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# bndkrdur

Bond key rate duration given zero curve

## Syntax

``KeyRateDuration = bndkrdur(ZeroData,CouponRate,Settle,Maturity)``
``KeyRateDuration = bndkrdur(___,Name,Value)``

## Description

example

````KeyRateDuration = bndkrdur(ZeroData,CouponRate,Settle,Maturity)` computes the key rate durations for one or more bonds given a zero curve and a set of key rates.```

example

````KeyRateDuration = bndkrdur(___,Name,Value)` adds optional name-value pair arguments. ```

## Examples

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This example shows how to compute 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 = 1×4 0.2986 0.8791 4.1353 9.5814 ```

This example shows how to use `datetime` inputs for `Settle` and `Maturity` and also use a table for `ZeroData` to compute 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 = table(datetime(ZeroDates,'ConvertFrom','datenum','Locale','en_US'), ZeroRates); krdur = bndkrdur(ZeroData,.0525,datetime('12/31/1998','Locale','en_US'),... datetime('11/15/2028','Locale','en_US'),'KeyRates',[2 5 10 30])```
```krdur = 1×4 0.2986 0.8791 4.1353 9.5814 ```

## Input Arguments

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Zero Curve, specified as a `numRates`-by-`2` matrix or a `numRates`-by-`2` table.

If `ZeroData` is represented as a `numRates`-by-`2` matrix, the first column is a MATLAB® serial date number and the second column is the accompanying zero rates.

If `ZeroData` is a table, the first column can be serial date numbers, date character vectors, or datetime arrays. The second column must be numeric data corresponding to the zero rates.

Data Types: `double` | `table`

Annual percentage rate used to determine the coupons payable on a bond, specified as decimal value using a scalar or a `NUMBONDS`-by-`1` vector.

Data Types: `double`

Settlement date for all bonds and zero curve, specified as a scalar using a serial date number, date character vector, or datetime array. `Settle` must be the same settlement date for all the bonds and the zero curve.

Data Types: `double` | `char` | `datetime`

Maturity date for bonds, specified as a scalar or a `NUMBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: `double` | `char` | `datetime`

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: ```KeyRateDuration = bndkrdur(ZeroData,.0525,'12/31/1998','11/15/2028','KeyRates',[2 5 10 30])```

Interpolation method used to obtain points from the zero curve, specified as the comma-separated pair consisting of `'InterpMethod'` and a character vector using one of the following values:

• `'linear'` (default)

• `'cubic'`

• `'pchip'`

Data Types: `char`

Value that zero curve is shifted up and down to compute duration, specified as the comma-separated pair consisting of `'ShiftValue'` and a scalar numeric value.

Data Types: `double`

Rates to perform the duration calculation, specified as the comma-separated pair consisting of `'KeyRates'` and a time to maturity using a scalar or a `NUMBONDS`-by-`1` vector.

Data Types: `double`

Compounding frequency of the curve, specified as the comma-separated pair consisting of `'CurveCompounding'` and a scalar using one of the following values:

• `1` — Annual compounding

• `2` — Semiannual compounding

• `3` — Compounding three times per year

• `4` — Quarterly compounding

• `6` — Bimonthly compounding

• `12` — Monthly compounding

.

Data Types: `double`

Basis of the curve, specified as the comma-separated pair consisting of `'CurveBasis'` and a scalar using one of the following values:

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Data Types: `double`

Number of coupon payments per year, specified as the comma-separated pair consisting of `'Period'` and a scalar or a `NUMBONDS`-by-`1` vector using the values: `0`, `1`, `2`, `3`, `4`, `6`, or `12`.

Data Types: `double`

Day-count of the instrument, specified as the comma-separated pair consisting of `'Basis'` and a scalar or a `NUMBONDS`-by-`1` vector using a supported value:

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Data Types: `double`

End-of-month rule flag, specified as the comma-separated pair consisting of `'EndMonthRule'` and a scalar or a `NUMBONDS`-by-`1` vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days.

• `0` = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

• `1` = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: `logical`

Bond Issue date, specified as the comma-separated pair consisting of `'IssueDate'` and a scalar or a `NUMBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.

Data Types: `double` | `char` | `datetime`

Irregular or normal first coupon date, specified as the comma-separated pair consisting of `'FirstCouponDate'` and a scalar or a `NUMBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.

Data Types: `double` | `char` | `datetime`

Irregular or normal last coupon date, specified as the comma-separated pair consisting of `'LastCouponDate'` and a scalar or a `NUMBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a `LastCouponDate`, the cash flow payment dates are determined from other inputs.

Data Types: `double` | `char` | `datetime`

Forward starting date of payments, specified as the comma-separated pair consisting of `'StartDate'` and a scalar or a `NUMBONDS`-by-`1` vector using serial date numbers, date character vectors, or datetime arrays. The `StartDate` is 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 a `StartDate`, the effective start date is the `Settle` date.

Data Types: `double` | `char` | `datetime`

Face value of the bond, specified as the comma-separated pair consisting of `'Face'` and a scalar or a `NUMBONDS`-by-`1` vector.

Data Types: `double`

## Output Arguments

collapse all

Key rate durations, returned as a `numBonds`-by-`numRates` matrix.

## Algorithms

`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`.

## References

[1] Golub, B., Tilman, L. Risk Management: Approaches for Fixed Income Markets. Wiley, 2000.

[2] Tuckman, B. Fixed Income Securities: Tools for Today's Markets. Wiley, 2002.