /10 ^12 ); a:=clock-ln(r1)/lambda; q: =1; else # BOUND STATE CHANGE:DEPARTURE; t [ 1 ] :=infinity; t:=sort(t); nocc:=nocc -1; nout1:=nout1 +1; end ... 2.5,4.4,2.5,4.8,3.5,infinity,infinity,infinit y, infinity,infinity ] : print("_______________________INPUT DATA____________________"); seeda:=873 41: seedb:=6428...

Ngày tải lên: 09/08/2014, 16:21

... 11 2, 11 3, 11 6, 11 7 Hedging 11 2, 11 5 11 7, 12 9, 13 1 13 2 Hedging parameter (delta) 11 2, 13 0 Hyperparameters 16 7, 16 9, 17 2, 17 4 Hyperprior density 17 2 Importance sampling 4, 82–86 Asian option 11 9 12 1 basket ... 590, 16 33, 2425, 367, 712 , 953, 19 89, 768, 600, 30 41, 18 14, 14 1, 10 511 , 7796, 14 62 ] ; x :¼ [293, 19 02, 12 72, 2987, 469, 318 5, 17 1...

Ngày tải lên: 09/08/2014, 16:21