protected override double CalcPv(IOption option, IMarketCondition market, double timeIncrement = 0.0)
{
var dayCount = market.DiscountCurve.Value.DayCount;
var startDate = market.ValuationDate;
var maturityDate = option.ExerciseDates.Last();
var t = dayCount.CalcDayCountFraction(market.ValuationDate, maturityDate) + timeIncrement;
var bsProcess = new BlackScholesProcess(
market.DiscountCurve.Value.ZeroRate(startDate, maturityDate),
market.DividendCurves.Value.Values.First().ZeroRate(startDate, maturityDate),
market.VolSurfaces.Value.Values.First().GetValue(maturityDate, option.Strike));
var pdeSolver = new SecondOrderPdeCrankNicolson(
bsProcess.Drift,
(t0, s) => 0.5 * Math.Pow(bsProcess.Diffusion(t0, s), 2.0),
market.DiscountCurve.Value.GetSpotRate);
double[] x;
double[] xGrid;
InitializeGrid(market.SpotPrices.Value.Values.First(), option.Strike, bsProcess.Diffusion(0, 0), t, out x, out xGrid);
var dt = t / _steps;
return(pdeSolver.Solve(
Enumerable.Range(0, _steps + 1).Select(i => i * dt).ToArray(),
xGrid,
x,
price => option.GetPayoff(new[] { price })[0].PaymentAmount
)[0][_gridSize]);
}
public double ReverseInduction()
{
var optionPrices = new double[_steps + 1][];
optionPrices[_steps] = new double[_steps + 1];
for (var j = 0; j < _steps + 1; ++j)
{
optionPrices[_steps][j] = _option.GetPayoff(new[] { _binomialTree.StateValue(_steps, j) }).Sum(x => x.PaymentAmount);
}
for (var i = _steps - 1; i >= 0; --i)
{
optionPrices[i] = new double[i + 1];
for (var j = 0; j <= i; ++j)
{
var pu = _binomialTree.Probability(i, j, BranchDirection.Up);
var pd = _binomialTree.Probability(i, j, BranchDirection.Down);
var dt = _binomialTree.Dt;
var df = Math.Exp(-_binomialTree.Process.GetDiscountRate(0.0) * dt);
var optionValue = df * (pu * optionPrices[i + 1][j + 1] + pd * optionPrices[i + 1][j]);
if (_option.Exercise == OptionExercise.European)
{
optionPrices[i][j] = optionValue;
}
else
{
optionPrices[i][j] = ((i * dt) >= _tExStart && (i * dt) <= _tExEnd)
? Math.Max(_option.GetPayoff(new[] { _binomialTree.StateValue(i, j) }).Sum(x => x.PaymentAmount), optionValue)
: optionValue;
}
}
}
return(optionPrices[0][0]);
}
public double payOffaMaturite(IOption option, List <DataFeed> priceList)
{
return(option.GetPayoff(priceList.Last().PriceList));
}
//private double originalPv(IOption option, IMarketCondition market) {
// var valueDate = market.ValuationDate;
// var dayCount = market.DiscountCurve.Value.DayCount;
// var tExStart = dayCount.CalcDayCountFraction(valueDate, option.ExerciseDates[0]);
// var tExEnd = dayCount.CalcDayCountFraction(valueDate, option.ExerciseDates.Last());
// var binomialTree = BuildTree(market, tExEnd, option.Strike, market.SpotPrices.Value.Values.First(), _steps);
// var treeEngine = new BinomialTreeWithNoDividend(binomialTree, option, _steps, tExStart, tExEnd);
// return treeEngine.ReverseInduction();
//}
private double BinomialDiscreteDividends(
IOption option, IMarketCondition market,
Date valueDate,
IDayCount dayCount,
double spotPrice,
double r,
double v,
Tuple <Date, double>[] dividends,
int steps, double tStart, double tEnd)
{
var dt = (tEnd - tStart) / steps;
var df = Math.Exp(-r * dt);
var u = Math.Exp(v * Math.Sqrt(dt));
var d = 1 / u;
var a = Math.Exp(r * dt);
var p = (a - d) / (u - d);
var uu = u * u;
if (dividends == null || dividends.Length == 0)
{
var binomialTree = BuildTree(market, tEnd, option.Strike, spotPrice, steps, vol: v, r: r);
var treeEngine = new BinomialTreeWithNoDividend(binomialTree, option, steps, tStart, tEnd);
return(treeEngine.ReverseInduction());
}
var cashDividendDate = dividends.First().Item1;
var cashDividendAmount = dividends.First().Item2;
var tCashDividend = dayCount.CalcDayCountFraction(valueDate, cashDividendDate);
var stepsBeforeDividend = Convert.ToInt16(Math.Floor(tCashDividend / (tEnd - tStart) * steps));
var stockPriceNodes = new List <double>();
var optionValueNodes = new List <double>();
var p0 = spotPrice * Math.Pow(d, stepsBeforeDividend);
stockPriceNodes.Add(p0);
foreach (int i in Enumerable.Range(1, stepsBeforeDividend))
{
stockPriceNodes.Add(stockPriceNodes[i - 1] * uu);
}
//option value for the node time step just before dividend
foreach (int i in Enumerable.Range(0, stepsBeforeDividend))
{
var valueNotExercising = BinomialDiscreteDividends(option, market, valueDate, dayCount,
spotPrice: stockPriceNodes[i] - cashDividendAmount,
r: r, v: v, dividends: dividends.Skip(1).ToArray(), steps: steps - stepsBeforeDividend,
tStart: tCashDividend,
tEnd: tEnd);
