public void BlackScholes()
{
NArray s;
using (var stream = new RandomNumberStream(StorageLocation.Host, RandomNumberGeneratorType.MRG32K3A))
{
var normal = new Normal(stream, 0, 1);
s = 100 * NMath.Exp(NArray.CreateRandom(5, normal) * 0.2);
}
double k = 90;
var volatility = 0.2;
var t = 5;
var df = Math.Exp(-0.005 * t);
var result = NArray.Evaluate(() =>
{
var f = s / df;
return(df * Finance.BlackScholes(CallPut.Call, f, k, volatility, t));
}, s);
var sds = s + 1e-6;
var check = (df * Finance.BlackScholes(CallPut.Call, sds / df, k, volatility, t)
- df * Finance.BlackScholes(CallPut.Call, s / df, k, volatility, t)) * 1e6;
Assert.IsTrue(TestHelpers.AgreesAbsolute(result[1], check));
}
public static void VectorForm(NArray variates, NArray optionPrices)
{
double deltaT = 1;
double r = 0.1;
double vol = 0.3;
var logStockPrice = Math.Log(100)
+ variates * Math.Sqrt(deltaT) * vol + (r - 0.5 * vol * vol) * deltaT;
var forwardStockPrices = NMath.Exp(logStockPrice + r * deltaT);
optionPrices.Assign(Finance.BlackScholes(-1, forwardStockPrices, 90, 0.2, 1));
}
public void BlackScholesPerformance()
{
double k = 90;
var volatility = 0.2;
var t = 5;
var s = new List <NArray>();
int batchCount = 1000;
int vectorLength = 5000;
using (var stream = new RandomNumberStream(StorageLocation.Host, RandomNumberGeneratorType.MRG32K3A))
{
var normal = new Normal(stream, 0, 1);
for (int i = 0; i < batchCount; ++i)
{
s.Add(100 * NMath.Exp(NArray.CreateRandom(vectorLength, normal) * 0.2));
}
}
var result = NArray.CreateLike(s.First());
double elapsedTime = TestHelpers.TimeitSeconds(() =>
{
for (int i = 0; i < batchCount; ++i)
{
NArray.Evaluate(() =>
{
return(Finance.BlackScholes(CallPut.Call, s[i], k, volatility, t));
}, new List <NArray>(), Aggregator.ElementwiseAdd, new List <NArray> {
result
});
}
});
Console.WriteLine(string.Format("Time per option price (single core): {0} ns", elapsedTime * 1e9 / (batchCount * vectorLength)));
Console.WriteLine(string.Format("Valuations per second (single core): {0:F0} million", batchCount * vectorLength / (elapsedTime * 1e6)));
}
public NArray Price(int timeIndex)
{
return(Finance.BlackScholes(-1, ForwardStockPrices(timeIndex), Strike, 0.2, 1));
}
public void TestBlackScholes()
{
var location = StorageLocation.Host;
using (var randomStream = new RandomNumberStream(location, RandomNumberGeneratorType.MRG32K3A, 111))
{
var normalDistribution = new Normal(randomStream, 0, 1);
double deltaT = 1;
double r = 0.1;
double vol = 0.3;
var options = new ParallelOptions();
options.MaxDegreeOfParallelism = 1;
var variates = NArray.CreateRandom(5000, normalDistribution);
NArray optionPrices = NArray.CreateLike(variates);
var watch = new Stopwatch(); watch.Start();
Parallel.For(0, 1000, options, (i) =>
{
optionPrices = NArray.CreateLike(variates);
var logStockPrice = Math.Log(100)
+ variates * Math.Sqrt(deltaT) * vol + (r - 0.5 * vol * vol) * deltaT;
var stockPrices = NMath.Exp(logStockPrice);
optionPrices.Assign(Finance.BlackScholes(-1, stockPrices, 90, 0.2, 1));
});
Console.WriteLine("Baseline sequential");
Console.WriteLine(watch.ElapsedMilliseconds); watch.Restart();
Parallel.For(0, 1000, (i) =>
{
optionPrices = NArray.CreateLike(variates);
var logStockPrice = Math.Log(100)
+ variates * Math.Sqrt(deltaT) * vol + (r - 0.5 * vol * vol) * deltaT;
