Date: 2021-03-03T22:25:38+00:00

Actual source code: ex2.c
petsc-3.14.5 2021-03-03
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      1: static char help[] = "Tests PetscRandom functions.\n\n";

      3: #include <petscsys.h>

      5: #define PETSC_MAXBSIZE     40
      6: #define DATAFILENAME "ex2_stock.txt"

      8: struct himaInfoTag {
      9:   PetscInt    n;
     10:   PetscReal   r;
     11:   PetscReal   dt;
     12:   PetscInt    totalNumSim;
     13:   PetscReal   *St0;
     14:   PetscReal   *vol;
     15: };
     16: typedef struct himaInfoTag himaInfo;

     18: PetscErrorCode readData(MPI_Comm,himaInfo *);
     19: PetscReal mcVal(PetscReal, PetscReal, PetscReal, PetscReal, PetscReal);
     20: void exchangeVal(PetscReal*, PetscReal*);
     21: PetscReal basketPayoff(PetscReal[], PetscReal[], PetscInt, PetscReal,PetscReal, PetscReal[]);
     22: PetscErrorCode stdNormalArray(PetscReal*, PetscInt,PetscRandom);
     23: PetscInt divWork(PetscMPIInt, PetscInt, PetscMPIInt);

     25: /*
     26:    Contributed by Xiaoyan Zeng <zengxia@iit.edu> and Liu, Kwong Ip" <kiliu@math.hkbu.edu.hk>

     28:    Example of usage:
     29:      mpiexec -n 4 ./ex2 -num_of_stocks 30 -interest_rate 0.4 -time_interval 0.01 -num_of_simulations 10000
     30: */

     32: int main(int argc, char *argv[])
     33: {
     34:   PetscReal      r,dt;
     35:   PetscInt       n;
     36:   unsigned long  i,myNumSim,totalNumSim,numdim;
     37:   PetscReal      *vol, *St0, x, totalx;
     38:   PetscMPIInt    size,rank;
     39:   PetscReal      *eps;
     40:   himaInfo       hinfo;
     41:   PetscRandom    ran;

     44:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     45:   PetscRandomCreate(PETSC_COMM_WORLD,&ran);
     46:   PetscRandomSetFromOptions(ran);

     48:   MPI_Comm_size(PETSC_COMM_WORLD, &size);       /* number of nodes */
     49:   MPI_Comm_rank(PETSC_COMM_WORLD, &rank);     /* my ranking */

     51:   hinfo.n           = 31;
     52:   hinfo.r           = 0.04;
     53:   hinfo.dt          = 1.0/12;   /* a month as a period */
     54:   hinfo.totalNumSim = 1000;

     56:   PetscOptionsGetInt(NULL,NULL,"-num_of_stocks",&(hinfo.n),NULL);
     57:   if (hinfo.n <1 || hinfo.n > 31) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only 31 stocks listed in stock.txt. num_of_stocks %D must between 1 and 31",hinfo.n);
     58:   PetscOptionsGetReal(NULL,NULL,"-interest_rate",&(hinfo.r),NULL);
     59:   PetscOptionsGetReal(NULL,NULL,"-time_interval",&(hinfo.dt),NULL);
     60:   PetscOptionsGetInt(NULL,NULL,"-num_of_simulations",&(hinfo.totalNumSim),NULL);

     62:   n           = hinfo.n;
     63:   r           = hinfo.r;
     64:   dt          = hinfo.dt;
     65:   totalNumSim = hinfo.totalNumSim;
     66:   PetscMalloc1(2*n+1,&hinfo.vol);
     67:   vol         = hinfo.vol;
     68:   St0         = hinfo.St0 = hinfo.vol + n;
     69:   readData(PETSC_COMM_WORLD,&hinfo);

     71:   numdim = n*(n+1)/2;
     72:   if (numdim%2 == 1) numdim++;
     73:   PetscMalloc1(numdim,&eps);

     75:   myNumSim = divWork(rank,totalNumSim,size);

     77:   x = 0;
     78:   for (i=0; i<myNumSim; i++) {
     79:     stdNormalArray(eps,numdim,ran);
     80:     x += basketPayoff(vol,St0,n,r,dt,eps);
     81:   }

     83:   MPI_Reduce(&x, &totalx, 1, MPIU_REAL, MPIU_SUM,0,PETSC_COMM_WORLD);
     84:   /* payoff = exp(-r*dt*n)*(totalx/totalNumSim);
     85:   PetscPrintf(PETSC_COMM_WORLD,"Option price = $%.3f using %ds of %s computation with %d %s for %d stocks, %d trading period per year, %.2f%% interest rate\n",
     86:    payoff,(int)(stop - start),"parallel",size,"processors",n,(int)(1/dt),r); */

