bondbyzero - Price bond from set of zero curves

Syntax

[Price, PriceNoAI, CFlowAmounts, CFlowDates] = bondbyzero(RateSpec, CouponRate, Settle, Maturity) [Price, PriceNoAI, CFlowAmounts, CFlowDates] = bondybyzero(RateSpec, CouponRate, Settle, Maturity, Name, Value)

Description

[Price, PriceNoAI, CFlowAmounts, CFlowDates] = bondbyzero(RateSpec, CouponRate, Settle, Maturity) returns a NINST-by-NUMCURVES matrix of clean bond prices. Each column arises from one of the zero curves.

[Price, PriceNoAI, CFlowAmounts, CFlowDates] = bondybyzero(RateSpec, CouponRate, Settle, Maturity,Name, Value) returns a NINST-by-NUMCURVES matrix of clean bond prices (each column arises from one of the zero curves) with additional options specified by one or more Name, Value pair arguments.

bondbyzero computes prices of vanilla bonds, stepped coupon bonds, and sinking fund bonds with no market purchase option and no call provisions.

Input Arguments

`RateSpec`	Structure containing the properties of an interest-rate structure. See `intenvset` for information on creating `RateSpec`. `RateSpec` can be a `NINST`-by-`2` input variable of `RateSpec`s, with the second input being the discount curve for the paying leg if different than the receiving leg. If only one curve is specified, than it is used to discount both legs.
`CouponRate`	Decimal annual rate. `CouponRate` is a `NINST`-by-`1` vector or `NINST`-by-`1` cell array of decimal annual rates, or decimal annual rate schedules. For the latter case of a variable coupon schedule, each element of the cell array is a `NumDates`-by-`2` cell array, where the first column is dates and the second column is its associated rate. The date indicates the last day that the coupon rate is valid.
`Settle`	Settlement date. `NINST`-by-`1` vector of serial date numbers or date strings representing the settlement date for each swap. `Settle` must be earlier than `Maturity`.
`Maturity`	Maturity date. `NINST`-by-`1` vector of dates representing the maturity date for each swap.

Name-Value Pair Arguments

Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

Note You can either use Period, Basis, EndMonthRule,IssueDate, FirstCouponDate, LastCouponDate, StartDate, and Face as name-value pair arguments in any order, or you can specify these as optional input arguments in the following order: [Price, PriceNoAI, CFlowAmounts, CFlowDates] = bondbyzero(RateSpec, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face). The ordered optional input syntax and name-value pair syntax cannot be combined.

AdjustCashFlowsBasis

Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals.
Default: False
Basis

Day-count basis of the instrument. A vector of integers.
0 = actual/actual
1 = 30/360 (SIA)
2 = actual/360
3 = actual/365
4 = 30/360 (BMA)
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/actual (ISDA)
13 = BUS/252
For more information, see basis.

Default: 0 (actual/actual)
BusinessDayConvention

Require payment dates to be business dates. NINST-by-1 cell array with possible choices for business day convention:
actual
follow
modifiedfollow
previous
modifiedprevious
Default: actual
EndMonthRule

NINST-by-1 vector representing the end-of-month rule. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days. When EndMonthRule is equal to 0, the end-of-month rule is ignored and the bond's coupon payment date is always the same numerical day of the month. When EndMonthRule is equal to 1, the bond's coupon payment date is always the last actual day of the month.
Default: 1
Face

Face or par value. Face is a NINST-by-1 vector or NINST-by-1 cell array of face values, or face value schedules. For the latter case, each element of the cell array is a NumDates-by-2 cell array, where the first column is dates and the second column is its associated face value. The date indicates the last day that the face value is valid.
Default: 100
FirstCouponDate

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.

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

Holidays used for business day convention. A NHOLIDAYS-by-1 of MATLAB date numbers.
Default: If none specified, holidays.m is used.
IssueDate

Date a bond is issued.
Default: If you do not specify an IssueDate, the cash flow payment dates are determined from other inputs.
LastCouponDate

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.

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

Coupons per year of the bond. A vector of integers. Allowed values are 1, 2, 3, 4, 6, and 12.

Default: 2
StartDate

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.

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

Output Arguments

`Price`	A `NINST`-by-`NUMCURVES` matrix of clean bond prices. Each column arises from one of the zero curves.
`PriceNoAI`	A `NINST`-by-`NUMCURVES` matrix of dirty bond price (clean + accrued interest). Each column arises from one of the zero curves.
`CFlowAmounts`	A `NINST`-by-`NUMCFS` matrix of cash flows for each bond
`CFlowDates`	A `NUMCFS`-by-`1` matrix of payment dates for each bond

Definitions

Vanilla Bond

A vanilla coupon bond is a security representing an obligation to repay a borrowed amount at a designated time and to make periodic interest payments until that time. The issuer of a bond makes the periodic interest payments until the bond matures. At maturity, the issuer pays to the holder of the bond the principal amount owed (face value) and the last interest payment.

