/// <summary>
/// TODO: Get this code into MATLAB using the .NET interface
/// Test swaption pricing
/// </summary>
private static void TestSwaptionPricing(string resultFile)
{
#region Swaption
// 1 EUR
var nominal = 1;
// Consider a ten-year semi-annual European swaption (10y x 5y), exercisable on each
// reset date, starting on 1-October-2020
var valuationDate = new DateTime(2015, 10, 1);
// Exercise date of the option = start date of swap
var exerciseDate = valuationDate.AddYears(2);
// Maturity of the underlying swap
var maturityDate = exerciseDate.AddYears(10);
// Strike (fixed interest rate payed by fixed leg)
var strike = 0.045;
// Tenor of the underlying swap in units of [months]
// = floating leg pays 6M-Libor
var tenor = 6;
var swaption = new Swaption(valuationDate, exerciseDate, maturityDate, tenor, strike, nominal);
#endregion Swaption
#region Initialize LIBOR market model
#region Initial yield curve
// Sample points of curve in units of [years]
var curveTimes = new[] { 1, 2, 3, 4, 5, 7, 10, 20 };
// annual interest rate in units of [1/year]
var yields = new[] { 0.01, 0.018, 0.024, 0.029, 0.033, 0.034, 0.035, 0.034 };
var maturityDates = curveTimes.Select(y => valuationDate.AddYears(y)).ToArray();
var yieldCurve = new YieldCurve(valuationDate, maturityDates, yields);
#endregion Initial yield curve
#region Model parameters
// Use the volatility term structure populaized by Riccardo Rebonato
// sigma_i(t) = (a * tau + b) * Math.Exp(-c * tau) + d; with tau = T[i] - t
// t is assumed to be in units of [years]
var volatiltyParameters = new[] { 0.3, -0.02, 0.7, 0.14 };
// Instantaneous correlations between the Brownian motions
// and hence the forward LIBOR rates
// rho(i,j) = exp(-beta * |T[i] - T[j]|)
const double beta = 0.08;
#endregion Model parameters
const int seed = 41;
var liborMarketModel = new LiborMarketModel(yieldCurve, beta, volatiltyParameters, swaption.TenorStructure, seed);
#endregion Initialize LIBOR market model
#region Strikes
const int nStrikes = 100;
const double strikeMin = 0;
const double strikeMax = 0.1;
const double step = (strikeMax - strikeMin) / (nStrikes - 1);
var strikes = new double[nStrikes];
for (var j = 0; j < strikes.Length; j++)
{
strikes[j] = strikeMin + step * j;
}
#endregion Strikes
#region Pricing
const int numberOfMonteCarloPaths = 100;
const int numberOfMonteCarloRuns = 100;
var prices = new double[numberOfMonteCarloRuns, nStrikes];
for (var k = 0; k < numberOfMonteCarloRuns; k++)
{
Utilities.DrawTextProgressBar(k + 1, numberOfMonteCarloRuns, "Monte Carlo run");
for (var i = 0; i < numberOfMonteCarloPaths; i++)
{
// Simulate forward LIBOR rate paths using Monto carlo simulation up to the
// exercise date of the swaption
var paths = liborMarketModel.SimulateForwardRates(swaption.ExerciseDate);
for (var j = 0; j < strikes.Length; j++)
{
swaption.Strike = strikes[j];
prices[k, j] += swaption.DiscountedPayoff(paths) / numberOfMonteCarloPaths;
}
}
}
#endregion Pricing
#region Export
try
{
// create a writer and open the file
var file = new StreamWriter(resultFile);
for (var j = 0; j < strikes.Length; j++)
{
file.Write("{0}\t", strikes[j]);
for (var k = 0; k < numberOfMonteCarloRuns; k++)
{
file.Write("{0}", prices[k, j]);
file.Write(k < numberOfMonteCarloRuns - 1 ? "\t" : "\n");
}
Utilities.DrawTextProgressBar(j + 1, strikes.Length, "Export results");
}
file.Close();
}
catch (Exception exception)
{
Console.WriteLine(exception.Message);
}
#endregion Export
}
/// <summary>
/// Test cap pricing function
/// </summary>
private static void TestCapPricing(string resultFile)
{
#region Cap
// 1 EUR
var principal = 1;
// Consider a ten-year semi-annual European swaption (10y x 5y), exercisable on each
// reset date, starting on 1-October-2020
var valuationDate = new DateTime(2015, 10, 1);
// Exercise date of the option = start date of swap
var startDate = valuationDate.AddYears(2);
// Strike (fixed interest rate payed by fixed leg)
var capRate = 0.045;
// Tenor of the underlying swap in units of [months]
// = floating leg pays 6M-Libor
var tenor = 6;
const int numberOfCaplets = 10;
var cap = new Cap(startDate, tenor, numberOfCaplets, capRate, principal);
#endregion Cap
#region Initialize LIBOR market model
#region Initial yield curve
// Sample points of curve in units of [years]
var curveTimes = new[] { 1, 2, 3, 4, 5, 7, 10, 20 };
// annual interest rate in units of [1/year]
var yields = new[] { 0.01, 0.018, 0.024, 0.029, 0.033, 0.034, 0.035, 0.034 };
var maturityDates = curveTimes.Select(y => valuationDate.AddYears(y)).ToArray();
var yieldCurve = new YieldCurve(valuationDate, maturityDates, yields);
#endregion Initial yield curve
#region Model parameters
// Use the volatility term structure populaized by Riccardo Rebonato
