instoptembnd

Construct bond with embedded option

Syntax

InstSet = instoptembnd(CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates)

InstSet = instoptembnd(InstSet,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates)

InstSet = instoptembnd(___,Name,Value)

[FieldList,ClassList,TypeString] = instoptembnd

Description

InstSet = instoptembnd(CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates) creates a new instrument set containing Bond with embedded option instruments.

InstSet = instoptembnd(InstSet,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates) adds Bond with embedded option instruments to an existing instrument set.

InstSet = instoptembnd(___,Name,Value) uses additional name-value pairs in addition to the required arguments in the previous syntax.

[FieldList,ClassList,TypeString] = instoptembnd lists field meta-data for the Bond option instrument.

Examples

Create a Bond With an Embedded Option

This example shows how to create a bond with an embedded option using the following data.

Settle = datetime(2007,1,1);
Maturity   = datetime(2010,1,1); 
CouponRate = 0.07;
OptSpec = 'call'; 
Strike= 100;  
ExerciseDates= [datetime(2008,1,1) datetime(2010,1,1)]; 
AmericanOpt=1;
Period = 1;

InstSet = instoptembnd(CouponRate, ...
Settle, Maturity, OptSpec, Strike,  ExerciseDates,'AmericanOpt', AmericanOpt, ...
'Period', Period);

% display the instrument
 instdisp(InstSet)

Index Type      CouponRate Settle         Maturity       OptSpec Strike ExerciseDates                Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face AmericanOpt
1     OptEmBond 0.07       01-Jan-2007    01-Jan-2010    call    100    01-Jan-2008   01-Jan-2010    1      0     1            NaN       NaN             NaN            NaN       100  1          
 

Input Arguments

InstSet — Instrument variable

structure

Instrument variable, specified only when adding Bond embedded option instruments to an existing instrument set. For more information on the InstSet variable, see instget.

Data Types: struct

CouponRate — Bond coupon rate

positive decimal value

Bond coupon rate, specified as a scalar or an NINST-by-1 decimal annual rate or NINST-by-1 cell array, where each element is a NumDates-by-2 cell array. The first column of the NumDates-by-2 cell array is dates and the second column is associated rates. The date indicates the last day that the coupon rate is valid.

Data Types: double | cell

Settle — Settlement date

datetime array | string array | date character vector

Settlement date, specified as a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

Maturity — Maturity date

datetime array | string array | date character vector

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

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

OptSpec — Definition of option

character vector with value 'call' or 'put' | cell array of character vectors with values 'call' or 'put'

Definition of option, specified as a scalar or an NINST-by-1 cell array of character vectors.

Data Types: char

Strike — Option strike price values

nonnegative integer

Option strike price value, specified as a scalar or an NINST-by-1 or an NINST-by-NSTRIKES depending on the type of option:

• European option — NINST-by-1 vector of strike price values.

• Bermuda option — NINST by number of strikes (NSTRIKES) matrix of strike price values. Each row is the schedule for one option. If an option has fewer than NSTRIKES exercise opportunities, the end of the row is padded with NaNs.

• American option — NINST-by-1 vector of strike price values for each option.

Data Types: double

ExerciseDates — Option exercise dates

datetime array | string array | date character vector

Option exercise dates, specified as scalar or an NINST-by-1, NINST-by-2, or NINST-by-NSTRIKES vector using a datetime array, string array, or date character vectors, depending on the type of option:

• For a European option, use a NINST-by-1 vector of dates. For a European option, there is only one ExerciseDates on the option expiry date.

• For a Bermuda option, use a NINST-by-NSTRIKES vector of dates.

• For an American option, use a NINST-by-2 vector of exercise date boundaries. The option can be exercised on any date between or including the pair of dates on that row.

