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/*
* Copyright 1993-2007 NVIDIA Corporation. All rights reserved.
*
* NOTICE TO USER:
*
* This source code is subject to NVIDIA ownership rights under U.S. and
* international Copyright laws. Users and possessors of this source code
* are hereby granted a nonexclusive, royalty-free license to use this code
* in individual and commercial software.
*
* NVIDIA MAKES NO REPRESENTATION ABOUT THE SUITABILITY OF THIS SOURCE
* CODE FOR ANY PURPOSE. IT IS PROVIDED "AS IS" WITHOUT EXPRESS OR
* IMPLIED WARRANTY OF ANY KIND. NVIDIA DISCLAIMS ALL WARRANTIES WITH
* REGARD TO THIS SOURCE CODE, INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY, NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE.
* IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL,
* OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE
* OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE
* OR PERFORMANCE OF THIS SOURCE CODE.
*
* U.S. Government End Users. This source code is a "commercial item" as
* that term is defined at 48 C.F.R. 2.101 (OCT 1995), consisting of
* "commercial computer software" and "commercial computer software
* documentation" as such terms are used in 48 C.F.R. 12.212 (SEPT 1995)
* and is provided to the U.S. Government only as a commercial end item.
* Consistent with 48 C.F.R.12.212 and 48 C.F.R. 227.7202-1 through
* 227.7202-4 (JUNE 1995), all U.S. Government End Users acquire the
* source code with only those rights set forth herein.
*
* Any use of this source code in individual and commercial software must
* include, in the user documentation and internal comments to the code,
* the above Disclaimer and U.S. Government End Users Notice.
*/
#include <math.h>
///////////////////////////////////////////////////////////////////////////////
// Polynomial approximation of cumulative normal distribution function
///////////////////////////////////////////////////////////////////////////////
static double CND(double d){
const double A1 = 0.31938153;
const double A2 = -0.356563782;
const double A3 = 1.781477937;
const double A4 = -1.821255978;
const double A5 = 1.330274429;
const double RSQRT2PI = 0.39894228040143267793994605993438;
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 both call and put
///////////////////////////////////////////////////////////////////////////////
static void BlackScholesBodyCPU(
float& callResult,
float& putResult,
float Sf, //Stock price
float Xf, //Option strike
float Tf, //Option years
float Rf, //Riskless rate
float Vf //Volatility rate
){
double S = Sf, X = Xf, T = Tf, R = Rf, V = Vf;
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);
//Calculate Call and Put simultaneously
double expRT = exp(- R * T);
callResult = (float)(S * CNDD1 - X * expRT * CNDD2);
putResult = (float)(X * expRT * (1.0 - CNDD2) - S * (1.0 - CNDD1));
}
////////////////////////////////////////////////////////////////////////////////
// Process an array of optN options
////////////////////////////////////////////////////////////////////////////////
extern "C" void BlackScholesCPU(
float *h_CallResult,
float *h_PutResult,
float *h_StockPrice,
float *h_OptionStrike,
float *h_OptionYears,
float Riskfree,
float Volatility,
int optN
){
for(int opt = 0; opt < optN; opt++)
BlackScholesBodyCPU(
h_CallResult[opt],
h_PutResult[opt],
h_StockPrice[opt],
h_OptionStrike[opt],
h_OptionYears[opt],
Riskfree,
Volatility
);
}
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