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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of NVIDIA CORPORATION nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#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));
}
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