agencyprice

Price callable bond using Agency OAS model

Syntax

Price = agencyprice(ZeroData,OAS,CouponRate,Settle,Maturity,Vol,CallDate)

Price = agencyprice(___,Name,Value)

Description

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

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

Compute the Agency Price

This example shows how to compute the agency Price.

Settle = datenum('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 = datenum('30-Dec-2013');
CouponRate = .022;
OAS = 6.53/10000;
Vol = .5117;
CallDate = datenum('30-Dec-2010');
Price = agencyprice(ZeroData, OAS, CouponRate, Settle, Maturity, Vol, CallDate)

Price = 99.4212

Input Arguments

ZeroData — Zero curve

matrix

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

OAS — Option-adjusted spreads

vector in decimals

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

CouponRate — Coupon rates

vector in decimals

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

Data Types: double

Settle — Settlement date

serial date number

Settlement date, specified as a scalar serial date number.

Note

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

Data Types: double

Maturity — Maturity date

serial date number

Maturity date, specified as a numBonds-by-1 vector.

Data Types: double

Vol — Volatilities

vector in decimals

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

CallDate — Call dates

vector

Call dates, specified as an numBonds-by-1 vector.

Data Types: double

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

'Basis' — Day-count basis

0 (actual/actual) (default) | integer from 0 to 13

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

For more information, see Basis.

Data Types: double

'CurveBasis' — Curve basis

0 (actual/actual) (default) | integer from 0 to 13

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

For more information, see Basis.

Data Types: double

'CurveCompounding' — Compounding frequency of the zero curve

2 (semiannual) (default) | possible values include: –1, 0, 1, 2, 3, 4, 6, 12.

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

'EndMonthRule' — End-of-month rule flag

1 (in effect) (default) | nonnegative integer [0,1]

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.

• 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' — face value of bond

100 (default) | vector

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

'FirstCouponDate' — Irregular first coupon date

if you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs (default) | serial date number

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a NINST-by-1 vector using a serial date numbers.

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

Data Types: double

'InterpMethod' — Interpolation method

'linear' (default) | 'cubic','pchip'

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

'IssueDate' — Bond issue date

if you do not specify an IssueDate, the cash flow payment dates are determined from other inputs (default) | serial date number

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a N-by-1 vector using serial date numbers.

Data Types: double

'LastCouponDate' — Irregular last coupon date

serial date number

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a N-by-1 vector using serial date numbers

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.

Data Types: double

'Period' — Coupons per year

2 per year (default) | vector

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

'StartDate' — Forward starting date of payments

Settle date (default) | serial date number

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 N-by-1 vector using serial date numbers.

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

Data Types: double

Output Arguments

Price — Prices

matrix

Prices returned as an numBonds-by-1 matrix.

More About

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.