Stepped Coupon Bond

A step-up and step-down bond is a debt security with a predetermined coupon structure over time. With these instruments, coupons increase (step up) or decrease (step down) at specific times during the life of the bond.

Sinking Fund Bond

A sinking fund bond is a coupon bond with a sinking fund provision. This provision obligates the issuer to amortize portions of the principal prior to maturity, affecting bond prices since the time of the principal repayment changes. This means that investors receive the coupon and a portion of the principal paid back over time. These types of bonds reduce credit risk, since it lowers the probability of investors not receiving their principal payment at maturity.

Examples

Price a 4% bond using a set of zero curves. Load the filederiv.mat, which provides ZeroRateSpec, the interest-rate term structure, needed to price the bond.

load deriv.mat; 
CouponRate = 0.04;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';
Price = bondbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)

Price =

   97.5334

Price the following single stepped coupon bonds using the following data:

% The data for the interest rate term structure is as follows:
Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2010';
StartDates = ValuationDate;
EndDates = {'Jan-1-2011'; 'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'};
Compounding = 1;

% Create RateSpec
RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);

% Bond Instrument
Settle = '01-Jan-2010';
Maturity = {'01-Jan-2011';'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'};
CouponRate = {{'01-Jan-2012' .0425;'01-Jan-2014' .0750}};
Period = 1;

% Compute the price of the single stepped coupon bonds
PZero= bondbyzero(RS, CouponRate, Settle, Maturity ,Period)

PZero =

  100.7246
  100.0945
  101.5900
  102.0820

Price a bond with sinking features without option provision with the following data:

% The data for the interest rate term structure is as follows:
Rates = 0.065;
ValuationDate = '1-Jan-2011';
StartDates = ValuationDate;
EndDates=  '1-Jan-2017';
Compounding = 1;

% Create RateSpec
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);

% Instrument
% The bond has a coupon rate of 7%, a period of one year and matures in
% 1-Jan-2017.
% Face decreases $10 after the first year and $10 after the second year.
CouponRate = 0.07;
Settle ='1-Jan-2011';
Maturity = '1-Jan-2017';
Period = 1;
Face = {{'1-Jan-2015' 100;'1-Jan-2016' 90;'1-Jan-2017' 80}};

Price = bondbyzero(RateSpec, CouponRate, Settle, Maturity, Period,...
[], [], [], [], [], [], Face) 

Price =

  102.3155

% Compare results with price of a vanilla bond
PriceVanilla = bondbyzero(RateSpec, CouponRate, Settle, Maturity,Period) 
PriceVanilla =

  102.4205

Search MATLAB Documentation
R2011b Documentation → Financial Derivatives Toolbox
View documentation for other releases	Learn more about Financial Derivatives Toolbox

`AdjustCashFlowsBasis`	Adjust the cash flows based on the actual period day count. `NINST`-by-`1` of logicals. Default: `False`
`Basis`	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (BMA) 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/actual (ISDA) 13 = BUS/252 For more information, see basis. Default: `0` (actual/actual)
`BusinessDayConvention`	Require payment dates to be business dates. `NINST`-by-`1` cell array with possible choices for business day convention: `actual` `follow` `modifiedfollow` `previous` `modifiedprevious` Default: `actual`
`EndMonthRule`	`NINST`-by-`1` vector representing the end-of-month rule. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. When `EndMonthRule` is equal to `0`, the end-of-month rule is ignored and the bond's coupon payment date is always the same numerical day of the month. When `EndMonthRule` is equal to `1`, the bond's coupon payment date is always the last actual day of the month. Default: `1`
`Face`	Face or par value. `Face` is a `NINST`-by-`1` vector or `NINST`-by-`1` cell array of face values, or face value schedules. For the latter case, each element of the cell array is a `NumDates`-by-`2` cell array, where the first column is dates and the second column is its associated face value. The date indicates the last day that the face value is valid. Default: `100`
`FirstCouponDate`	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. Default: If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.
`Holidays`	Holidays used for business day convention. A `NHOLIDAYS`-by-`1` of MATLAB date numbers. Default: If none specified, `holidays.m` is used.
`IssueDate`	Date a bond is issued. Default: If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.

`LastCouponDate`	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. Default: If you do not specify a `LastCouponDate`, the cash flow payment dates are determined from other inputs.
`Period`	Coupons per year of the bond. A vector of integers. Allowed values are 1, 2, 3, 4, 6, and 12. Default: `2`
`StartDate`	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. Default: If you do not specify `StartDate`, the effective start date is the `Settle` date.