public static double[] ArithmeticAsianOptionPricing(ArithmeticAsianOptionProb prob)
{
double s = prob.SpotPrice;
double k = prob.StrikePrice;
double r = prob.InterestRate;
double t = prob.Maturity;
double sigma = prob.Volatility;
int n = prob.ObservationTime;
OptionTypeEnum optionType = prob.OptionType;
int pathNum = prob.PathNumber;
ControlVariateMethod method = prob.VariateMethod;
return(GetAAOPrice(s, k, t, r, sigma, optionType, method, pathNum, n));
}
public ArithmeticAsianOptionProb(double?spotPrice, double?volatility, double?interestRate,
double?maturity, double?strikePrice, int?observationTime, OptionTypeEnum optionType,
int?pathNumber, ControlVariateMethod variateMethod)
{
SpotPrice = spotPrice ?? default(double);
Volatility = volatility ?? default(double);
InterestRate = interestRate ?? default(double);
Maturity = maturity ?? default(double);
StrikePrice = strikePrice ?? default(double);
ObservationTime = observationTime ?? default(int);
OptionType = optionType;
PathNumber = pathNumber ?? default(int);
VariateMethod = variateMethod;
}
private static double[] GetAAOPrice(double s, double k, double t, double r, double sigma, OptionTypeEnum optionType, ControlVariateMethod method, int pathNum, int n)
{
const int seed = 11151;
double Dt = t / n;
double drift = Math.Exp((r - 0.5 * Math.Pow(sigma, 2)) * Dt);
Normal normal = new Normal();
normal.RandomSource = new Random(seed);
List <Double> arithPayoff = new List <Double>();
List <Double> geoPayoff = new List <Double>();
for (int i = 1; i <= pathNum; i++)
{
double growthFactor = drift * Math.Exp(sigma * Math.Sqrt(Dt) * normal.Sample());
List <Double> spath = new List <double>();
spath.Add(s * growthFactor);
double logSpathSum = Math.Log(spath.ElementAt(0));
for (int j = 2; j <= n; j++)
{
growthFactor = drift * Math.Exp(sigma * Math.Sqrt(Dt) * normal.Sample());
double tmp = spath.ElementAt(spath.Count - 1) * growthFactor;
spath.Add(tmp);
logSpathSum += Math.Log(tmp);
}
double arithMean = GetMeanVarStd(spath)[0];
double geoMean = Math.Exp((1.0 / n) * logSpathSum);
if (optionType == OptionTypeEnum.Call)
{
arithPayoff.Add(Math.Exp(-r * t) * Math.Max(arithMean - k, 0));
geoPayoff.Add(Math.Exp(-r * t) * Math.Max(geoMean - k, 0));
}
else
{
arithPayoff.Add(Math.Exp(-r * t) * Math.Max(k - arithMean, 0));
geoPayoff.Add(Math.Exp(-r * t) * Math.Max(k - geoMean, 0));
}
spath.Clear();
}
double[] arithPayoffMvs = GetMeanVarStd(arithPayoff);
double arithPayoffMean = arithPayoffMvs[0];
double arithPayoffVar = arithPayoffMvs[1];
double arithPayoffStd = arithPayoffMvs[2];
double[] geoPayoffMvs = GetMeanVarStd(geoPayoff);
double geoPayoffMean = geoPayoffMvs[0];
double geoPayoffVar = geoPayoffMvs[1];
double geoPayoffStd = geoPayoffMvs[2];
List <double> pointMultiplyList = new List <double>();
for (int iter = 0; iter < arithPayoff.Count; iter++)
{
pointMultiplyList.Add(arithPayoff[iter] * geoPayoff[iter]);
}
double covXY = GetMeanVarStd(pointMultiplyList)[0] - arithPayoffMean * geoPayoffMean;
double theta = covXY / geoPayoffVar;
double geoPrice = getGeoAsianOptionPrice(s, k, r, t, sigma, n, optionType);
List <double> controlVar = new List <double>();
for (int iter = 0; iter < arithPayoff.Count; iter++)
{
double tempVar = arithPayoff[iter] + theta * (geoPrice - geoPayoff[iter]);
controlVar.Add(tempVar);
}
double[] controlVarMvs = GetMeanVarStd(controlVar);
double controlVarMaen = controlVarMvs[0];
double controlVarVar = controlVarMvs[1];
double controlVarStd = controlVarMvs[2];
double lbound = 0;
double ubound = 0;
double[] results = new double[3];
if (method == ControlVariateMethod.None)
{
lbound = arithPayoffMean - (1.96 * arithPayoffStd) / Math.Sqrt(pathNum);
ubound = arithPayoffMean + (1.96 * arithPayoffStd) / Math.Sqrt(pathNum);
results[0] = lbound;
results[1] = arithPayoffMean;
results[2] = ubound;
}
else
{
lbound = controlVarMaen - (1.96 * controlVarStd) / Math.Sqrt(pathNum);
ubound = controlVarMaen + (1.96 * controlVarStd) / Math.Sqrt(pathNum);
results[0] = lbound;
results[1] = controlVarMaen;
results[2] = ubound;
}
return(results);
}
