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127 lines
4.7 KiB
C++
127 lines
4.7 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 <math.h>
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#include "binomialOptions_common.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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extern "C" void BlackScholesCall(float &callResult, 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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// 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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}
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////////////////////////////////////////////////////////////////////////////////
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// Process an array of OptN options on CPU
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// Note that CPU code is for correctness testing only and not for benchmarking.
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////////////////////////////////////////////////////////////////////////////////
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static double expiryCallValue(double S, double X, double vDt, int i) {
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double d = S * exp(vDt * (2.0 * i - NUM_STEPS)) - X;
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return (d > 0) ? d : 0;
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}
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extern "C" void binomialOptionsCPU(float &callResult, TOptionData optionData) {
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static double Call[NUM_STEPS + 1];
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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 dt = T / (double)NUM_STEPS;
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const double vDt = V * sqrt(dt);
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const double rDt = R * dt;
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// Per-step interest and discount factors
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const double If = exp(rDt);
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const double Df = exp(-rDt);
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// Values and pseudoprobabilities of upward and downward moves
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const double u = exp(vDt);
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const double d = exp(-vDt);
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const double pu = (If - d) / (u - d);
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const double pd = 1.0 - pu;
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const double puByDf = pu * Df;
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const double pdByDf = pd * Df;
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///////////////////////////////////////////////////////////////////////
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// Compute values at expiration date:
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// call option value at period end is V(T) = S(T) - X
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// if S(T) is greater than X, or zero otherwise.
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// The computation is similar for put options.
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///////////////////////////////////////////////////////////////////////
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for (int i = 0; i <= NUM_STEPS; i++) Call[i] = expiryCallValue(S, X, vDt, i);
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////////////////////////////////////////////////////////////////////////
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// Walk backwards up binomial tree
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////////////////////////////////////////////////////////////////////////
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for (int i = NUM_STEPS; i > 0; i--)
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for (int j = 0; j <= i - 1; j++)
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Call[j] = puByDf * Call[j + 1] + pdByDf * Call[j];
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callResult = (float)Call[0];
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}
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