private static void GeneratePaths(float[] paths, float r, float sigma, float dt, int numSims, int numTimesteps)
{
//
int tid = (BlockIndex.X * BlockDimension.X) + ThreadIndex.X;
int step = GridDimension.X * BlockDimension.X;
// Compute parameters
float drift = (r - (0.5f * sigma * sigma)) * dt;
float diffusion = sigma * DeviceMath.Sqrt(dt);
// Simulate the paths
for (int i = tid; i < numSims; i += step)
{
// Current output index
int output = i;
// Simulate the path
float s = 1.0f;
for (int t = 0; t < numTimesteps; t++, output += numSims)
{
s *= DeviceMath.Exp(drift + (diffusion * NormalRNG.NextFloat()));
paths[output] = s;
}
}
}
private static void BlackScholesGPUKernel(float[] callResult, float[] putResult, float[] stockPrice, float[] optionStrike, float[] optionYears, float riskFree, float volatility)
{
// Thread index
int ThreadId = BlockDimension.X * BlockIndex.X + ThreadIndex.X;
// Total number of threads in execution grid
int TotalThreads = BlockDimension.X * GridDimension.X;
// No matter how small execution grid is, or how many options we're processing,
// by using this loop we'll get perfect memory coalescing
for (int OptionIndex = ThreadId; OptionIndex < callResult.Length; OptionIndex += TotalThreads)
{
float s = stockPrice[OptionIndex];
float x = optionStrike[OptionIndex];
float t = optionYears[OptionIndex];
// Calculate the square root of the time to option expiration, in years
float SqrtT = DeviceMath.Sqrt(t);
// Calculate the Black-Scholes parameters
float d1 = (DeviceMath.Log(s / x) + (riskFree + 0.5f * volatility * volatility) * t) / (volatility * SqrtT);
float d2 = d1 - volatility * SqrtT;
// Plug the parameters into the Cumulative Normal Distribution (CND)
float K1 = 1.0f / (1.0f + 0.2316419f * DeviceMath.Abs(d1));
float CndD1 = RSQRT2PI * DeviceMath.Exp(-0.5f * d1 * d1) *
(K1 * (A1 + K1 * (A2 + K1 * (A3 + K1 * (A4 + K1 * A5)))));
if (d1 > 0)
{
CndD1 = 1.0f - CndD1;
}
float K2 = 1.0f / (1.0f + 0.2316419f * DeviceMath.Abs(d2));
float CndD2 = RSQRT2PI * DeviceMath.Exp(-0.5f * d2 * d2) *
(K2 * (A1 + K2 * (A2 + K2 * (A3 + K2 * (A4 + K2 * A5)))));
if (d2 > 0)
{
CndD2 = 1.0f - CndD2;
}
// Calculate the discount rate
float ExpRT = DeviceMath.Exp(-1.0f * riskFree * t);
// Calculate the values of the call and put options
callResult[OptionIndex] = s * CndD1 - x * ExpRT * CndD2;
putResult[OptionIndex] = x * ExpRT * (1.0f - CndD2) - s * (1.0f - CndD1);
}
}
