/// <summary>
/// Computes the multi-factored volatilities given a particular input volatility grid, using principal component analysis.
/// (See Pedersen, M. B. (1998) Calibrating Libor market models. Working paper, Financial Research Department, SimCorp.)
/// </summary>
/// <param name="inputVolMat"></param>
public void Populate(Matrix inputVolMat)
{
if (!_volFixed)
{
for (int i = 0; i < _timeGrid.ExpiryCount; i++)
{
var currentRow = SingleRowOfVolatilities(i, inputVolMat.RowD(i));
for (int j = _timeGrid.ExpiryGrid[i]; j < _timeGrid.ExpiryGrid[i + 1]; j++)
{
for (int k = 0; k < _timeGrid.MaxTenor - j; k++)
{
for (int l = 0; l < _factors; l++)
{
_volatility[j][k, l] = currentRow[k, l];
}
}
}
}
}
else
{
throw new Exception("Cannot alter finalised volatility.");
}
}
/// <summary>
/// Computes the implied volatility of swaption with given expiry and tenor, or a caplet with given expiry,
/// with the volatility at one particular expiry time bucket replaced with temporary values.
/// A caplet implied volatility is equivalent to that of a swaption with the tenor length of 1.
/// Saves computation time when checking the effect of a simple perturbation.
/// </summary>
/// <param name="expiry"></param>
/// <param name="tenor"></param>
/// <param name="newRow">Indicating the expiry time bucket to be replaced.</param>
/// <param name="replacedRow">New interest rate volatility values for the expiry time bucket.</param>
/// <returns></returns>
public double FindImpliedVolatility(int expiry, int tenor, Matrix newRow, int replacedRow)
{
int exp = expiry - 1;
int ten = tenor - 1;
double result;
if (exp >= _timeGrid.ExpiryGrid[replacedRow])
{
result = _storedImpliedVolSq[exp][ten];
for (int i = _timeGrid.ExpiryGrid[replacedRow]; i < Math.Min(_timeGrid.ExpiryGrid[replacedRow + 1], expiry); i++)
{
var tempVector = new DenseVector(_factors);
for (int j = 0; j <= ten; j++)
{
tempVector = tempVector + _weights.Get(expiry, tenor, j + 1) * newRow.RowD(j + exp - i);
}
double tempSum = tempVector * tempVector;
result += tempSum - _storedImpliedVolTerm[exp][ten][i];
}
result = Math.Sqrt(result / expiry);
}
else
{
result = _storedImpliedVol[exp][ten];
}
return(result);
}