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ConvertibleBond

ConvertibleBond instrument object

Description

Create and price a ConvertibleBond instrument object for one of more Convertible Bond instruments using this workflow:

  1. Use fininstrument to create a ConvertibleBond instrument object for one of more Convertible Bond instruments.

  2. Use finmodel to specify a BlackScholes model for the ConvertibleBond instrument object.

  3. Use finpricer to specify a FiniteDifference pricing method for one or more ConvertibleBond instruments.

For more information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

For more information on the available models and pricing methods for a ConvertibleBond instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

ConvertibleBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date,'ConversionRatio',conversion_ratio_value) creates a ConvertibleBond object for one of more Convertible Bond instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments CouponRate, Maturity, and ConversionRatio.

example

ConvertibleBondObj = fininstrument(___,Name,Value) sets optional properties using name-value pair arguments in addition to the required arguments in the previous syntax. For example, ConvertibleBondObj = fininstrument("ConvertibleBond",'CouponRate',CouponRate, 'Maturity',Maturity,'ConversionRatio',ConvRatio,'Period',Period,'Spread',Spread,'CallSchedule',CallSchedule,'CallExerciseStyle',"american") creates an ConvertibleBond instrument with an American exercise and a call schedule. You can specify multiple name-value pair arguments.

Input Arguments

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Instrument type, specified as a string with the value of "ConvertibleBond", a character vector with the value of 'ConvertibleBond', an NINST-by-1 string array with values of "ConvertibleBond", or an NINST-by-1 cell array of character vectors with values of 'ConvertibleBond'.

Data Types: char | cell | string

ConvertibleBond Name-Value Pair Arguments

Specify required and 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: ConvertibleBondObj = fininstrument("ConvertibleBond",'CouponRate',CouponRate, 'Maturity',Maturity,'ConversionRatio',ConvRatio,'Period',Period,'Spread',Spread,'CallSchedule',CallSchedule,'CallExerciseStyle',"american")
Required ConvertibleBond Name-Value Pair Arguments

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Coupon rate for the ConvertibleBond object, specified as the comma-separated pair consisting of 'CouponRate' as a scalar decimal or an NINST-by-1 vector of decimals for an annual rate or a timetable where the first column is dates and the second column is associated rates. The date indicates the last day that the coupon rate is valid.

Note

If you are creating one or more ConvertibleBond instruments and use a timetable, the timetable specification applies to all of the ConvertibleBond instruments. CouponRate does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

Maturity date for the ConvertibleBond object, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, serial date number, date character vector, date string or an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

If you use date character vectors or date strings, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

Data Types: char | cell | double | string | datetime

Number of shares convertible from one bond, specified as the comma-separated pair consisting of 'ConversionRatio' and a scalar numeric or an NINST-by-1 numeric vector or a timetable where the first column is dates and the second column is associated ratios. The date in the first column indicates the last day that the conversion ratio is valid.

Note

If you are creating one or more ConvertibleBond instruments and use a timetable, the timetable specification applies to all of the ConvertibleBond instruments. ConversionRatio does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

Optional ConvertibleBond Name-Value Pair Arguments

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Number of basis points over the reference rate, specified as the comma-separated pair consisting of 'Spread' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Call schedule, specified as the comma-separated pair consisting of 'CallSchedule' and a timetable of call dates and strikes.

If you use a date character vector or date string for the dates in this timetable, the format must be recognizable by datetime because the CallSchedule property is stored as a datetime.

Note

For the ConvertibleBond instrument, you can use a CallSchedule with a CallExerciseStyle and a PutSchedule with a PutExerciseStyle simultaneously.

Data Types: timetable

Call option exercise style, specified as the comma-separated pair consisting of 'CallExerciseStyle' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: string | char | cell

Put schedule, specified as the comma-separated pair consisting of 'PutSchedule' and a timetable of call dates and strikes.

If you use a date character vector or date string for dates in this timetable, the format must be recognizable by datetime because the PutSchedule property is stored as a datetime.

Note

For he ConvertibleBond instrument, you can use a CallSchedule with a CallExerciseStyle and a PutSchedule with a PutExerciseStyle simultaneously.

