// Calculate Yield from dirty price
public static double YieldFromFullPrice(double fullPrice, double yieldGuess, Date[] CashFlowsDate, double[] CashFlows,
int freq, Dc dc, Date SettlementDate, Compounding compounding, double FaceValue)
{
int N = CashFlowsDate.GetLength(0); // number of Cash flows dates
int k = Array.FindIndex(CashFlowsDate, n => n > SettlementDate); // get index of first cash flow after settlement date
Date[] Dates = new Date[N - k]; // array with pay dates after settlement
double[] Flows = new double[N - k]; // flows after settlement
Array.Copy(CashFlowsDate, k, Dates, 0, N - k); // fill array with needed data
Array.Copy(CashFlows, k, Flows, 0, N - k); // fill array with needed data
// define my function: we should find yield that match starting price
NumMethod.myMethodDelegate fname =
y_ => fullPrice - FullPriceFromYield(y_, Dates, Flows,
freq, dc, SettlementDate, compounding, FaceValue);
// return yield
return(NumMethod.NewRapNum(fname, yieldGuess));
}
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
}
public static void SimpleBootstrap()
{
#region data
// Array of discount factor
double[] df = new double[] { 0.994236269575566, 0.991625192926998, 0.989041421054714, 0.986231394133455, 0.983496974873945, 0.980646228901972, 0.977577789248498, 0.974244477497738, 0.97067019775667, 0.966860206840406, 0.96281976156406, 0.958481789220407, 0.953769370400552, 0.948855174348367, 0.94375920324068, 0.93838613470982, 0.93274533960824, 0.926957758932136, 0.92108389607756 };
// array of yf of each caplet
double[] yf = new double[] { 0.255555555555556, 0.261111111111111, 0.252777777777778, 0.244444444444444, 0.261111111111111, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.252777777777778, 0.255555555555556, 0.252777777777778, 0.252777777777778, 0.255555555555556, 0.255555555555556, 0.252777777777778 };
// array of expiry of each caplet
double[] T_1 = new double[] { 0.252054794520548, 0.50958904109589, 0.758904109589041, 1, 1.25753424657534, 1.50684931506849, 1.75616438356164, 2.00547945205479, 2.25479452054795, 2.5041095890411, 2.75342465753425, 3.0027397260274, 3.25205479452055, 3.5041095890411, 3.75342465753425, 4.0027397260274, 4.25479452054795, 4.50684931506849, 4.75616438356164 };
int N = df.Length; // number of elements
double[] fwd = new double[N]; // to contain forward rate
double[] atmfwd = new double[N]; // to contain ATM forward Cap strike
double[] capletVol = new double[N]; // to contain each caplet volatilities
double[] capPrice = new double[N]; // to contain Cap price
double df_ini = 0.99702; // first discount factor on T[0]
// Cap Volatility from the market
double[] capVol = new double[] { 0.5458, 0.5458, 0.5458, 0.55289, 0.557646575342466, 0.569168493150685, 0.582581643835616, 0.595015616438357, 0.563876164383561, 0.532736712328767, 0.501597260273972, 0.470798904109589, 0.470699178082192, 0.470598356164384, 0.470498630136986, 0.470348767123288, 0.465635342465753, 0.460921917808219, 0.456259726027397 };
#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; // Shorter Cap is the same Cap without last caplet
// calculate cap price using cal vol
for (int i = 0; i < N; i++)
{
shorterCap = 0.0;
// Note: here I use cap Vol
for (int j = 0; j <= i; j++)
