Bond key rate duration given zero curve
KRDUR = bndkrdur(ZeroData, CouponRate,
Settle, Maturity) KRDUR = bndkrdur(ZeroData, CouponRate, Settle,
Maturity, 'Parameter1', Value1, 'Parameter2',
Zero curve represented as a numRates-by-2 matrix where the first column is a MATLAB® date number and the second column is accompanying zero rates.
numBonds-by-1 vector of coupon rates in decimal form.
Scalar MATLAB date number for the settlement date for all the bonds and the zero data. Settle must be the same settlement date for all the bonds and the zero curve.
numBonds-by-1 vector of maturity dates.
(Optional) Coupons per year of the bond. A vector of integers. Acceptable values are 0, 1, 2 (default), 3, 4, 6, and 12.
(Optional) Interpolation method used to obtain points from the zero curve. Acceptable values are:
(Optional) Scalar value that zero curve is shifted up and down to compute duration. Default is .01 (100 basis points).
(Optional) Rates to perform the duration calculation, specified as a time to maturity. By default, KeyRates is set to each of the zero dates.
(Optional) Compounding frequency of the curve. Default is semiannual.
(Optional) Basis of the curve, where the choices are identical to Basis below. Default is 0 (actual/actual).
(Optional) Day-count basis of the bond instrument. A vector of integers:
For more information, see basis.
(Optional) End-of-month rule. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days. The values are:
(Optional) Date when a bond was issued.
(Optional) Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.
(Optional) Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.
(Optional) Date when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date. If you do not specify StartDate, the effective start date is the Settle date.
(Optional) Face or par value. Default = 100. Face has no impact on key rate duration.
KRDUR = bndkrdur(ZeroData, CouponRate, Settle, Maturity)
KRDUR = bndkrdur(ZeroData, CouponRate, Settle, Maturity, 'Parameter1', Value1, 'Parameter2', Value2, ...)
The output argument KRDUR is a numBonds-by-numRates matrix of key rate durations.
bndkrdur computes the key rate durations for one or more bonds given a zero curve and a set of key rates. By default, the key rates are each of the zero curve rates. For each key rate, the duration is computed by shifting the zero curve up and down by a specified amount (ShiftValue) at that particular key rate, computing the present value of the bond in each case with the new zero curves, and then evaluating the following:
Note: The shift to the curve is computed by shifting the particular key rate by the ShiftValue and then interpolating the values of the curve in the interval between the previous and next key rates. For the first key rate, any curve values before the date are equal to the ShiftValue; likewise, for the last key rate, any curve values after the date are equal to the ShiftValue.
Find the key rate duration of a bond for key rate times of 2, 5, 10, and 30 years.
ZeroRates = [0.0476 .0466 .0465 .0468 .0473 .0478 ... .0493 .0539 .0572 .0553 .0530]'; ZeroDates = daysadd('31-Dec-1998',[30 360 360*2 360*3 360*5 ... 360*7 360*10 360*15 360*20 360*25 360*30],1); ZeroData = [ZeroDates ZeroRates]; krdur = bndkrdur(ZeroData,.0525,'12/31/1998',... '11/15/2028','KeyRates',[2 5 10 30])
krdur = 0.2986 0.8791 4.1354 9.5811
Golub, B.W. and L.M. Tilman, Risk Management: Approaches for Fixed Income Markets Wiley, 2000.
Tuckman, B. Fixed Income Securities: Tools for Today's Markets Wiley, 2002.