var exerciseValue = option.GetPayoff(new[] { stockPriceNodes[i] }).Sum(x => x.PaymentAmount);
if (option.Exercise == OptionExercise.American)
{
optionValueNodes.Add(Math.Max(valueNotExercising, exerciseValue));
}
else
{
optionValueNodes.Add(valueNotExercising);
}
}
//option value before dividend , reverse induction, normal binomial
foreach (int j in Enumerable.Range(0, stepsBeforeDividend - 1).Reverse())
{
foreach (int i in Enumerable.Range(0, j))
{
stockPriceNodes[i] = d * stockPriceNodes[i + 1];
var valueNotExercising = (p * optionValueNodes[i + 1] + (1 - p) * optionValueNodes[i]) * df;
if (option.Exercise == OptionExercise.American)
{
var exerciseValue = option.GetPayoff(new[] { stockPriceNodes[i] }).Sum(x => x.PaymentAmount);
optionValueNodes[i] = Math.Max(valueNotExercising, exerciseValue);
}
else
{
optionValueNodes[i] = valueNotExercising;
}
}
}
return(optionValueNodes[0]);
}
/// <summary>
/// 计算期权现值
/// </summary>
/// <param name="option">期权</param>
/// <param name="markets">市场</param>
/// <returns>计算结果</returns>
public override double[] CalcPvs(IOption option, IMarketCondition[] markets)
{
if (AnalyticalOptionPricerUtil.isForwardFuturesOption(option.UnderlyingProductType))
{
//market = market.UpdateCondition(new UpdateMktConditionPack<Dictionary<string, IYieldCurve>>(m => m.DividendCurves, new Dictionary<string, IYieldCurve> { { "", market.DiscountCurve.Value} }));
markets = markets.Select(x =>
x.UpdateCondition(new UpdateMktConditionPack <Dictionary <string, IYieldCurve> >(m => m.DividendCurves, new Dictionary <string, IYieldCurve> {
{ "", x.DiscountCurve.Value }
}))
).ToArray();
}
var stochasticProcesses = CreateStochasticProcess1Ds(option, markets);
var nProcess = stochasticProcesses.Length;
var partitioner = Partitioner.Create(0, NumSimulations, NumSimulations / ParallelDegrees + 1);
var partitionerPvs = Enumerable.Range(0, nProcess).Select(x => new List <double>()).ToArray();
var parallelOption = new ParallelOptions()
{
MaxDegreeOfParallelism = ParallelDegrees
};
var size = option.ObservationDates.Length * 2 + 3;
List <double>[] result = null;
if (MonteCarloCollectPath)
{
result = new List <double> [NumSimulations + 1];
}
Parallel.ForEach(partitioner, parallelOption,
(range, loopState) =>
{
var pvs = Enumerable.Range(0, nProcess).Select(x => new List <double>()).ToArray();
var random = new MersenneTwister();
for (var n = range.Item1; n < range.Item2; ++n)
{
var paths = PathGenerator.GeneratePath(stochasticProcesses,
markets.Select(x => x.SpotPrices.Value.Values.First()).ToArray(),
markets.Select(x => x.ValuationDate.Value).ToArray(),
option.ObservationDates,
option.Calendar,
option.DayCount,
random);
for (var i = 0; i < nProcess; ++i)
{
pvs[i].Add(
option.GetPayoff(paths[i]).Sum(cf => cf.PaymentAmount * markets[i].DiscountCurve.Value.GetDf(markets[i].ValuationDate.Value, cf.PaymentDate))
);
//pvs[i].Add(option.GetPayoff(paths[i]).Sum(cf => cf.PaymentAmount * market.DiscountCurve.Value.GetDf(market.ValuationDate.Value, cf.PaymentDate)));
}
//antithetic path
for (var i = 0; i < nProcess; ++i)
{
pvs[i].Add(option.GetPayoff(paths[i + nProcess]).Sum(cf => cf.PaymentAmount * markets[i].DiscountCurve.Value.GetDf(markets[i].ValuationDate.Value, cf.PaymentDate)));
//pvs[i].Add(option.GetPayoff(paths[i + nProcess]).Sum(cf => cf.PaymentAmount * market.DiscountCurve.Value.GetDf(market.ValuationDate.Value, cf.PaymentDate)));
}
if (MonteCarloCollectPath)
{
var originalPathPrices = from e in paths[0].ToList() orderby e.Key select e.Value;
//original path price evolution
//result[n].AddRange(prices.ToList());
result[n] = originalPathPrices.ToList();
//pv
result[n].Add(pvs[0].First());
var antiPathPrices = from e in paths[1].ToList() orderby e.Key select e.Value;
//antipath price evolution
result[n].AddRange(antiPathPrices);
//pv
result[n].Add(pvs[0].Last());
//expected pv
result[n].Add(pvs[0].Average());
}
}
lock (partitionerPvs)
{
for (var i = 0; i < nProcess; ++i)
{
partitionerPvs[i].Add(pvs[i].Average());
}
}
//
});
if (MonteCarloCollectPath)
{
result[NumSimulations] = Enumerable.Repeat(0.0, 2 * (option.ObservationDates.Length + 1)).ToList();
result[NumSimulations].Add(partitionerPvs[0].Average());
var resultStr = result.Select(digits => string.Join(",", digits)).ToArray();
var folder = Environment.GetFolderPath(Environment.SpecialFolder.UserProfile);
var filename = folder + "/MonteCarlo.csv";
File.WriteAllLines(filename, resultStr);
}
//return partitionerPvs[0].Average();
return(partitionerPvs.Select(x => x.Average()).ToArray());
}