Date: 2013-07-02T14:38:35+00:00

Actual source code: ex2.c
petsc-3.4.2 2013-07-02

      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:   int    n;
     10:   double r;
     11:   double dt;
     12:   int    totalNumSim;
     13:   double *St0;
     14:   double *vol;
     15: };
     16: typedef struct himaInfoTag himaInfo;

     18: /* function protype */
     19: PetscErrorCode readData(MPI_Comm comm,himaInfo *hinfo);
     20: double mcVal(double St, double r, double vol, double dt, double eps);
     21: void exchange(double *a, double *b);
     22: double basketPayoff(double vol[], double St0[], int n, double r,double dt, double eps[]);
     23: void stdNormalArray(double *eps, int size,PetscRandom ran);
     24: unsigned long divWork(int id, unsigned long num, int np);

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

     29:    Example of usage:
     30:      mpiexec -n 4 ./ex2 -num_of_stocks 30 -interest_rate 0.4 -time_interval 0.01 -num_of_simulations 10000
     31: */

     35: int main(int argc, char *argv[])
     36: {
     37:   /* double         payoff; */
     38:   double         r,dt;
     39:   int            n;
     40:   unsigned long  i,myNumSim,totalNumSim,numdim;
     41:   double         *vol, *St0, x, totalx;
     42:   int            np,myid;
     43:   double         *eps;
     44:   himaInfo       hinfo;
     45:   PetscRandom    ran;
     47:   PetscBool      flg;

     49:   PetscInitialize(&argc,&argv,(char*)0,help);
     50: #if defined(PETSC_USE_COMPLEX)
     51:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This example does not work for scalar type complex\n");
     52: #endif
     53:   PetscRandomCreate(PETSC_COMM_WORLD,&ran);
     54: #if defined(PETSC_HAVE_SPRNG)
     55:   PetscRandomSetType(ran,PETSCSPRNG);
     56: #elif defined(PETSC_HAVE_RAND)
     57:   PetscRandomSetType(ran,PETSCRAND);
     58: #endif
     59:   PetscRandomSetFromOptions(ran);

     61:   MPI_Comm_size(PETSC_COMM_WORLD, &np);       /* number of nodes */
     62:   MPI_Comm_rank(PETSC_COMM_WORLD, &myid);     /* my ranking */

     64:   PetscOptionsHasName(NULL, "-check_generators", &flg);
     65:   if (flg) {
     66:     PetscRandomGetValue(ran,(PetscScalar*)&r);
     67:     PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d] rval: %g\n",myid,r);
     68:     PetscSynchronizedFlush(PETSC_COMM_WORLD);
     69:   }

     71:   hinfo.n           = 31;
     72:   hinfo.r           = 0.04;
     73:   hinfo.dt          = 1.0/12;   /* a month as a period */
     74:   hinfo.totalNumSim = 1000;

     76:   PetscOptionsGetInt(NULL,"-num_of_stocks",&(hinfo.n),NULL);
     77:   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);
     78:   PetscOptionsGetReal(NULL,"-interest_rate",&(hinfo.r),NULL);
     79:   PetscOptionsGetReal(NULL,"-time_interval",&(hinfo.dt),NULL);
     80:   PetscOptionsGetInt(NULL,"-num_of_simulations",&(hinfo.totalNumSim),NULL);

     82:   n           = hinfo.n;
     83:   r           = hinfo.r;
     84:   dt          = hinfo.dt;
     85:   totalNumSim = hinfo.totalNumSim;
     86:   vol         = hinfo.vol = (double*)malloc(sizeof(double)*(2*n+1));
     87:   St0         = hinfo.St0 = hinfo.vol + n;
     88:   readData(PETSC_COMM_WORLD,&hinfo);

     90:   numdim = n*(n+1)/2;
     91:   if (numdim%2 == 1) numdim++;
     92:   eps = (double*)malloc(sizeof(double)*numdim);

     94:   myNumSim = divWork(myid,totalNumSim,np);

