/// <summary>
/// Computes the shifted quarterly cash forward rate for a specific future time.
/// </summary>
/// <param name="forwardDate"></param>
/// <param name="discount">Discount factors used.</param>
/// <param name="shift">Shifts used.</param>
/// <returns></returns>
public static double ShiftedCashForwardRate(int forwardDate, QuarterlyDiscounts discount, QuarterlyShifts shift)
{
double rate = 4 * (discount.Get(forwardDate) / discount.Get(forwardDate + 1) - 1);
rate += shift.Get(forwardDate);
return(rate);
}
///<summary>
///</summary>
///<param name="discount"></param>
///<param name="shift"></param>
public void Populate(QuarterlyDiscounts discount, QuarterlyShifts shift)
{
var forward = new double[_maxTenor + 1];
var accumForward = new double[_maxTenor + 1];
var accumForwardTimesRate = new double[_maxTenor + 1];
var accumForwardTimesShiftedRate = new double[_maxTenor + 1];
accumForward[0] = 0;
accumForwardTimesRate[0] = 0;
accumForwardTimesShiftedRate[0] = 0;
var w = new double[_maxTenor];
var h = new double[_maxTenor];
for (int i = 0; i < _maxExpiry; i++)
{
for (int j = 0; j < _maxTenor - i; j++)
{
//See "Engineering BGM" page 34 for explicit formula. Function definitions can be found in chapter 4.
forward[j + 1] = RateAnalytics.ForwardContract(i + 1, i + j + 2, discount);
accumForward[j + 1] = accumForward[j] + forward[j + 1];
accumForwardTimesRate[j + 1]
= accumForwardTimesRate[j] + forward[j + 1] * RateAnalytics.CashForwardRate(i + j + 1, discount);
accumForwardTimesShiftedRate[j + 1]
= accumForwardTimesShiftedRate[j] + forward[j + 1] * RateAnalytics.ShiftedCashForwardRate(i + j + 1, discount, shift);
h[j] = 0.25 * RateAnalytics.ShiftedCashForwardRate(i + j + 1, discount, shift) / (1 + 0.25 * RateAnalytics.CashForwardRate(i + j + 1, discount));
for (int k = 0; k < j + 1; k++)
{
w[k] = forward[k + 1] * RateAnalytics.ShiftedCashForwardRate(i + k + 1, discount, shift) / accumForwardTimesShiftedRate[j + 1];
_weights[i][j][k] = w[k] - h[k] * ((accumForwardTimesRate[j + 1] - accumForwardTimesRate[k]) / accumForwardTimesShiftedRate[j + 1]
- (1 - accumForward[k] / accumForward[j + 1]) * accumForwardTimesRate[j + 1] / accumForwardTimesShiftedRate[j + 1]);
}
}
}
}
/// <summary>
/// The "shift" of the swap rate, or shifted swap rate - actual swap rate.
/// </summary>
/// <param name="expiry"></param>
/// <param name="tenor"></param>
/// <param name="discount"></param>
/// <param name="shift"></param>
/// <returns></returns>
public static double SwapShift(int expiry, int tenor, QuarterlyDiscounts discount, QuarterlyShifts shift)
{
double numerator = 0;
double denominator = 0;
for (int i = 0; i < tenor; i++)
{
double forward = ForwardContract(expiry, expiry + i + 1, discount);
numerator += forward * shift.Get(expiry + i);
denominator += forward;
}
return(numerator / denominator);
}
/// <summary>
/// Computes the swap rate of a quarterly swap.
/// </summary>
/// <param name="expiry">Expiry time in quarters.</param>
/// <param name="tenor">Length of the swap in quarters.</param>
/// <param name="discount">Discount factors used.</param>
/// <returns></returns>
public static double SwapRate(int expiry, int tenor, QuarterlyDiscounts discount)
{
double numerator = 0;
double denominator = 0;
for (int i = 0; i < tenor; i++)
{
double forward = ForwardContract(expiry, expiry + i + 1, discount);
numerator += forward * CashForwardRate(expiry + i, discount);
denominator += forward;
}
return(numerator / denominator);
}
/// <summary>
/// Computes the quarterly cash forward rate for a specific future time.
/// </summary>
/// <param name="forwardDate"></param>
/// <param name="discount">Discount factors used.</param>
/// <returns></returns>
public static double CashForwardRate(int forwardDate, QuarterlyDiscounts discount)
{
double rate = 4 * (discount.Get(forwardDate) / discount.Get(forwardDate + 1) - 1);
return(rate);
}
/// <summary>
///
/// </summary>
/// <param name="paymentDate">Contract payment time, in quarters.</param>
/// <param name="settleDate">Delivery time, in quarters.</param>
/// <param name="discount">Discount factors used.</param>
/// <returns></returns>
public static double ForwardContract(int paymentDate, int settleDate, QuarterlyDiscounts discount)
{
return(discount.Get(settleDate) / discount.Get(paymentDate));
}