public static List <Dictionary <Date, double> > GeneratePath(
IStochasticProcess1D[] processes,
double[] x0,
Date[] startDates,
Date[] observationDates,
ICalendar calendar,
IDayCount basis,
Random random)
{
var currentX = x0.ToList();
var processArray = processes.ToArray();
var count = processArray.Count();
var results = new List <Dictionary <Date, double> > [count * 2]
.Select(x => new Dictionary <Date, double>())
.ToList();
var normalRandomSamples = GetRandomSamples(random, observationDates.Length);
//original path
for (var i = 0; i < processArray.Length; ++i)
{
var start = startDates[i];
var obsDates = observationDates.Where(x => x > start).ToArray();
results[i][start] = currentX[i];
var currentT = 0.0;
for (int j = 0; j < obsDates.Count(); j++)
{
var dt = basis.CalcDayCountFraction(start, obsDates[j]);
currentX[i] = processArray[i].Evolve(currentT, currentX[i], dt, normalRandomSamples[j]);
currentT += dt;
results[i][obsDates[j]] = currentX[i];
start = obsDates[j];
}
}
//antithetic path
currentX = x0.ToList();
for (var i = 0; i < processArray.Length; ++i)
{
var start = startDates[i];
var obsDates = observationDates.Where(x => x > start).ToArray();
results[i + count][start] = currentX[i];
var currentT = 0.0;
for (int j = 0; j < obsDates.Count(); j++)
{
var step = basis.CalcDayCountFraction(start, obsDates[j]);
currentX[i] = processArray[i].Evolve(currentT, currentX[i], step, -normalRandomSamples[j]);
currentT += step;
results[i + count][obsDates[j]] = currentX[i];
start = obsDates[j];
}
}
return(results);
}
public static List <Dictionary <Date, List <double> > > GeneratePathND(
IStochasticProcessNd process,
double[] x0,
Date startDate,
Date[] obsDates,
ICalendar calendar,
IDayCount basis,
Random random)
{
var currentX = x0.ToList();
var results = new List <Dictionary <Date, List <double> > > [2]
.Select(x => new Dictionary <Date, List <double> >())
.ToList();
var normalRandomSamples = new List <List <double> >();
for (var i = 0; i < obsDates.Length; ++i) // i for each market
{
normalRandomSamples.Add(GetRandomSamples(random, process.Size));
}
//original path
obsDates = obsDates.Where(x => x > startDate).ToArray();
results[0][startDate] = currentX;
var currentT = 0.0;
for (var i = 0; i < obsDates.Count(); i++)
{
var dt = basis.CalcDayCountFraction(startDate, obsDates[i]);
currentX = process.Evolve(currentT, currentX, dt, normalRandomSamples[i]);
currentT += dt;
results[0][obsDates[i]] = currentX;
startDate = obsDates[i];
}
//antithetic path
obsDates = obsDates.Where(x => x > startDate).ToArray();
results[1][startDate] = currentX;
currentT = 0.0;
for (var i = 0; i < obsDates.Count(); i++)
{
var dt = basis.CalcDayCountFraction(startDate, obsDates[i]);
currentX = process.Evolve(currentT, currentX, dt, normalRandomSamples[i].Select(x => - x).ToList());
currentT += dt;
results[1][obsDates[i]] = currentX;
startDate = obsDates[i];
}
return(results);
}
private static List <double> GetRandomSamples(Random baseGen, int steps)
{
lock (baseGen)
{
var randomSamples = new List <double>();
for (int i = 0; i < steps; i++)
{
var temp = Normal.Sample(baseGen, 0, 1);
randomSamples.Add(temp);
}
return(randomSamples);
}
}