{
capPrice[i] += Formula.CapletBlack(T_1[j], yf[j], 100, atmfwd[i], capVol[i], df[j], fwd[j]);
}
// Note: here I use Caplet vol
for (int j = 0; j < i; j++)
{
shorterCap += Formula.CapletBlack(T_1[j], yf[j], 100, atmfwd[i], capletVol[j], df[j], fwd[j]);
}
// Inizialize Newton Raphson solver
NumMethod.myMethodDelegate fname =
s => capPrice[i] - shorterCap - Formula.CapletBlack(T_1[i], yf[i], 100, atmfwd[i], s, df[i], fwd[i]);
capletVol[i] = NumMethod.NewRapNum(fname, 0.20); // the missing caplet volatility
}
// Print results
Console.WriteLine("Time ATMCapStrike CapletVol CapVol");
for (int i = 0; i < capletVol.Length; i++)
{
// Caplet expiry is T_1+yf (expiry + caplet year factor)
Console.WriteLine("{0:N2} {1:p5} {2:p5} {3:p5}", T_1[i] + yf[i],
atmfwd[i], capletVol[i], capVol[i]);
}
}
public static void SimpleBootstrapOneCaplet()
{
#region InputData
double[] yf = new double[] { 0.25278, 0.25556, 0.25556, 0.25 };
double[] T = new double[] { 0.25, 0.50, 0.75, 1.0 };
double[] df = new double[] { 0.99406, 0.99153, 0.98904, 0.98633 };
// One curve framework: traditional fwd calc
double[] fwd = new double[4];
fwd[0] = ((0.99695 / df[0]) - 1) / yf[0];
for (int i = 1; i < df.Length; i++)
{
fwd[i] = ((df[i - 1] / df[i]) - 1) / yf[i];
}
double K = 0.0102;
double sigma1Y3M = 0.2402;
double sigma1Y = 0.2364;
#endregion
// Price of 1Y3M (18 months) Cap @ vol = sigma1Y3M
double pxCap1Y3M = Formula.CapBlack(T, yf, 1, K, sigma1Y3M, df, fwd);
// Price of 1Y Cap @ vol=sigma1Y
double pxCap1Y = 0.0;
for (int i = 0; i < df.Length - 1; i++)
{
pxCap1Y += Formula.CapletBlack(T[i], yf[i], 1, K, sigma1Y, df[i], fwd[i]);
}
// Price of 3M Caplet starting in 1Y
double pxCaplet3M = pxCap1Y3M - pxCap1Y;
// Inizialize Newton-Raphson algorithm to find Caplet implied vol
NumMethod.myMethodDelegate fname =
s => pxCaplet3M - Formula.CapletBlack(T[3], yf[3], 1, K, s, df[3], fwd[3]);
// vol is the implied vol of 3M Caplet starting in 1Y. (0.20 is a starting guess)
double implVol = NumMethod.NewRapNum(fname, 0.20);
// array of caplet volatility (PieceWiseConstant under1Y)
double[] capletVol = new double[] { sigma1Y, sigma1Y, sigma1Y, implVol };
// printing results
Console.WriteLine("1Y Cap Vol {0:p5}", sigma1Y);
Console.WriteLine("1Y3M Cap Vol {0:p5}", sigma1Y3M);
Console.WriteLine("Calculated Implied 3M Caplet Vol Starting in 1Y: {0:p5}", implVol);
double pxCaplet = 0.0;
double pxCap = 0.0;
Console.WriteLine("\nUsing Caplet Volatilities");
for (int i = 0; i < df.Length; i++)
{
pxCaplet = Formula.CapletBlack(T[i], yf[i], 1, K, capletVol[i], df[i], fwd[i]);
pxCap += pxCaplet;
Console.WriteLine("Caplet #: {0} CapletVol:{1:p4} Px: {2:n5} Cumulated Price: {3:n7}", i + 1, capletVol[i], pxCaplet, pxCap);
}
Console.WriteLine("Price Cap as sum of Caplets using Caplet Vol: {0:n7}", pxCap);
// reset
pxCaplet = 0.0;
pxCap = 0.0;
Console.WriteLine("\nUsing Cap Volatilities");
for (int i = 0; i < df.Length; i++)
{
pxCaplet = Formula.CapletBlack(T[i], yf[i], 1, K, sigma1Y3M, df[i], fwd[i]);
pxCap += pxCaplet;
Console.WriteLine("Caplet #: {0} CapletVol:{1:p4} Px: {2:n5} Cumulated Price: {3:n7}", i + 1, sigma1Y3M, pxCaplet, pxCap);
}
Console.WriteLine("Price Cap as sum of Caplets using Cap Vol: {0:n7}", pxCap); // pxCap = pxCap1Y3M
}
