# agencyprice

Price callable bond using Agency OAS model

## Description

example

Price = agencyprice(ZeroData,OAS,CouponRate,Settle,Maturity,Vol,CallDate) computes the price for a callable bond, given OAS, using the Agency OAS model.

example

Price = agencyprice(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

## Examples

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This example shows how to compute the agency Price.

Settle = '20-Jan-2010';
ZeroRates = [.07 .164 .253 1.002 1.732 2.226 2.605 3.316 ...
3.474 4.188 4.902]'/100;
ZeroDates = daysadd(Settle,360*[.25 .5 1 2 3 4 5 7 10 20 30],1);
ZeroData = [ZeroDates ZeroRates];

Maturity = datetime(2013,12,30);
CouponRate = .022;
OAS = 6.53/10000;
Vol = .5117;
CallDate = datetime(2010,12,30);
Price = agencyprice(ZeroData, OAS, CouponRate, Settle, Maturity, Vol, CallDate)
Price = 99.4212

## Input Arguments

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Zero curve, specified as an numRates-by-2 matrix where the first column is zero dates and the second column is the accompanying zero rates.

Data Types: double

Option-adjusted spreads, specified as an numBonds-by-1 vector expressed as a decimal (that is, 50 basis points is entered as .005).

Data Types: double

Coupon rates, specified as an numBonds-by-1 vector in decimals.

Data Types: double

Settlement date, specified as a scalar datetime, string, or date character vector.

Note

The Settle date must be an identical settlement date for all the bonds and the zero curve.

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

Maturity date, specified as a scalar string or character vector or numBonds-by-1 vector using a datetime array, string array, or date character vectors.

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

Volatilities specified as a scalar or an numBonds-by-1 vector in decimals. Vol is the volatility of interest rates corresponding to the time of the CallDate.

Data Types: double

Call dates, specified as a scalar string or character vector or an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

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

### 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: Price = agencyprice(ZeroData,OAS,CouponRate,Settle,Maturity,Vol,CallDate,'Basis',7,'Face',1000)

Day-count basis, specified as the comma-separated pair consisting of 'Basis' and a N-by-1 vector using 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

Curve basis, specified as the comma-separated pair consisting of 'CurveBasis' and a N-by-1 vector using 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

Compounding frequency of the zero curve, specified as the comma-separated pair consisting of 'CurveCompounding' and a N-by-1 vector using the supported values: –1, 0, 1, 2, 3, 4, 6, and 12.

Data Types: double

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a nonnegative integer [0, 1] using a N-by-1 vector with date character vectors or a datetime array.

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

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

Data Types: logical

Face value of bond, specified as the comma-separated pair consisting of 'Face' and an N-by-1 vector of numeric values.

Data Types: double

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar string or character vector or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

Interpolation method, specified as the comma-separated pair consisting of 'InterpMethod' and a N-by-1 vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar string or character vector or an N-by-1 vector using a datetime array, string array, or date character vectors.

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar string or character vector or an N-by-1 vector using a datetime array, string array, or date character vectors.

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

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.

Coupons per year, specified as the comma-separated pair consisting of 'Period' and an N-by-1 vector. Values for Period are 0, 1, 2, 3, 4, 6, and 12.

Data Types: double

Forward starting date of payments (the date from which a bond cash flow is considered), specified as the comma-separated pair consisting of 'StartDate' and a scalar string or character vector or an N-by-1 vector using a datetime array, string array, or date character vectors.

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

If you do not specify StartDate, the effective start date is the Settle date.

## Output Arguments

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Prices returned as an numBonds-by-1 matrix.

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### Agency OAS Model

The BMA European Callable Securities Formula provides a standard methodology for computing price and option-adjusted spread for European Callable Securities (ECS).

## References

[1] SIFMA, The BMA European Callable Securities Formula, https://www.sifma.org.

## Version History

Introduced before R2006a

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