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87 lines
3.9 KiB
C++
87 lines
3.9 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 <math.h>
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////////////////////////////////////////////////////////////////////////////////
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// Polynomial approximation of cumulative normal distribution function
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////////////////////////////////////////////////////////////////////////////////
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static double CND(double d) {
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const double A1 = 0.31938153;
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const double A2 = -0.356563782;
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const double A3 = 1.781477937;
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const double A4 = -1.821255978;
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const double A5 = 1.330274429;
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const double RSQRT2PI = 0.39894228040143267793994605993438;
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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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////////////////////////////////////////////////////////////////////////////////
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// Black-Scholes formula for both call and put
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////////////////////////////////////////////////////////////////////////////////
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static void BlackScholesBodyCPU(float &callResult, float &putResult,
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float Sf, // Stock price
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float Xf, // Option strike
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float Tf, // Option years
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float Rf, // Riskless rate
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float Vf // Volatility rate
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) {
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double S = Sf, X = Xf, T = Tf, R = Rf, V = Vf;
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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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// Calculate Call and Put simultaneously
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double expRT = exp(-R * T);
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callResult = (float)(S * CNDD1 - X * expRT * CNDD2);
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putResult = (float)(X * expRT * (1.0 - CNDD2) - S * (1.0 - CNDD1));
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}
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////////////////////////////////////////////////////////////////////////////////
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// Process an array of optN options
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////////////////////////////////////////////////////////////////////////////////
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extern "C" void BlackScholesCPU(float *h_CallResult, float *h_PutResult,
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float *h_StockPrice, float *h_OptionStrike,
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float *h_OptionYears, float Riskfree,
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float Volatility, int optN) {
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for (int opt = 0; opt < optN; opt++)
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BlackScholesBodyCPU(h_CallResult[opt], h_PutResult[opt], h_StockPrice[opt],
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h_OptionStrike[opt], h_OptionYears[opt], Riskfree,
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Volatility);
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}
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