# floatdiscmargin

Discount margin for floating-rate bond

## Syntax

``Margin = floatdiscmargin(Price,SpreadSettle,Maturity,RateInfo,LatestFloatingRate)``
``Margin = floatdiscmargin(___,Name,Value)``

## Description

example

````Margin = floatdiscmargin(Price,SpreadSettle,Maturity,RateInfo,LatestFloatingRate)` calculates the discount margin or zero discount margin for a floating-rate bond.The input `RateInfo` determines whether the discount margin or the zero discount margin is calculated. Principal schedules are supported using `Principal`.```

example

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

## Examples

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Use `floatdiscmargin` to compute the discount margin and zero discount margin for a floating-rate note.

Define data for the floating-rate note.

```Price = 99.99; Spread = 50; Settle = datetime(2011,1,20); Maturity = datetime(2012,1,15); LatestFloatingRate = 0.05; StubRate = 0.049; SpotRate = 0.05; Reset = 4; Basis = 2;```

Compute the discount margin.

```dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... [StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)```
```dMargin = 48.4810 ```

Usually you want to set `AdjustCashFlowsBasis` to `true`, so cash flows are calculated with adjustments on accrual amounts.

Create an annualized zero-rate term structure to calculate the zero discount margin.

```Rates = [0.0500; 0.0505; 0.0510; 0.0520]; StartDates = [datetime(2011,1,20); datetime(2011,4,15); datetime(2011,7,15); datetime(2011,11,15)]; EndDates = [datetime(2011,4,15); datetime(2011,7,15); datetime(2011,11,15); datetime(2012,1,15)]; ValuationDate = datetime(2011,1,20); RateSpec = intenvset('Compounding', Reset, 'Rates', Rates,... 'StartDates', StartDates, 'EndDates', EndDates,... 'ValuationDate', ValuationDate, 'Basis', Basis);```

Calculate the zero discount margin using the previous yield curve.

```dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... RateSpec, LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)```
```dMargin = 46.0689 ```

## Input Arguments

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Bond prices where discount margin is to be computed, specified as a `NINST`-by-`1` matrix.

Note

The spread is calculated against the clean price (the function internally does not add the accrued interest to the price specified by the `Price` input). If the spread is required against the dirty price, the price of a bond that includes the accrued interest, you must supply the dirty price for the `Price` input.

Data Types: `double`

Number of basis points over the reference rate, specified as a `NINST`-by-`1` matrix.

Data Types: `double`

Settlement date of the floating-rate bonds, specified as a scalar or a `NINST`-by-`1` vector using a datetime array, string array, or date character vectors. If supplied as a `NINST`-by-`1` vector of dates, all settlement dates must be the same (only a single settlement date is supported)

To support existing code, `floatdiscmargin` also accepts serial date numbers as inputs, but they are not recommended.

Data Types: `char` | `string` | `datetime`

Maturity date of the floating-rate bond, specified as a `NINST`-by-`1` vector using a datetime array, string array, or date character vectors.

To support existing code, `floatdiscmargin` also accepts serial date numbers as inputs, but they are not recommended.

Data Types: `char` | `string` | `datetime`

interest-rate information, specified as `NINST`-by-`2` vector where the:

• First column is the stub rate between the settlement date and the first coupon rate.

• Second column is the reference rate for the term of the floating coupons (for example, the 3-month LIBOR from settlement date for a bond with a `Reset` of `4`).

Note

If the `RateInfo` argument is an annualized zero-rate term structure created by `intenvset` (Financial Instruments Toolbox), the zero discount margin is calculated.

Data Types: `double`

Rate for the next floating payment set at the last reset date, specified as `NINST`-by-`1` vector.

Data Types: `double`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: ```Margin = floatdiscmargin(Price,Spread,Settle,Maturity,RateInfo,LatestFloatingRate,'Reset',2,'Basis',5)```

Frequency of payments per year, specified as `NINST`-by-`1` vector.

Data Types: `double`

Day-count basis used for time factor calculations, specified as a `NINST`-by-`1` vector. Values are:

• 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`

Notional principal amounts, specified as a `NINST`-by-`1` vector or a `NINST`-by-`1` cell array where each element is a `NUMDATES`-by-`2` cell array where the first column is dates and the second column is the associated principal amount. The date indicates the last day that the principal value is valid.

Data Types: `double` | `cell`

End-of-month rule flag, specified as a `NINST`-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`

Adjusts cash flows according to the accrual amount, specified as a `NINST`-by-`1` vector of logicals.

Note

Usually you want to set `AdjustCashFlowsBasis` to `1`, so cash flows are calculated with adjustments on accrual amounts. The default is set to `0` to be consistent with `floatbyzero` (Financial Instruments Toolbox).

Data Types: `logical`

Dates for holidays, specified as `NHOLIDAYS`-by-`1` vector using a datetime array, string array, or date character vectors. Holidays are used in computing business days.

To support existing code, `floatdiscmargin` also accepts serial date numbers as inputs, but they are not recommended.

Data Types: `char` | `string` | `datetime`

Business day conventions, specified as a `NINST`-by-`1` cell array of character vectors of business day conventions to be used in computing payment dates. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

• `'actual'` — Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.

• `'follow'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.

• `'modifiedfollow'` — Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.

• `'previous'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.

• `'modifiedprevious'` — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types: `char` | `cell`

## Output Arguments

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Discount margin, returned as a `NINST`-by-`1` vector of the discount margin if `RateInfo` is specified as a `NINST`-by-`2` vector of stub and spot rates.

If `RateInfo` is specified as an annualized zero rate term structure created by `intenvset` (Financial Instruments Toolbox), `Margin` is returned as a `NINST`-by-`NCURVES` matrix of the zero discount margin.

 Fabozzi, Frank J., Mann, Steven V. Floating-Rate Securities. John Wiley and Sons, New York, 2000.

 Fabozzi, Frank J., Mann, Steven V. Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures and Valuation. John Wiley and Sons, New York, 2010.

 O'Kane, Dominic, Sen, Saurav. “Credit Spreads Explained.” Lehman Brothers Fixed Income Quantitative Research, March 2004.