Data Types: timetable

Put option exercise style, specified as the comma-separated pair consisting of 'PutExerciseStyle' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: string | cell | char

Frequency of payments per year, specified as the comma-separated pair consisting of 'Period' and a scalar integer or an NINST-by-1 vector of integers. Possible values for Period are 1, 2, 3, 4, 6, and 12.

Data Types: double

Day count basis, specified as the comma-separated pair consisting of 'Basis' and scalar integer or an NINST-by-1 vector of integers 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

Notional principal amount or principal value schedule, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric or NINST-by-1 numeric vector or a timetable.

Principal accepts a timetable, where the first column is dates and the second column is the associated notional principal value. The date indicates the last day that the principal value is valid.

Data Types: double | timetable

Flag indicating whether cash flow adjusts for the day count convention, specified as the comma-separated pair consisting of 'DaycountAdjustedCashFlow' and a scalar logical or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

Business day conventions, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array. 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). Possible 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 nonbusiness 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 | string

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array. An example follows.

H = holidays(datetime('today'),datetime(2025,12,15));
ConvertibleBondObj = fininstrument("ConvertibleBond",'CouponRate',0.34,'Maturity',datetime(2025,12,15),...
'ConversionRatio',ConvRatio,'CallSchedule',schedule,'CallExerciseStyle',"american",'Holidays',H)

Data Types: double | cell | datetime | string

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month with 30 or fewer days, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar logical value or an NINST-by-1 vector of logical values of true or false.

  • If you set EndMonthRule to false, the software ignores the rule, meaning that a payment date is always the same numerical day of the month.

  • If you set EndMonthRule to true, the software sets the rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

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

If you use date character vectors or date strings, the format must be recognizable by datetime because the IssueDate property is stored as a datetime.

Data Types: double | char | cell | string | datetime

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

When you specify both FirstCouponDate and LastCouponDate, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify FirstCouponDate, the cash flow payment dates are determined from other inputs.

If you use date character vectors or date strings, the format must be recognizable by datetime because the FirstCouponDate property is stored as a datetime.

Data Types: double | char | cell | string | datetime

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

If you specify LastCouponDate but not FirstCouponDate, LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify LastCouponDate, the cash flow payment dates are determined from other inputs.

If you use date character vectors or date strings, the format must be recognizable by datetime because the LastCouponDate property is stored as a datetime.

Data Types: double | char | cell | string | datetime

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, serial date number, date character vector, date string or an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

If you use date character vectors or date strings, the format must be recognizable by datetime because the StartDate property is stored as a datetime.

Data Types: char | cell | double | string | datetime

User-defined name for one of more instruments, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: char | cell | string

Properties

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Coupon annual rate, returned as a scalar decimal or an NINST-by-1 or timetable.

Data Types: double | timetable

Maturity date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Number of shares convertible from one bond, returned as a scalar numeric or an NINST-by-1 numeric vector an a timetable.

Data Types: double | timetable

Number of basis points over the reference rate, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Call schedule, returned as a timetable.

Data Types: timetable

Put schedule, returned as a timetable.

Data Types: timetable

Coupons per year, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

Day count basis, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

Notional principal amount or principal value schedule, returned as a scalar numeric or an NINST-by-1 numeric vector or a timetable.

Data Types: timetable | double

Flag indicating whether cash flow adjusted for day count convention, returned as scalar logical or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

Business day conventions, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Holidays used in computing business days, returned as datetimes or an NINST-by-1 vector of datetimes.

Data Types: datetime

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month with 30 or fewer days, returned as a scalar logical or an NINST-by-1 vector of logicals.

Data Types: logical

Bond issue date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Irregular first coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Irregular last coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Forward starting date of payments, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

This property is read-only.

Call option exercise style, returned as a scalar string or NINST-by-1 string array with values of "European", "American", or "Bermuda".

Data Types: string

This property is read-only.

Put option exercise style, returned as a scalar string or an NINST-by-1 string array with values of "European", "American", or "Bermuda".

Data Types: string

User-defined name for the instrument, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Object Functions

setCallExercisePolicySet call exercise policy for OptionEmbeddedFixedBond, OptionEmbeddedFloatBond, or ConvertibleBond instrument
setPutExercisePolicySet put exercise policy for OptionEmbeddedFixedBond, OptionEmbeddedFloatBond, or ConvertibleBond instrument

Examples

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This example shows the workflow to price a ConvertibleBond instrument when you use a BlackScholes model and a FiniteDifference pricing method.

