public void C9_9_4_European()
{
var opt = _testOption;
var k = opt.T / numberOfSteps;
var discounting = Math.Exp(-opt.r * k);
var binParams = new CRRStrategy(opt.sig, opt.r, k);; // Factory
var bn = new BinomialMethod(discounting, binParams, numberOfSteps);
bn.ModifyLattice(opt.K);
// Phase III: Backward Induction and compute option price
Vector <double> RHS = new Vector <double>(bn.BasePyramidVector());
if (binParams.BinomialType == BinomialType.Additive)
{
RHS[RHS.MinIndex] = opt.K * Math.Exp(numberOfSteps * binParams.DownValue);
for (int j = RHS.MinIndex + 1; j <= RHS.MaxIndex; j++)
{
RHS[j] = RHS[j - 1] * Math.Exp(binParams.UpValue - binParams.DownValue);
}
}
var pay = opt.PayoffVector(RHS);
var pr = bn.GetPrice(pay);
Assert.AreEqual(pr, 2.8307, 0.01);
}
public void C9_9_9_2_TheLeisenReimerMethod()
{
var opt = _testOption;
var numberOfSteps = 99;
var k = opt.T / numberOfSteps;
var discounting = Math.Exp(-opt.r * k);
var S = opt.K;
var binParams = new LeisenReimerStrategy(numberOfSteps, S, opt.K, opt.T, opt.r, opt.sig);
var bn = new BinomialMethod(discounting, binParams, numberOfSteps);
bn.ModifyLattice(S);
// Phase III: Backward Induction and compute option price
var RHS = new Vector <double>(bn.BasePyramidVector());
var pay = opt.PayoffVector(RHS);
var pr = bn.GetPrice(pay);
Assert.AreEqual(pr, 2.8307, 0.01);
}
/* public static double EarlyImpl(double P, double S)
* {
*
* double K = 10.0;
*
* if (P > K - S)
* {
* return P;
* }
* return K - S;
* }*/
// This could be made into a member function of Option
public static void Main()
{
// Phase I: Create and initialise the option
IOptionFactory fac = getFactory();
int N = 200;
Console.Write("Number of time steps: ");
N = Convert.ToInt32(Console.ReadLine());
double S;
Console.Write("Underlying price: ");
S = Convert.ToDouble(Console.ReadLine());
Option opt = fac.create();
double k = opt.T / N;
// Create basic lattice
double discounting = Math.Exp(-opt.r * k);
// Phase II: Create the binomial method and forward induction
BinomialLatticeStrategy binParams = getStrategy(opt.sig, opt.r, k, S, opt.K, N); // Factory
BinomialMethod bn = new BinomialMethod(discounting, binParams, N);
bn.modifyLattice(S);
// Phase III: Backward Induction and compute option price
Vector <double> RHS = new Vector <double>(bn.BasePyramidVector());
if (binParams.bType == BinomialType.Additive)
{
RHS[RHS.MinIndex] = S * Math.Exp(N * binParams.downValue());
for (int j = RHS.MinIndex + 1; j <= RHS.MaxIndex; j++)
{
RHS[j] = RHS[j - 1] * Math.Exp(binParams.upValue() - binParams.downValue());
}
}
Vector <double> Pay = opt.PayoffVector(RHS);
double pr = bn.getPrice(Pay);
Console.WriteLine("European {0}", pr);
// Binomial method with early exercise
BinomialMethod bnEarly = new BinomialMethod(discounting, binParams, N, opt.EarlyImpl);
bnEarly.modifyLattice(S);
Vector <double> RHS2 = new Vector <double>(bnEarly.BasePyramidVector());
Vector <double> Pay2 = opt.PayoffVector(RHS2);
double pr2 = bnEarly.getPrice(Pay2);
Console.WriteLine("American {0}", pr2);
// Display in Excel; first create array of asset mesh points
int startIndex = 0;
Vector <double> xarr = new Vector <double>(N + 1, startIndex);
xarr[xarr.MinIndex] = 0.0;
for (int j = xarr.MinIndex + 1; j <= xarr.MaxIndex; j++)
{
