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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 <math.h>
#include "binomialOptions_common.h"
#include "realtype.h"
///////////////////////////////////////////////////////////////////////////////
// Polynomial approximation of cumulative normal distribution function
///////////////////////////////////////////////////////////////////////////////
static real CND(real d) {
const real A1 = (real)0.31938153;
const real A2 = (real)-0.356563782;
const real A3 = (real)1.781477937;
const real A4 = (real)-1.821255978;
const real A5 = (real)1.330274429;
const real RSQRT2PI = (real)0.39894228040143267793994605993438;
real K = (real)(1.0 / (1.0 + 0.2316419 * (real)fabs(d)));
real cnd = (real)RSQRT2PI * (real)exp(-0.5 * d * d) *
(K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5)))));
if (d > 0) cnd = (real)1.0 - cnd;
return cnd;
}
extern "C" void BlackScholesCall(real &callResult, TOptionData optionData) {
real S = optionData.S;
real X = optionData.X;
real T = optionData.T;
real R = optionData.R;
real V = optionData.V;
real sqrtT = (real)sqrt(T);
real d1 = (real)(log(S / X) + (R + (real)0.5 * V * V) * T) / (V * sqrtT);
real d2 = d1 - V * sqrtT;
real CNDD1 = CND(d1);
real CNDD2 = CND(d2);
// Calculate Call and Put simultaneously
real expRT = (real)exp(-R * T);
callResult = (real)(S * CNDD1 - X * expRT * CNDD2);
}
////////////////////////////////////////////////////////////////////////////////
// Process an array of OptN options on CPU
// Note that CPU code is for correctness testing only and not for benchmarking.
////////////////////////////////////////////////////////////////////////////////
static real expiryCallValue(real S, real X, real vDt, int i) {
real d = S * (real)exp(vDt * (real)(2 * i - NUM_STEPS)) - X;
return (d > (real)0) ? d : (real)0;
}
extern "C" void binomialOptionsCPU(real &callResult, TOptionData optionData) {
static real Call[NUM_STEPS + 1];
const real S = optionData.S;
const real X = optionData.X;
const real T = optionData.T;
const real R = optionData.R;
const real V = optionData.V;
const real dt = T / (real)NUM_STEPS;
const real vDt = (real)V * (real)sqrt(dt);
const real rDt = R * dt;
// Per-step interest and discount factors
const real If = (real)exp(rDt);
const real Df = (real)exp(-rDt);
// Values and pseudoprobabilities of upward and downward moves
const real u = (real)exp(vDt);
const real d = (real)exp(-vDt);
const real pu = (If - d) / (u - d);
const real pd = (real)1.0 - pu;
const real puByDf = pu * Df;
const real pdByDf = pd * Df;
///////////////////////////////////////////////////////////////////////
// Compute values at expiration date:
// call option value at period end is V(T) = S(T) - X
// if S(T) is greater than X, or zero otherwise.
// The computation is similar for put options.
///////////////////////////////////////////////////////////////////////
for (int i = 0; i <= NUM_STEPS; i++) Call[i] = expiryCallValue(S, X, vDt, i);
////////////////////////////////////////////////////////////////////////
// Walk backwards up binomial tree
////////////////////////////////////////////////////////////////////////
for (int i = NUM_STEPS; i > 0; i--)
for (int j = 0; j <= i - 1; j++)
Call[j] = puByDf * Call[j + 1] + pdByDf * Call[j];
callResult = (real)Call[0];
}
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