     88:   PetscFree(vol);
     89:   PetscFree(eps);
     90:   PetscRandomDestroy(&ran);
     91:   PetscFinalize();
     92:   return ierr;
     93: }

     95: PetscErrorCode stdNormalArray(PetscReal *eps, PetscInt numdim, PetscRandom ran)
     96: {
     97:   PetscInt       i;
     98:   PetscScalar    u1,u2;
     99:   PetscReal      t;

    103:   for (i=0; i<numdim; i+=2) {
    104:     PetscRandomGetValue(ran,&u1);
    105:     PetscRandomGetValue(ran,&u2);

    107:     t        = PetscSqrtReal(-2*PetscLogReal(PetscRealPart(u1)));
    108:     eps[i]   = t * PetscCosReal(2*PETSC_PI*PetscRealPart(u2));
    109:     eps[i+1] = t * PetscSinReal(2*PETSC_PI*PetscRealPart(u2));
    110:   }
    111:   return(0);
    112: }

    115: PetscReal basketPayoff(PetscReal vol[], PetscReal St0[], PetscInt n, PetscReal r,PetscReal dt, PetscReal eps[])
    116: {
    117:   PetscReal Stk[PETSC_MAXBSIZE], temp;
    118:   PetscReal payoff;
    119:   PetscInt  maxk,i,j;
    120:   PetscInt  pointcount=0;

    122:   for (i=0;i<n;i++) Stk[i] = St0[i];

    124:   for (i=0;i<n;i++) {
    125:     maxk = 0;
    126:     for (j=0;j<(n-i);j++) {
    127:       Stk[j] = mcVal(Stk[j],r,vol[j],dt,eps[pointcount++]);
    128:       if ((Stk[j]/St0[j]) > (Stk[maxk]/St0[maxk])) maxk = j;
    129:     }
    130:     exchangeVal(Stk+j-1,Stk+maxk);
    131:     exchangeVal(St0+j-1,St0+maxk);
    132:     exchangeVal(vol+j-1,vol+maxk);
    133:   }

    135:   payoff = 0;
    136:   for (i=0; i<n; i++) {
    137:     temp = (Stk[i]/St0[i]) - 1;
    138:     if (temp > 0) payoff += temp;
    139:   }
    140:   return payoff;
    141: }

    143: PetscErrorCode readData(MPI_Comm comm,himaInfo *hinfo)
    144: {
    145:   PetscInt       i;
    146:   FILE           *fd;
    147:   char           temp[50];
    149:   PetscMPIInt    rank;
    150:   PetscReal      *v = hinfo->vol, *t = hinfo->St0;
    151:   PetscInt       num=hinfo->n;

    154:   MPI_Comm_rank(comm,&rank);
    155:   if (!rank) {
    156:     PetscFOpen(PETSC_COMM_SELF,DATAFILENAME,"r",&fd);
    157:     for (i=0;i<num;i++) {
    158:       double vv,tt;
    159:       if (fscanf(fd,"%s%lf%lf",temp,&vv,&tt) != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Badly formatted input file\n");
    160:       v[i] = vv;
    161:       t[i] = tt;
    162:     }
    163:     fclose(fd);
    164:   }
    165:   MPI_Bcast(v,2*num,MPIU_REAL,0,PETSC_COMM_WORLD);
    166:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] vol %g, ... %g; St0 %g, ... %g\n",rank,hinfo->vol[0],hinfo->vol[num-1],hinfo->St0 [0],hinfo->St0[num-1]); */
    167:   return(0);
    168: }

    170: void exchangeVal(PetscReal *a, PetscReal *b)
    171: {
    172:   PetscReal t;

    174:   t  = *a;
    175:   *a = *b;
    176:   *b = t;
    177: }

    179: PetscReal mcVal(PetscReal St, PetscReal r, PetscReal vol, PetscReal dt, PetscReal eps)
    180: {
    181:   return (St * PetscExpReal((r-0.5*vol*vol)*dt + vol*PetscSqrtReal(dt)*eps));
    182: }

    184: PetscInt divWork(PetscMPIInt id, PetscInt num, PetscMPIInt size)
    185: {
    186:   PetscInt numit;

    188:   numit = (PetscInt)(((PetscReal)num)/size);
    189:   numit++;
    190:   return numit;
    191: }

    193: /*TEST

    195:    build:
    196:       requires: !comple
    197:       output_file: output/ex1_1.out

    199:    test:
    200:       nsize: 2
    201:       output_file: output/ex1_1.out
    202:       localrunfiles: ex2_stock.txt

    204: TEST*/