/// <summary>
/// More general Constructor
/// </summary>
/// <param name="yieldCurve"></param>
/// <param name="correlation"></param>
/// <param name="volatility"></param>
/// <param name="tenorStructure"></param>
/// <param name="randomSeed"></param>
public LiborMarketModel(YieldCurve yieldCurve,
Matrix <double> correlation,
Func <double, double>[] volatility,
DateTime[] tenorStructure,
int randomSeed = 42)
{
YieldCurve = yieldCurve;
RandomGenerator = new MersenneTwister(randomSeed);
Correlation = correlation;
Volatility = volatility;
SettleDate = yieldCurve.SettleDate;
// Use continuous time in units of years for tenor structure
T = Vector <double> .Build
.DenseOfEnumerable(Utilities.ConvertToDayCountFraction(SettleDate, tenorStructure));
// Initial discount factors: T[i] :-> B(0, T[i]) i =0, ..., n = length(T)-1
InitialDiscountFactor = yieldCurve.GetDiscountFactors(tenorStructure);
#region Tenors
// tenors (day-count fraction) in units of [years]
// Alpha[i] = T[i]-T[i+1], i = 0,...,n - 1
Alpha = Vector <double> .Build.DenseOfEnumerable(T.Skip(1)) - Vector <double> .Build.DenseOfEnumerable(T.Take(T.Count - 1));
// Choose terminal measure, can be an value between 0,..., n = length(T)-1
NumeraireIndex = T.Count - 1;
#endregion Tenors
#region Initial Forward rate
NumRates = T.Count - 1;
// B[i]
var zeroBond0 = Vector <double> .Build
.DenseOfEnumerable(InitialDiscountFactor.Take(NumRates));
// B[i+1]
var zeroBond1 = Vector <double> .Build
.DenseOfEnumerable(InitialDiscountFactor.Skip(1));
// Initial forward LIBOR rate
// L[i] = L(0, T[i],T[i+1]) = 1/alpha[i] * (B[i]/B[i+1] - 1); i = 0,..., n - 1
// L[i](t) : 0 <= t <= T[i]
InitialForwardRate = (zeroBond0.PointwiseDivide(zeroBond1).Subtract(1)).PointwiseDivide(Alpha);
#endregion Initial Forward rate
// Delta for smile
Delta = Vector <double> .Build.Dense(NumRates);
}
/// <summary>
/// Simulate forward rates and corresponding zero rates on the
/// interval [settleDate, tmax]
/// step in [months]
/// </summary>
public LiborMarketModelPath SimulateForwardRates(DateTime maxDate, int step = 3)
{
#region Numeraire
// Numeraire at time 0: N(0) = B(0, T[k])
var intialNumeraire = InitialDiscountFactor[NumeraireIndex];
#endregion Numeraire
#region Time discertization
// Initialize rates
//t = linspace(0, length(model.T(end-1)), 100);
// Use 3 Month time step
var dates = Utilities.TenorStructure(SettleDate, maxDate, step);
// Convert to continous time in units of [years]
var t = Utilities.ConvertToDayCountFraction(SettleDate, dates);
#endregion Time discertization
#region Forward rate
// Initialize forward rate with its at time t = 0 value;
var forwaredRates = Matrix <double> .Build.Dense(NumRates, t.Length);
forwaredRates.SetColumn(0, InitialForwardRate);
// Propagate forward rates
for (var j = 0; j < t.Length - 1; j++)
{
var dt = t[j + 1] - t[j];
var forwardrate = PropagteForwardRate(t[j], forwaredRates.Column(j), NumeraireIndex, dt);
forwaredRates.SetColumn(j + 1, forwardrate);
}
#endregion Forward rate
#region Numeraire adjusted discount factor
// Initialize numeraire-adjusted-discount factor with its at time t = 0 value;
// D[i] = B[i]/B[k], where B[k] is the numeraire , i = 0, ..., n = length(T)-1
// D[i]: 0 <= t <= min(T[i], T[k])
// numeraireAdjustedDiscountFactors
var discountFactors = Matrix <double> .Build.Dense(T.Count, t.Length);
discountFactors.SetColumn(0, InitialDiscountFactor.Divide(intialNumeraire));
// Numeraire-adjusted discount factors
for (var j = 1; j < t.Length; j++)
{
// forward rate for time t[j]
var forwardRate = forwaredRates.Column(j);
var discountFactor = Vector <double> .Build.Dense(T.Count);
for (var i = 0; i < discountFactor.Count; i++)
{
#region Check time
// Discount factor is not defined
if (t[j] > Math.Min(T[i], T[NumeraireIndex]))
{
discountFactor[i] = double.NaN;
continue;
}
#endregion Check time
#region Compute numeraire adjusted discount factors from forward rate
if (i == NumeraireIndex)
{
discountFactor[i] = 1;
}
else if (i < NumeraireIndex)
{
var prod = 1.0;
for (var k = i; k <= NumeraireIndex - 1; k++)
{
prod *= 1 + Alpha[k] * forwardRate[k];
}
discountFactor[i] = prod;
}
else if (i > NumeraireIndex)
{
var prod = 1.0;
for (var k = NumeraireIndex; k <= i - 1; k++)
{
prod *= 1 + Alpha[k] * forwardRate[k];
}
discountFactor[i] = 1.0 / prod;
}
#endregion Compute numeraire adjusted discount factors from forward rate
}
discountFactors.SetColumn(j, discountFactor);
}
#endregion Numeraire adjusted discount factor
#region Result
return(new LiborMarketModelPath
{
SettleDate = SettleDate,
Dates = dates,
Tenors = Alpha,
TenorStructure = Utilities.ConvertFromDayCountFraction(SettleDate, T.ToArray()),
ForwardRates = forwaredRates,
NumeraireAdjustedDiscountFactors = discountFactors,
InitialNumeraire = intialNumeraire
});
#endregion Result
}