// sigma_i(t) = (a * tau + b) * Math.Exp(-c * tau) + d; with tau = T[i] - t
// t is assumed to be in units of [years]
var volatilityParamaters = new[] { 0.3, -0.02, 0.7, 0.14 };
// Instantaneous correlations between the Brownian motions
// and hence the forward LIBOR rates
// rho(i,j) = exp(-beta * |T[i] - T[j]|)
const double beta = 0.08;
#endregion Model parameters
var seed = DateTime.Now.Millisecond;
var liborMarketModel = new LiborMarketModel(yieldCurve, beta, volatilityParamaters, cap.TenorStructure, seed);
#endregion Initialize LIBOR market model
#region Pricing
#region Cap rates
const int nCapRates = 100;
const double capRateMin = 0;
const double capRateMax = 0.4;
const double step = (capRateMax - capRateMin) / (nCapRates - 1);
var capRates = new double[nCapRates];
for (var j = 0; j < capRates.Length; j++)
{
capRates[j] = capRateMin + step * j;
}
#endregion Cap rates
#region Monte Carlo
const int numberOfMonteCarloPaths = 100;
var prices = new double[nCapRates];
for (var i = 0; i < numberOfMonteCarloPaths; i++)
{
// Simulate forward LIBOR rate paths using Monto carlo simulation up to the
// exercise date of the swaption
var paths = liborMarketModel.SimulateForwardRates(cap.MaturityDate);
for (var j = 0; j < capRates.Length; j++)
{
cap.CapRate = capRates[j];
prices[j] += cap.DiscountedPayoff(paths) / numberOfMonteCarloPaths;
}
// Utilities.DrawTextProgressBar(i + 1, numberOfMonteCarloPaths, "Monte Carlo");
}
#endregion Monte Carlo
#region Black-Caplet formula
// Use the volatility term structure populaized by Riccardo Rebonato
// sigma_i(t) = (a * tau + b) * Math.Exp(-c * tau) + d; with tau = T[i] - t
// t is assumed to be in units of [years]
Func <double, double> volatilityFunction = t =>
{
var a = volatilityParamaters[0];
var b = volatilityParamaters[1];
var c = volatilityParamaters[2];
var d = volatilityParamaters[3];
return((a * t + b) * Math.Exp(-c * t) + d);
};
var blackPrices = new double[nCapRates];
for (var i = 0; i < capRates.Length; i++)
{
cap.CapRate = capRates[i];
blackPrices[i] = cap.Value(yieldCurve, 0, volatilityFunction);
Utilities.DrawTextProgressBar(i + 1, capRates.Length, "Black-Caplet formula");
}
#endregion Black-Caplet formula
#endregion Pricing
#region Export
try
{
// create a writer and open the file
var file = new StreamWriter(resultFile);
for (var i = 0; i < capRates.Length; i++)
{
file.WriteLine("{0}\t{1}\t{2}", capRates[i], prices[i], blackPrices[i]);
Utilities.DrawTextProgressBar(i + 1, capRates.Length, "Export results");
}
file.Close();
}
catch (Exception exception)
{
Console.WriteLine(exception.Message);
}
#endregion Export
}
/// <summary>
/// Export
/// </summary>
private static void TestLiborMarketModel(string fowardrateFile, string yieldCurveFile)
{
#region Swaption
// 1 EUR
var nominal = 1;
// Consider a ten-year semi-annual European swaption (10y x 5y), exercisable on each
// reset date, starting on 1-October-2020
var valuationDate = new DateTime(2015, 10, 1);
// Exercise date of the option = start date of swap
var exerciseDate = valuationDate.AddYears(2);
// Maturity of the underlying swap
var maturityDate = exerciseDate.AddYears(10);
// Strike (fixed interest rate payed by fixed leg)
var strike = 0.045;
// Tenor of the underlying swap in units of [months]
// = floating leg pays 6M-Libor
var tenor = 6;
var swaption = new Swaption(valuationDate, exerciseDate, maturityDate, tenor, strike, nominal);
#endregion Swaption
#region Initialize LIBOR market model
#region Initial yield curve
// Sample points of curve in units of [years]
var curveTimes = new[] { 1, 2, 3, 4, 5, 7, 10, 20 };
// annual interest rate in units of [1/year]
var yields = new[] { 0.01, 0.018, 0.024, 0.029, 0.033, 0.034, 0.035, 0.036 };
var maturityDates = curveTimes.Select(y => valuationDate.AddYears(y)).ToArray();
var yieldCurve = new YieldCurve(valuationDate, maturityDates, yields);
#endregion Initial yield curve
#region Model parameters
// Use the volatility term structure populaized by Riccardo Rebonato
// sigma_i(t) = (a * tau + b) * Math.Exp(-c * tau) + d; with tau = T[i] - t
// t is assumed to be in units of [years]
var volatiltyParameters = new[] { 0.3, -0.02, 0.7, 0.14 };
// Instantaneous correlations between the Brownian motions
// and hence the forward LIBOR rates
// rho(i,j) = exp(-beta * |T[i] - T[j]|)
const double beta = 0.08;
#endregion Model parameters
const int seed = 41;
var liborMarketModel = new LiborMarketModel(yieldCurve, beta, volatiltyParameters, swaption.TenorStructure, seed);
#endregion Initialize LIBOR market model
var paths = liborMarketModel.SimulateForwardRates(swaption.ExerciseDate, 1);
liborMarketModel.YieldCurve.Export(Path.Combine(DataFolder, yieldCurveFile));
paths.Export(Path.Combine(DataFolder, fowardrateFile));
}