/// <summary>
/// Simulate state variables needed for the pricing step of the exposure calculation. State variables
/// are not independent variables of the adjoint algorithmic differentation, and therefore can be simulated in advance.
/// </summary>
/// <param name="model"></param>
/// <param name="allZeroRatesT0"></param>
/// <param name="timePoints"></param>
/// <param name="graph"></param>
/// <param name="pricers"></param>
public void SimulateModel(out LinearGaussianModel model, out IEnumerable<NArray> allZeroRatesT0,
out TimePoint[] timePoints, out SimulationGraph graph, out List<IPricer> pricers)
{
var testDate = new DateTime(2015, 12, 1);
graph = new SimulationGraph(StorageLocation.Host, testDate);
var context = graph.Context;
context.Settings.SimulationCount = 5000;
var fixedLeg = Enumerable.Range(0, 40).Select(i => new FixedCashflowDeal()
{
Notional = -1e6,
Rate = 0.002,
Currency = Currency.EUR,
StartDate = testDate.AddMonths(3 * i),
EndDate = testDate.AddMonths(3 * (i + 1))
});
var floatingLeg = Enumerable.Range(0, 40).Select(i => new FloatingCashflowDeal()
{
Notional = 1e6,
Currency = Currency.EUR,
StartDate = testDate.AddMonths(3 * i),
EndDate = testDate.AddMonths(3 * (i + 1))
});
var correlationMatrix = context.Factory.CreateNArray(new double[,] {
{ 1.0, -0.92, 0.5},
{ -0.92, 1.0, -0.8},
{ 0.5, -0.8, 1.0}
});
var identifiers = new string[] { "IR_DiscountFactor_EUR_Factor0", "IR_DiscountFactor_EUR_Factor1",
"IR_DiscountFactor_EUR_Factor2"};
CorrelationHelper.AddMultivariateModelWeightsProvider(context, identifiers, correlationMatrix);
pricers = fixedLeg.Select(d => new FixedCashflowPricer(d) as IPricer)
.Concat(floatingLeg.Select(d => new FloatingCashflowPricer(d) as IPricer)).ToList();
foreach (var pricer in pricers) pricer.Register(graph);
var testVariates0 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor0");
var testVariates1 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor1");
var testVariates2 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor2");
var testFactor = graph.RegisterModel<MeanRevertingNormalPathModel>("IR_DiscountFactor_EUR_Factor0");
model = graph.RegisterModel<LinearGaussianModel>("EUR");
var numeraire = graph.RegisterModel<NumeraireModel>("EUR");
model.Factors[0].Sigma = 0.02; model.Factors[0].Lambda = 0.05;
model.Factors[1].Sigma = 0.03; model.Factors[1].Lambda = 0.2;
model.Factors[2].Sigma = 0.01; model.Factors[2].Lambda = 1.0;
var years = new double[] { 0, 1/365.35, 7/365.25, 14/365.25, 1/12, 2/12, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 };
var zeroRatesInPercent = new double[] { -0.3, -0.3, -0.29, -0.29, -0.3, -0.31, -0.31, -0.32, -0.32, -0.33, -0.34, -0.35, -0.35, -0.33, -0.28, -0.2, -0.11, -0.01, 0.1, 0.2, 0.37, 0.56, 0.71, 0.75, 0.76, 0.75, 0.75, 0.72, 0.7, 0.67, 0.64 };
model.ZeroRatesT0 = new Curve(years.Zip(zeroRatesInPercent,
(y, r) => new DataPoint(
testDate.AddDays(y * 365.25),
NArray.CreateScalar(r / 100)
)).ToArray());
var runner = graph.ToSimulationRunner();
runner.Prepare();
runner.Simulate();
timePoints = graph.Context.Settings.SimulationTimePoints;
allZeroRatesT0 = model.ZeroRatesT0.Data.Select(d => d.Value);
}
/// <summary>
/// Test building blocks of interest rate swap exposure calculation.