xarr[j] = xarr[j - 1] + k;
}
// Display lattice in Excel
ExcelMechanisms exl = new ExcelMechanisms();
try
{
// public void printLatticeInExcel(Lattice<double> lattice, Vector<double> xarr, string SheetName)
string sheetName = "Lattice";
exl.printLatticeInExcel(bnEarly.getLattice(), xarr, sheetName);
}
catch (Exception e)
{
Console.WriteLine(e);
}
}
public void C9_9_ExcelOutput()
{
var opt = _testOption;
var steps = 50;
var S = opt.K;
double k = opt.T / steps;
double discounting = Math.Exp(-opt.r * k);
var binParams = new CRRStrategy(opt.sig, opt.r, k);; // Factory
var bn = new BinomialMethod(discounting, binParams, steps, opt.EarlyImpl);
bn.ModifyLattice(opt.K);
// Phase III: Backward Induction and compute option price
Vector <double> RHS = new Vector <double>(bn.BasePyramidVector());
if (binParams.BinomialType == BinomialType.Additive)
{
RHS[RHS.MinIndex] = S * Math.Exp(steps * binParams.DownValue);
for (int j = RHS.MinIndex + 1; j <= RHS.MaxIndex; j++)
{
RHS[j] = RHS[j - 1] * Math.Exp(binParams.UpValue - binParams.DownValue);
}
}
var pay = opt.PayoffVector(RHS);
var pr = bn.GetPrice(pay);
// Display lattice in Excel
var file = Path.GetTempFileName();
file = Path.ChangeExtension(file, "xlsx");
ExcelMechanisms exl = new ExcelMechanisms(file);
try
{
// Display in Excel; first create array of asset mesh points
int startIndex = 0;
Vector <double> xarr = new Vector <double>(steps + 1, startIndex);
xarr[xarr.MinIndex] = 0.0;
for (int j = xarr.MinIndex + 1; j <= xarr.MaxIndex; j++)
{
xarr[j] = xarr[j - 1] + k;
}
string sheetName = "Lattice";
exl.printLatticeInExcel(bn.GetOptionLattice, xarr, sheetName);
exl.Save();
}
catch (Exception e)
{
Console.WriteLine(e);
}
Assert.AreEqual(pr, 3.0732, 0.01);
}
public void C9_9_7_PadeApproximation()
{
var opt = new Library.Binominal.Option
{
K = 65,
type = 1,
T = 0.25,
r = 0.08,
sig = 0.3
};
double PriceWithJR(int numSteps, int type)
{
opt.type = type;
var steps = numSteps;
var S = 60;
double k = opt.T / steps;
double discounting = Math.Exp(-opt.r * k);
var binParams = new PadeJRStrategy(opt.sig, opt.r, k); // Factory
var bn = new BinomialMethod(discounting, binParams, steps);
bn.ModifyLattice(S);
// Phase III: Backward Induction and compute option price
var RHS = new Vector <double>(bn.BasePyramidVector());
var pay = opt.PayoffVector(RHS);
return(bn.GetPrice(pay));
}
double PriceWithCRR(int numSteps, int type)
{
opt.type = type;
var steps = numSteps;
var S = 60;
double k = opt.T / steps;
double discounting = Math.Exp(-opt.r * k);
var binParams = new PadeCRRStrategy(opt.sig, opt.r, k); // Factory
var bn = new BinomialMethod(discounting, binParams, steps);
bn.ModifyLattice(S);
// Phase III: Backward Induction and compute option price
var RHS = new Vector <double>(bn.BasePyramidVector());
var pay = opt.PayoffVector(RHS);
return(bn.GetPrice(pay));
}
Assert.AreEqual(PriceWithCRR(100, 1), 2.1399, 0.01);
Assert.AreEqual(PriceWithCRR(100, 2), 5.8527, 0.01);
Assert.AreEqual(PriceWithCRR(200, 1), 2.1365, 0.01);
Assert.AreEqual(PriceWithCRR(200, 2), 5.8494, 0.01);
Assert.AreEqual(PriceWithJR(100, 1), 2.1386, 0.01);
Assert.AreEqual(PriceWithJR(100, 2), 5.8516, 0.01);
Assert.AreEqual(PriceWithJR(200, 1), 2.1344, 0.01);
Assert.AreEqual(PriceWithJR(200, 2), 5.8473, 0.01);
}