MonteCarlo_gold.cpp

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#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include <curand.h>

//#include "curand_kernel.h"
#include "helper_cuda.h"

////////////////////////////////////////////////////////////////////////////////
// Common types
////////////////////////////////////////////////////////////////////////////////
#include "MonteCarlo_common.h"

////////////////////////////////////////////////////////////////////////////////
// Black-Scholes formula for Monte Carlo results validation
////////////////////////////////////////////////////////////////////////////////
#define A1 0.31938153
#define A2 -0.356563782
#define A3 1.781477937
#define A4 -1.821255978
#define A5 1.330274429
#define RSQRT2PI 0.39894228040143267793994605993438

// Polynomial approximation of
// cumulative normal distribution function
double CND(double d) {
  double K = 1.0 / (1.0 + 0.2316419 * fabs(d));

  double cnd = RSQRT2PI * exp(-0.5 * d * d) *
               (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))));

  if (d > 0) cnd = 1.0 - cnd;

  return cnd;
}

// Black-Scholes formula for call value
extern "C" void BlackScholesCall(float &callValue, TOptionData optionData) {
  double S = optionData.S;
  double X = optionData.X;
  double T = optionData.T;
  double R = optionData.R;
  double V = optionData.V;

  double sqrtT = sqrt(T);
  double d1 = (log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT);
  double d2 = d1 - V * sqrtT;
  double CNDD1 = CND(d1);
  double CNDD2 = CND(d2);
  double expRT = exp(-R * T);

  callValue = (float)(S * CNDD1 - X * expRT * CNDD2);
}

////////////////////////////////////////////////////////////////////////////////
// CPU Monte Carlo
////////////////////////////////////////////////////////////////////////////////
static double endCallValue(double S, double X, double r, double MuByT,
                           double VBySqrtT) {
  double callValue = S * exp(MuByT + VBySqrtT * r) - X;
  return (callValue > 0) ? callValue : 0;
}

extern "C" void MonteCarloCPU(TOptionValue &callValue, TOptionData optionData,
                              float *h_Samples, int pathN) {
  const double S = optionData.S;
  const double X = optionData.X;
  const double T = optionData.T;
  const double R = optionData.R;
  const double V = optionData.V;
  const double MuByT = (R - 0.5 * V * V) * T;
  const double VBySqrtT = V * sqrt(T);

  float *samples;
  curandGenerator_t gen;

  checkCudaErrors(curandCreateGeneratorHost(&gen, CURAND_RNG_PSEUDO_DEFAULT));
  unsigned long long seed = 1234ULL;
  checkCudaErrors(curandSetPseudoRandomGeneratorSeed(gen, seed));

  if (h_Samples != NULL) {
    samples = h_Samples;
  } else {
    samples = (float *)malloc(pathN * sizeof(float));
    checkCudaErrors(curandGenerateNormal(gen, samples, pathN, 0.0, 1.0));
  }

  // for(int i=0; i<10; i++) printf("CPU sample = %f\n", samples[i]);

  double sum = 0, sum2 = 0;

  for (int pos = 0; pos < pathN; pos++) {
    double sample = samples[pos];
    double callValue = endCallValue(S, X, sample, MuByT, VBySqrtT);
    sum += callValue;
    sum2 += callValue * callValue;
  }

  if (h_Samples == NULL) free(samples);

  checkCudaErrors(curandDestroyGenerator(gen));

  // Derive average from the total sum and discount by riskfree rate
  callValue.Expected = (float)(exp(-R * T) * sum / (double)pathN);
  // Standard deviation
  double stdDev = sqrt(((double)pathN * sum2 - sum * sum) /
                       ((double)pathN * (double)(pathN - 1)));
  // Confidence width; in 95% of all cases theoretical value lies within these
  // borders
  callValue.Confidence =
      (float)(exp(-R * T) * 1.96 * stdDev / sqrt((double)pathN));
}