/// </summary>
public void TestBasics(LinearGaussianModel model, IEnumerable<NArray> allZeroRatesT0,
TimePoint[] timePoints, SimulationGraph graph)
{
bool testModel = true;
if (testModel)
{
var check1 = model[1, timePoints[1].DateTime.AddDays(182)].First();
Assert.IsTrue(TestHelpers.AgreesAbsolute(check1, 1.0015314301020275));
var check2 = model[1, timePoints[1].DateTime.AddDays(91)].First();
Assert.IsTrue(TestHelpers.AgreesAbsolute(check2, 1.0007451895710209));
var check3 = model.ForwardRate(1,
timePoints[1].DateTime.AddDays(91), timePoints[1].DateTime.AddDays(182)).First();
Assert.IsTrue(TestHelpers.AgreesAbsolute(check3, -0.0031509366920208916));
}
bool testProfile = true;
if (testProfile)
{
var testVariates0 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor0");
var testVariates1 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor1");
var testVariates2 = graph.RegisterFactor<NormalVariates>("IR_DiscountFactor_EUR_Factor2");
var check = Descriptive.Correlation(testVariates1.Value, testVariates2.Value);
// check 3M rolling tenor
var percentiles = new double[] { 1, 10, 50, 90, 99 };
var measures = new List<IList<double>>();
for (int i = 0; i < timePoints.Length; ++i)
{
var tenorMonths = 3;
var tenorYears = tenorMonths / 12.0;
var df = model[i, timePoints[i].DateTime.AddMonths(3)];
var zeroRate = -NMath.Log(df) / tenorYears;
var values = NMath.Percentiles(zeroRate, percentiles).ToList();
measures.Add(values);
}
var times = timePoints.Select(p => p.YearsFromBaseDate).ToArray();
var profile10 = measures.Select(p => p[1]).ToArray();
var profile90 = measures.Select(p => p[3]).ToArray();
}
bool testForwardRate = true;
if (testForwardRate)
{
// check 3M rolling tenor
var percentiles = new double[] { 1, 10, 50, 90, 99 };
var measures = new List<IList<double>>();
for (int i = 0; i < timePoints.Length; ++i)
{
var tenorMonths = 3;
var tenorYears = tenorMonths / 12.0;
var forwardRate = model.ForwardRate(i, timePoints[i].DateTime.AddMonths(3), timePoints[i].DateTime.AddMonths(6));
var values = NMath.Percentiles(forwardRate, percentiles).ToList();
measures.Add(values);
}
var times = timePoints.Select(p => p.YearsFromBaseDate).ToArray();
var profile10 = measures.Select(p => p[1]).ToArray();
var profile90 = measures.Select(p => p[3]).ToArray();
}
bool testAAD = true;
if (testAAD)
{
// just get the result
var result0 = NArray.Evaluate(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
return df;
});
// get the result and single derivative
var result1 = NArray.Evaluate(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
return df;
}, model.ZeroRatesT0[6].Value);
var log = new StringBuilder();
// get the result and all derivatives (and log output)
var result2 = NArray.Evaluate(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
return df;
}, log, allZeroRatesT0.ToArray());
// now forward rate and all derivatives
var result3 = NArray.Evaluate(() =>
{
var df = model.ForwardRate(10, timePoints[10].DateTime.AddMonths(3), timePoints[10].DateTime.AddMonths(6));
return df;
}, allZeroRatesT0.ToArray());
var unbumped0 = model[10, timePoints[10].DateTime.AddMonths(3)];
var expected0 = unbumped0.DebugDataView.ToArray();
var unbumped3 = model.ForwardRate(10, timePoints[10].DateTime.AddMonths(3), timePoints[10].DateTime.AddMonths(6));
var expected3 = unbumped3.DebugDataView.ToArray();
var obtained0 = result1[0].DebugDataView.ToArray();
var obtained1 = result1[0].DebugDataView.ToArray();
var obtained2 = result2[0].DebugDataView.ToArray();
var obtained3 = result3[0].DebugDataView.ToArray();
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected0, obtained0));
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected0, obtained1));
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected0, obtained2));
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected3, obtained3));
var logCheck = log.ToString();
var obtained_deriv1 = result1[1].DebugDataView.ToArray();
var obtained_deriv2 = result2[7].DebugDataView.ToArray();
var obtained_deriv3 = result3[7].DebugDataView.ToArray();
model.ZeroRatesT0.Data[6] = new DataPoint(model.ZeroRatesT0.Data[6].Time, model.ZeroRatesT0.Data[6].Value + 1e-6);
var bumped0 = model[10, timePoints[10].DateTime.AddMonths(3)];
var bumped3 = model.ForwardRate(10, timePoints[10].DateTime.AddMonths(3), timePoints[10].DateTime.AddMonths(6));
var expected_deriv1 = ((bumped0 - unbumped0) / 1e-6)
.DebugDataView.ToArray();
var expected_deriv3 = ((bumped3 - unbumped3) / 1e-6)
.DebugDataView.ToArray();
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected_deriv1, obtained_deriv1, 1e-5));
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected_deriv1, obtained_deriv2, 1e-5));
Assert.IsTrue(TestHelpers.AgreesAbsolute(expected_deriv3, obtained_deriv3, 1e-5));
}
bool checkTimings = true;
if (checkTimings)
{
// check timings
Console.WriteLine("Immediate execution");
VectorAccelerator.Tests.TestHelpers.Timeit(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
}, 10, 10);
Console.WriteLine(); Console.WriteLine("Deferred execution no derivatives");
VectorAccelerator.Tests.TestHelpers.Timeit(() =>
{
NArray.Evaluate(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
return df;
});
}, 10, 10);
Console.WriteLine(); Console.WriteLine("Deferred execution all derivatives");
VectorAccelerator.Tests.TestHelpers.Timeit(() =>
{
NArray.Evaluate(() =>
{
var df = model[10, timePoints[10].DateTime.AddMonths(3)];
return df;
}, allZeroRatesT0.ToArray());
}, 10, 10);
}
}