To support existing code, instoptembnd 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: InstSet = instoptembnd(InstSet,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates,'Period',1,'AmericanOp',1)

AmericanOpt — Option type

0 European/Bermuda (default) | integer with values 0 or 1

Option type, specified as the comma-separated pair consisting of 'AmericanOpt' and a scalar or an NINST-by-1 positive integer flags with values:

• 0 — European/Bermuda

• 1 — American

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 a scalar or an NINST-by-1 vector.

Data Types: double

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 scalar or an NINST-by-1 vector of integers.

• 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

EndMonthRule — End-of-month rule flag

1 (in effect) (default) | nonnegative integer with values 0 or 1

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar nonnegative integer or an 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: double

IssueDate — Bond issue date

datetime array | string array | date character vector

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

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

FirstCouponDate — Irregular first coupon date

datetime array | string array | date character vector

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

To support existing code, instoptembnd 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. If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

LastCouponDate — Irregular last coupon date

datetime array | string array | date character vector

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

To support existing code, instoptembnd 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. If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

StartDate — Forward starting date of payments

datetime array | string array | date character vector

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 or an NINST-by-1 vector using a datetime array, string array, or date character vectors. The StartDate is the date when a bond actually starts (that is, the date from which a bond's cash flows can be considered). To make an option embedded bond instrument forward starting, specify this date as a future date.

To support existing code, instoptembnd 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.

Face — Face value

100 (default) | NINST-by-1 vector | NINST-by-1 cell array

Face or par value, specified as the comma-separated pair consisting of 'Face' and a scalar or an NINST-by-1 vector or an 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 associated face value. The date indicates the last day that the face value is valid.

Note

Instruments without a Face schedule are treated as either vanilla bonds or stepped coupon bonds with embedded options.

Data Types: double

Output Arguments

InstSet — Variable containing a collection of instruments

structure

Variable containing a collection of instruments, returned as a structure. Instruments are broken down by type and each type can have different data fields. Each stored data field has a row vector or string for each instrument. For more information on the InstSet variable, see instget.

FieldList — Name of each data field for Bond embedded option instrument

cell array of character vectors

Name of each data field for a Bond embedded option instrument, returned as an NFIELDS-by-1 cell array of character vectors.

ClassList — Data class for each field

cell array of character vectors

Data class for each field, returned as an NFIELDS-by-1 cell array of character vectors. The class determines how arguments are parsed. Valid character vectors are 'dble', 'date', and 'char'.

TypeString — Type of instrument

character vector

Type of instrument, returned as a character vector. For a Bond embedded option instrument, TypeString = 'OptEmBond'.

More About

Vanilla Bond with Embedded Option

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. A vanilla bond with an embedded option is where an option contract has an underlying asset of a vanilla bond.

Stepped Coupon Bond with Callable and Puttable Features

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. Stepped coupon bonds can have options features (call and puts).

Sinking Fund Bond with Call Embedded Option

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.

The bond may have a sinking fund call option provision allowing the issuer to retire the sinking fund obligation either by purchasing the bonds to be redeemed from the market or by calling the bond via a sinking fund call, whichever is cheaper. If interest rates are high, then the issuer buys back the requirement amount of bonds from the market since bonds are cheap, but if interest rates are low (bond prices are high), then most likely the issuer is buying the bonds at the call price. Unlike a call feature, however, if a bond has a sinking fund call option provision, it is an obligation, not an option, for the issuer to buy back the increments of the issue as stated. Because of this, a sinking fund bond trades at a lower price than a non-sinking fund bond.

Amortizing Callable or Puttable Bond

Amortizing callable or puttable bonds work under a scheduled Face.

An amortizing callable bond gives the issuer the right to call back the bond, but instead of paying the Face amount at maturity, it repays part of the principal along with the coupon payments. An amortizing puttable bond, repays part of the principal along with the coupon payments and gives the bondholder the right to sell the bond back to the issuer.

Version History

Introduced in R2008a

R2022b: Serial date numbers not recommended

Although instoptembnd supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.