binomialOptions_gold.cpp

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#include <math.h>
#include <stdio.h>

#include "binomialOptions_common.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;
}

extern "C" void BlackScholesCall(float &callResult, TOptionData optionData)
{
    double S     = optionData.S;
    double X     = optionData.X;
    double T     = optionData.T;
    double R     = optionData.R;
    double V     = optionData.V;
    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);
}

////////////////////////////////////////////////////////////////////////////////
// Process an array of OptN options on CPU
// Note that CPU code is for correctness testing only and not for benchmarking.
////////////////////////////////////////////////////////////////////////////////

static double expiryCallValue(double S, double X, double vDt, int i)
{
    double d = S * exp(vDt * (2.0 * i - NUM_STEPS)) - X;
    return (d > 0) ? d : 0;
}

extern "C" void binomialOptionsCPU(float &callResult, TOptionData optionData)
{
    static double Call[NUM_STEPS + 1];
    const double  S = optionData.S;
    const double  X = optionData.X;
    const double  T = optionData.T;
    const double  R = optionData.R;
    const double  V = optionData.V;

    const double dt  = T / (double)NUM_STEPS;
    const double vDt = V * sqrt(dt);
    const double rDt = R * dt;

    // Per-step interest and discount factors
    const double If = exp(rDt);
    const double Df = exp(-rDt);

    // Values and pseudoprobabilities of upward and downward moves
    const double u      = exp(vDt);
    const double d      = exp(-vDt);
    const double pu     = (If - d) / (u - d);
    const double pd     = 1.0 - pu;
    const double puByDf = pu * Df;
    const double 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 = (float)Call[0];
}