var stockPrices = NMath.Exp(logStockPrice);
optionPrices.Assign(Finance.BlackScholes(-1, stockPrices, 90, 0.2, 1));
});
Console.WriteLine("Baseline threaded");
Console.WriteLine(watch.ElapsedMilliseconds);
NArray optionPrices2 = NArray.CreateLike(variates);
watch.Restart();
var vectorOptions = new DeferredExecution.VectorExecutionOptions()
{
MultipleThreads = true
};
Parallel.For(0, 1000, options, (i) =>
{
optionPrices2 = NArray.CreateLike(variates);
NArray.Evaluate(optionPrices2, () =>
{
var logStockPrice = Math.Log(100)
+ variates * Math.Sqrt(deltaT) * vol + (r - 0.5 * vol * vol) * deltaT;
var stockPrices = NMath.Exp(logStockPrice);
return(Finance.BlackScholes(-1, stockPrices, 90, 0.2, 1));
});
});
Console.WriteLine("Deferred sequential");
Console.WriteLine(watch.ElapsedMilliseconds);
Console.WriteLine(CheckitString((optionPrices.Storage as ManagedStorage <double>).Array, (optionPrices2.Storage as ManagedStorage <double>).Array));
watch.Restart();
Parallel.For(0, 1000, (i) =>
{
//optionPrices2 = NArray.CreateLike(variates);
optionPrices2 = NArray.Evaluate(() =>
{
var logStockPrice = Math.Log(100)
+ variates * Math.Sqrt(deltaT) * vol + (r - 0.5 * vol * vol) * deltaT;
var stockPrices = NMath.Exp(logStockPrice);
return(Finance.BlackScholes(-1, stockPrices, 90, 0.2, 1));
});
});
Console.WriteLine("Deferred threaded");
Console.WriteLine(watch.ElapsedMilliseconds); watch.Restart();
Console.WriteLine(CheckitString((optionPrices.Storage as ManagedStorage <double>).Array, (optionPrices2.Storage as ManagedStorage <double>).Array));
}
}
public void Example1()
{
var location = StorageLocation.Host;
var watch = new System.Diagnostics.Stopwatch(); watch.Start();
using (var randomStream = new RandomNumberStream(location, RandomNumberGeneratorType.MRG32K3A, 111))
{
var normal = new Normal(randomStream, 0, 1);
var test = NArray.CreateRandom(1000, normal);
for (int i = 0; i < 363 * 100; ++i)
{
test.FillRandom(normal);
}
}
watch.Stop();
var elapsed = watch.ElapsedMilliseconds * 5000 / (100 * 1000);
NArray a, b;
using (var randomStream = new RandomNumberStream(location, RandomNumberGeneratorType.MRG32K3A, 111))
{
var normal = new Normal(randomStream, 0, 1);
a = NArray.CreateRandom(5000, normal);
b = NArray.CreateRandom(5000, normal);
}
var expressions = new StringBuilder();
var result = NArray.Evaluate(() =>
{
return(a * b + a * NMath.Exp(b));
}, expressions);
var expressionsDiff = new StringBuilder();
var resultDiff = NArray.Evaluate(() =>
{
return(a * b + a * NMath.Exp(2 * b));
}, expressionsDiff, a, b);
var output = expressionsDiff.ToString();
var expressionsDiff2 = new StringBuilder();
var s = NMath.Exp(a) + 5;
var resultDiff2 = NArray.Evaluate(() =>
{
return(Finance.BlackScholes(CallPut.Call, s, 5, 1, 1));
//return NMath.Exp(NMath.Sqrt(a));
}, expressionsDiff2, s);
var check = (Finance.BlackScholes(CallPut.Call, s + 1e-6, 5, 1, 1) - Finance.BlackScholes(CallPut.Call, s, 5, 1, 1)) / 1e-6;
var expected = check.DebugDataView.Take(10).ToArray();
var obtained = resultDiff2[1].DebugDataView.Take(10).ToArray();
var output2 = expressionsDiff2.ToString();
Console.Write(output2);
VectorAccelerator.Tests.TestHelpers.Timeit(() =>
{
var resultTiming = NArray.Evaluate(() =>
{
return(Finance.BlackScholes(CallPut.Call, s, 5, 1, 1));
}, expressionsDiff2);
});
}
