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

... =1 2 (2 .1) Choose X0∈0 15 , say X0=3. Then X 1 =30 mod 24 =14 X2 =12 9 mod 24 =1 .The following sequence forRi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 applications in finance and MCMC J. S. Dagpunar© 2007 John Wiley & Sons, Ltd6 Introduction to simulation and Monte Carlo Since Xn +1 depends ... Xn +1 −binomialXn 1 −pn =0 1 2ContentsPreface xiGlossary xiii 1 Introduction to simulation and Monte Carlo 1 1 .1 Evaluating a definite integral 2 1. 2 Monte Carlo is integral estimation 4 1. 3...

Matematik simulation and monte carlo with applications in finance and mcmc phần 2 pdf

... Odd 1 06 1 29 1 302 31 1 630360 016 0 1 29 292 1 642 16 293 Odd 1 20 1 07 1 452 31 1 950,706,376 02 31 1 742,938,285 02 31 1 1,226,874 ,15 9 02 31 1 62,089, 911 02 31 1 1,343, 714 ,438 ... aXi 1 +c. For example, in the generator (2 .1) X7= 9 13 +3mod 16  In binary arithmetic, X7= 10 01  × 11 01  + 11 mod 10 000. . Now 10 01  × 11 01  + 11  = 011 000000000 10 00 11 01 0 011 + ... 5h5h 6h6h 7h7h 8h8h 9h9h 1 fi99 94 95 10 8 10 8 88 11 1 92 11 1 94ei 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0not available, but the asymptotic normality of the...

Matematik simulation and monte carlo with applications in finance and mcmc phần 3 ppsx

... 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00 012 702 51 512 9 0 019 37 000057 12 0 018 72 000039 242 51 52 418 00 017 6 000008 50 00 015 6 ... +2 1/ √2 + 1/ √2= 1 4e√2x +1 x<−√22 1/ √2 +x +1/ √2 1/ √2 +2 1/ √2 +1/ √2=√2x +24x≤√224/√2 − 1/ √2e−√2x +1 1/√2 +2 1/ √2 +1/ √2= 1 − 1 4e−√2x +1 x>√22b ... independent U0 1 random variables. 1 U= 1 2 1 R 1 V = 1 − 1  1 /2R2− 1 22 1 √Y =VUIf U < 1 4−Y2 1 /2deliver Y + 1 2else goto 1 Using Maple to reduce the mathematical...

Matematik simulation and monte carlo with applications in finance and mcmc phần 4 pptx

... (£) 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 22 21 54 022 22 18 11 8 Simulation and ﬁnance6.4 Asian options6.4 .1 Naive simulation Result (6 .15 ) showed ... callasiannaiveaasianimppoststratbKc 1 Varc 1 c2Varc2v.r.r.c03552 214 9 00300 2 211 6 0000 313 (6 81, 119 2)03504 16 66 00399 4 17 08 0000374 (843 ,14 76)03457 14 52 00486 7 15 21 0000483 (750 ,13 13)0 15 502 012 ... 0.3500700 210 07002463 , 0.79 211 80343 813 394 31 , 0.][0.299999999999999988 , -0. 014 00280084028005 31 , 0.3 217 979 514 67 419 185 ,0.897 914 249803398 512 ] and so⎛⎜⎜⎝Z 1 Z2Z3Z4⎞⎟⎟⎠=⎛⎜⎜⎝ 1 070 714 143050350070...

Matematik simulation and monte carlo with applications in finance and mcmc phần 5 ppsx

... 1 054233 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 014 99, 1. 247404803, 1. 370 810 129,2.376 811 957, 2.37738 619 3, 2.56439 019 2, ... ThenPU 1 >u 1 = 1 −u 1 n and PUj +1 >uj +1 Uj= uj= 1 −uj +1 1 −ujn−jfor j =1 n 1. Let R 1 Rnbe n uniform random numbers in U0 1 . Invertingthe...

Matematik simulation and monte carlo with applications in finance and mcmc phần 6 doc

... 2303 317 10 66 11 81 923 7756 2656 879 12 32 697 3368 4866767 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 62Single component MH and Gibbs sampling 16 7a ... of (8.22),  10 + 1 ≥u 11 leads to  10 + 1 ≥ R 11  10 + 1 0, that is ≥ 0R 1/ 10 + 1 11 Finally, e−≥ u 12 leads to e−≥ R 12 e−0, that is ≤ 0−ln R 12 So the ... <r2r 1/  1 +r 1/ 2≤ 1 Let X =R 1/  1 /R 1/  1 +R 1/ 2. Then the joint density of R 1 and X isfR 1 Xr 1 X∝r2x= x− 1  1 −x 1 r/ 1 over...

Matematik simulation and monte carlo with applications in finance and mcmc phần 7 ppt

... 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:266666666666666664> ... 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, 0.48, 0 .14 , 0 .16 , 0.32, 0.29, 0.32, 0.48, 1. 14,0. 31, 0.40, 0 .66, 0. 21, 0. 91, 0 .18 ,0.97, ... 1. 416 47 616 7]264666666666666666666666666666666664666666666666666666666666666666664Problem 1. 2Use a Monte Carlo method to find a 95% confidence interval forZ 1 1 Z 1 1 exp À0:5 x2þðy À 1 2Àxðy À 1 10 !&'dx dy:SolutionPut z ¼ y À 1 . Then the integral...

Matematik simulation and monte carlo with applications in finance and mcmc phần 8 pot

... 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 from 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 718 4466 ln 10 097þ 0:028 611 111 11 ﬃﬃﬃﬃﬃﬃﬃﬃ 10 3p ﬃﬃﬃﬃﬃﬃﬃﬃ252pﬃﬃﬃ2pþ 2:4 811 112 4 À ... localj,u1,t,x,u2,r2,r1,y,w,v,tprev,sum1,sum2,mean,s1,m;sum1:=0;sum2:=0;for m from 1 to k do;s1:=0;tprev: =10 ^( -10 );for j from 1 to n do;u1:=evalf(rand() /10 ^12 ); u2:=evalf(rand()/ 10 ^12 );t:=fsolve(x-x*ln(x)-(j -1+ u1)/n,x=tprev,tprev...

Matematik simulation and monte carlo with applications in finance and mcmc phần 9 ppt

... 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,infinity,infinity,infinity]:print("_______________________INPUTDATA____________________");seeda:=873 41: seedb:=64287:print("Arrival and serv ... paths’ = 10 000‘point estimate of price’ = 2.744 216 2 61 ‘estimated standard error’ = 0 .10 0 311 80 91 266664666666646.7.2 Monte Carlo with importance and stratifiedsamplingNow definex0¼Xni 1 qixiexp...

Matematik simulation and monte carlo with applications in finance and mcmc phần 10 potx

... 11 2, 11 3, 11 6, 11 7Hedging 11 2, 11 5 11 7, 12 9, 13 1 13 2Hedging parameter (delta) 11 2, 13 0Hyperparameters 16 7, 16 9, 17 2, 17 4Hyperprior density 17 2Importance sampling 4, 82–86Asian option 11 9 12 1basket ... 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 11, 8277, 356, 822, 2303, 317 , 10 66, 11 81, 923, 7756, 2656, 879, 12 32, ... purchasing foreign 11 6Customers, rejected 14 9 15 1, 15 5Delta, see Hedging parameter (delta)Delta hedging, see HedgingDerivative, financial 1, 10 7, 11 1, 12 9 Simulation and Monte Carlo: With applications...

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