public static void CapletVol20Y_InputInterp()
{
#region Data
// We load a set of data (not real)
DataForCapletExample1 d = new DataForCapletExample1();
double[] df = d.df();
double[] yf = d.yf();
double[] T = d.T();
double[] fwd = d.fwd();
double[] atmfwd = d.atmfwd();
double[] capVol = d.capVol();
double[] avT = d.avT();
double[] avcapVol = d.avcapVol();
#endregion
// All Data available
double[] CapletVol = Formula.CapletVolBootstrapping(T, df, fwd, yf, capVol, atmfwd);
// Cubic input
SimpleCubicInterpolator CubicInt = new SimpleCubicInterpolator(avT, avcapVol);
double[] cubicInterpCapVol = CubicInt.Curve(T);
double[] CapletVolCubicInput = Formula.CapletVolBootstrapping(T, df, fwd, yf, cubicInterpCapVol, atmfwd);
// Linear Input
LinearInterpolator LinearInt = new LinearInterpolator(avT, avcapVol);
double[] linearInterpCapVol = LinearInt.Curve(T);
double[] CapletVolLinearInput = Formula.CapletVolBootstrapping(T, df, fwd, yf, linearInterpCapVol, atmfwd);
#region print results
ExcelMechanisms exl = new ExcelMechanisms();
Vector <double> CapletVol_ = new Vector <double>(CapletVol, 1);
Vector <double> CapletVolCubicInput_ = new Vector <double>(CapletVolCubicInput, 1);
Vector <double> CapletVolLinearInput_ = new Vector <double>(CapletVolLinearInput, 1);
Vector <double> xarr = new Vector <double>(T, 1);
List <string> labels = new List <string>()
{
"CapletVol All input", "CapVol Cubic Input", "CapVol Linear Input"
};
List <Vector <double> > yarrs = new List <Vector <double> >()
{
CapletVol_, CapletVolCubicInput_, CapletVolLinearInput_
};
exl.printInExcel <double>(xarr, labels, yarrs, "Caplet Vol Input Interpolation", "Term", "Volatility");
#endregion
}
public void Solve()
{
#region data
DataForCapletExample1 d = new DataForCapletExample1();
df = d.df();
yf = d.yf();
T = d.T();
fwd = d.fwd();
atmfwd = d.atmfwd();
x = d.avT(); // available maturity for market data
y = d.avcapVol(); // available Cap volatility from market
capPremium = new double[x.Length];
#endregion end data
double cP = 0.0;
// Calculate Cap price using Cap volatility available
for (int i = 0; i < x.Length; i++)
{
int maxJ = Array.IndexOf(T, x[i]); // right index
cP = 0.0;
for (int j = 0; j <= maxJ; j++)
{
cP += Formula.CapletBlack(T[j], yf[j], 1, atmfwd[maxJ], y[i], df[j], fwd[j]);
}
capPremium[i] = cP; // collecting values
}
#region Setting up minimisation
// Starting missing caplet vol guess
double[] VolGuess = Enumerable.Repeat(y[0], y.Length).ToArray();
double epsg = 0.000000000001; // original setting
double epsf = 0;
double epsx = 0;
int maxits = 0;
alglib.minlmstate state;
alglib.minlmreport rep;
// Number of equation to match
int NConstrains = x.Length;
// see alglib documentation
alglib.minlmcreatev(NConstrains, VolGuess, 0.000001, out state);
alglib.minlmsetcond(state, epsg, epsf, epsx, maxits);
alglib.minlmoptimize(state, function_fvec, null, null);
alglib.minlmresults(state, out VolGuess, out rep);
#endregion
// Minimisation Done!
// Uncomment to change interpolator
LinearInterpolator interp = new LinearInterpolator(x, VolGuess);
// SimpleCubicInterpolator interp = new SimpleCubicInterpolator(x, VolGuess);
double[] Vols = interp.Curve(T); // Vols from interpolator
#region print results
ExcelMechanisms exl = new ExcelMechanisms();
Vector <double> CapVol = new Vector <double>(Vols, 1);
Vector <double> xarr = new Vector <double>(T, 1);
List <string> labels = new List <string>()
{
"CapVol"
};
List <Vector <double> > yarrs = new List <Vector <double> >()
{
CapVol
};
exl.printInExcel <double>(xarr, labels, yarrs, "Caplet vs Cap Vol", "Term", "Volatility");
#endregion
}
public static void SimpleBootstrap20Y()
{
#region data
// We load a set of data (not real)
DataForCapletExample1 data1 = new DataForCapletExample1();
double[] df = data1.df();
double[] yf = data1.yf();
double[] T = data1.T();
int N = df.Length;
double[] fwd = new double[N];
double[] atmfwd = new double[N];
double[] capletVol = new double[N];
double[] capPrice = new double[N];
double df_ini = data1.df_ini;
double[] capVol = data1.capVol();
#endregion
// calculate fwd
fwd[0] = ((df_ini / df[0]) - 1) / yf[0];
for (int i = 1; i < df.Length; i++)
{
fwd[i] = ((df[i - 1] / df[i]) - 1) / yf[i];
}
// calculate ATM strike
double summ = 0.0;
for (int i = 0; i < df.Length; i++)
{
summ += yf[i] * df[i];
atmfwd[i] = (df_ini - df[i]) / summ;
}
double shorterCap = 0.0;
// calculate cap price using flat vol
for (int i = 0; i < N; i++)
{
shorterCap = 0.0;
for (int j = 0; j <= i; j++)
{
capPrice[i] += Formula.CapletBlack(T[j], yf[j], 100, atmfwd[i], capVol[i], df[j], fwd[j]);
}
for (int j = 0; j < i; j++)
{
shorterCap += Formula.CapletBlack(T[j], yf[j], 100, atmfwd[i], capletVol[j], df[j], fwd[j]);
}
NumMethod.myMethodDelegate fname =
s => capPrice[i] - shorterCap - Formula.CapletBlack(T[i], yf[i], 100, atmfwd[i], s, df[i], fwd[i]);
capletVol[i] = NumMethod.NewRapNum(fname, 0.20);
}
#region print results
ExcelMechanisms exl = new ExcelMechanisms();
Vector <double> CapletVol = new Vector <double>(capletVol, 1);
Vector <double> CapVol = new Vector <double>(capVol, 1);
Vector <double> xarr = new Vector <double>(T, 1);
List <string> labels = new List <string>()
{
"CapletVol", "CapVol"
};
List <Vector <double> > yarrs = new List <Vector <double> >()
{
CapletVol, CapVol
};
exl.printInExcel <double>(xarr, labels, yarrs, "Caplet vs Cap Vol", "Term", "Volatility");
#endregion
}
