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https://github.com/NVIDIA/cuda-samples.git
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141 lines
5.1 KiB
C++
141 lines
5.1 KiB
C++
/* Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of NVIDIA CORPORATION nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <curand.h>
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//#include "curand_kernel.h"
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#include "helper_cuda.h"
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////////////////////////////////////////////////////////////////////////////////
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// Common types
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////////////////////////////////////////////////////////////////////////////////
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#include "MonteCarlo_common.h"
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////////////////////////////////////////////////////////////////////////////////
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// Black-Scholes formula for Monte Carlo results validation
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////////////////////////////////////////////////////////////////////////////////
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#define A1 0.31938153
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#define A2 -0.356563782
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#define A3 1.781477937
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#define A4 -1.821255978
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#define A5 1.330274429
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#define RSQRT2PI 0.39894228040143267793994605993438
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// Polynomial approximation of
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// cumulative normal distribution function
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double CND(double d) {
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double K = 1.0 / (1.0 + 0.2316419 * fabs(d));
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double cnd = RSQRT2PI * exp(-0.5 * d * d) *
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(K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))));
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if (d > 0) cnd = 1.0 - cnd;
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return cnd;
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}
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// Black-Scholes formula for call value
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extern "C" void BlackScholesCall(float &callValue, TOptionData optionData) {
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double S = optionData.S;
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double X = optionData.X;
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double T = optionData.T;
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double R = optionData.R;
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double V = optionData.V;
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double sqrtT = sqrt(T);
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double d1 = (log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT);
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double d2 = d1 - V * sqrtT;
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double CNDD1 = CND(d1);
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double CNDD2 = CND(d2);
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double expRT = exp(-R * T);
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callValue = (float)(S * CNDD1 - X * expRT * CNDD2);
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}
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////////////////////////////////////////////////////////////////////////////////
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// CPU Monte Carlo
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////////////////////////////////////////////////////////////////////////////////
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static double endCallValue(double S, double X, double r, double MuByT,
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double VBySqrtT) {
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double callValue = S * exp(MuByT + VBySqrtT * r) - X;
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return (callValue > 0) ? callValue : 0;
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}
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extern "C" void MonteCarloCPU(TOptionValue &callValue, TOptionData optionData,
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float *h_Samples, int pathN) {
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const double S = optionData.S;
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const double X = optionData.X;
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const double T = optionData.T;
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const double R = optionData.R;
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const double V = optionData.V;
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const double MuByT = (R - 0.5 * V * V) * T;
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const double VBySqrtT = V * sqrt(T);
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float *samples;
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curandGenerator_t gen;
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checkCudaErrors(curandCreateGeneratorHost(&gen, CURAND_RNG_PSEUDO_DEFAULT));
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unsigned long long seed = 1234ULL;
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checkCudaErrors(curandSetPseudoRandomGeneratorSeed(gen, seed));
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if (h_Samples != NULL) {
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samples = h_Samples;
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} else {
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samples = (float *)malloc(pathN * sizeof(float));
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checkCudaErrors(curandGenerateNormal(gen, samples, pathN, 0.0, 1.0));
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}
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// for(int i=0; i<10; i++) printf("CPU sample = %f\n", samples[i]);
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double sum = 0, sum2 = 0;
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for (int pos = 0; pos < pathN; pos++) {
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double sample = samples[pos];
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double callValue = endCallValue(S, X, sample, MuByT, VBySqrtT);
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sum += callValue;
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sum2 += callValue * callValue;
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}
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if (h_Samples == NULL) free(samples);
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checkCudaErrors(curandDestroyGenerator(gen));
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// Derive average from the total sum and discount by riskfree rate
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callValue.Expected = (float)(exp(-R * T) * sum / (double)pathN);
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// Standard deviation
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double stdDev = sqrt(((double)pathN * sum2 - sum * sum) /
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((double)pathN * (double)(pathN - 1)));
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// Confidence width; in 95% of all cases theoretical value lies within these
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// borders
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callValue.Confidence =
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(float)(exp(-R * T) * 1.96 * stdDev / sqrt((double)pathN));
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}
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