     96:   x = 0;
     97:   for (i=0; i<myNumSim; i++) {
     98:     stdNormalArray(eps,numdim,ran);
     99:     x += basketPayoff(vol,St0,n,r,dt,eps);
    100:   }

    102:   MPI_Reduce(&x, &totalx, 1, MPI_DOUBLE, MPI_SUM,0,PETSC_COMM_WORLD);
    103:   /* payoff = exp(-r*dt*n)*(totalx/totalNumSim);
    104:   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",
    105:    payoff,(int)(stop - start),"parallel",np,"processors",n,(int)(1/dt),r); */

    107:   free(vol);
    108:   free(eps);
    109:   PetscRandomDestroy(&ran);
    110:   PetscFinalize();
    111:   return 0;
    112: }

    114: void stdNormalArray(double *eps, int size, PetscRandom ran)
    115: {
    116:   int            i;
    117:   double         u1,u2,t;

    120:   for (i=0; i<size; i+=2) {
    121:     PetscRandomGetValue(ran,(PetscScalar*)&u1);CHKERRABORT(PETSC_COMM_WORLD,ierr);
    122:     PetscRandomGetValue(ran,(PetscScalar*)&u2);CHKERRABORT(PETSC_COMM_WORLD,ierr);

    124:     t        = sqrt(-2*log(u1));
    125:     eps[i]   = t * cos(2*PETSC_PI*u2);
    126:     eps[i+1] = t * sin(2*PETSC_PI*u2);
    127:   }
    128: }

    131: double basketPayoff(double vol[], double St0[], int n, double r,double dt, double eps[])
    132: {
    133:   double Stk[PETSC_MAXBSIZE], temp;
    134:   double payoff;
    135:   int    maxk,i,j;
    136:   int    pointcount=0;

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

    140:   for (i=0;i<n;i++) {
    141:     maxk = 0;
    142:     for (j=0;j<(n-i);j++) {
    143:       Stk[j] = mcVal(Stk[j],r,vol[j],dt,eps[pointcount++]);
    144:       if ((Stk[j]/St0[j]) > (Stk[maxk]/St0[maxk])) maxk = j;
    145:     }
    146:     exchange(Stk+j-1,Stk+maxk);
    147:     exchange(St0+j-1,St0+maxk);
    148:     exchange(vol+j-1,vol+maxk);
    149:   }

    151:   payoff = 0;
    152:   for (i=0; i<n; i++) {
    153:     temp = (Stk[i]/St0[i]) - 1;
    154:     if (temp > 0) payoff += temp;
    155:   }
    156:   return payoff;
    157: }

    161: PetscErrorCode readData(MPI_Comm comm,himaInfo *hinfo)
    162: {
    163:   int            i;
    164:   FILE           *fd;
    165:   char           temp[50];
    167:   PetscMPIInt    rank;
    168:   double         *v = hinfo->vol, *t = hinfo->St0;
    169:   int            num=hinfo->n;

    172:   MPI_Comm_rank(comm,&rank);
    173:   if (!rank) {
    174:     PetscFOpen(PETSC_COMM_SELF,DATAFILENAME,"r",&fd);
    175:     for (i=0;i<num;i++) fscanf(fd,"%s%lf%lf",temp,v+i,t+i);
    176:     fclose(fd);
    177:   }
    178:   MPI_Bcast(v,2*num,MPI_DOUBLE,0,PETSC_COMM_WORLD);
    179:   /* 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]); */
    180:   return(0);
    181: }

    183: void exchange(double *a, double *b)
    184: {
    185:   double t;

    187:   t  = *a;
    188:   *a = *b;
    189:   *b = t;
    190: }

    192: double mcVal(double St, double r, double vol, double dt, double eps)
    193: {
    194:   return (St * exp((r-0.5*vol*vol)*dt + vol*sqrt(dt)*eps));
    195: }

    197: unsigned long divWork(int id, unsigned long num, int np)
    198: {
    199:   unsigned long numit;

    201:   numit = (unsigned long)(((double)num)/np);
    202:   numit++;
    203:   return numit;
    204: }