Create ConvertibleBond Instrument Object

Use fininstrument to create a ConvertibleBond instrument object.

CouponRate = 0;
Maturity = datetime(2014,10,1);
ConvRatio = 2;
Period = 1;
Spread = 0.05;

CallExDates = datetime(2014,10,1);
CallStrike = 115;
CallSchedule = timetable(CallExDates, CallStrike);

ConvBond = fininstrument("ConvertibleBond",'CouponRate',CouponRate,'Maturity',Maturity,'ConversionRatio',ConvRatio,'Period',Period,'Spread',Spread,'CallSchedule',CallSchedule,'CallExercisestyle',"american",'Name',"Convertible_Bond")
ConvBond = 
  ConvertibleBond with properties:

                  CouponRate: 0
             ConversionRatio: 2
                      Spread: 0.0500
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                    Maturity: 01-Oct-2014
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                CallSchedule: [1x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "american"
            PutExerciseStyle: [0x0 string]
                        Name: "Convertible_Bond"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

AssetPrice = 50;
Volatility = 0.3;

BSModel = finmodel("BlackScholes",'Volatility',Volatility)
BSModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a ratecurve object using ratecurve.

StartDate = datetime(2014,1,1);
EndDate = datetime(2015,1,1);
Rate = 0.1;

ZeroCurve = ratecurve('zero',StartDate,EndDate,Rate,'Compounding',-1,'Basis',1)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2015
                Rates: 0.1000
               Settle: 01-Jan-2014
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create FiniteDifference Pricer Object

Use finpricer to create a FiniteDifference pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

outPricer = finpricer("FiniteDifference",'Model',BSModel,'SpotPrice',AssetPrice,'DiscountCurve',ZeroCurve)
outPricer = 
  FiniteDifference with properties:

     DiscountCurve: [1x1 ratecurve]
             Model: [1x1 finmodel.BlackScholes]
         SpotPrice: 50
    GridProperties: [1x1 struct]
      DividendType: "continuous"
     DividendValue: 0

Price ConvertibleBond Instrument

Use price to compute the price and sensitivities for the ConvertibleBond instrument.

[Price, outPR] = price(outPricer,ConvBond,"all")
Price = 104.3812
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results
ans=1×7 table
    Price     Delta      Gamma     Lambda      Theta       Rho       Vega 
    ______    ______    _______    _______    _______    _______    ______

    104.38    1.3012    0.04195    0.62329    0.72984    -21.883    17.947

This example shows the workflow to price multiple ConvertibleBond instruments when you use a BlackScholes model and a FiniteDifference pricing method.

Create ConvertibleBond Instrument Object

Use fininstrument to create a ConvertibleBond instrument object for three Convertible Bond instruments.

ConvRatio = 2;
Period = 1;
Spread = 0.05;

CallExDates = datetime(2014,10,1);
CallStrike = 115;
CallSchedule = timetable(CallExDates, CallStrike);

ConvBond = fininstrument("ConvertibleBond",'CouponRate',[0 ; 0.1 ; 0.2],'Maturity',datetime([2014,10,1 ; 2014,11,1 ; 2014,12,1]),'ConversionRatio',[2 ; 4 ; 6],'Period',Period,'Spread',Spread,'CallSchedule',CallSchedule,'CallExercisestyle',"american",'Name',"Convertible_Bond")
ConvBond=3×1 object
  3x1 ConvertibleBond array with properties:

    CouponRate
    ConversionRatio
    Spread
    Period
    Basis
    EndMonthRule
    Principal
    DaycountAdjustedCashFlow
    BusinessDayConvention
    Holidays
    Maturity
    IssueDate
    FirstCouponDate
    LastCouponDate
    StartDate
    CallSchedule
    PutSchedule
    CallExerciseStyle
    PutExerciseStyle
    Name

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

AssetPrice = 50;
Volatility = 0.3;

BSModel = finmodel("BlackScholes",'Volatility',Volatility)
BSModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a ratecurve object using ratecurve.

StartDate = datetime(2014,1,1);
EndDate = datetime(2015,1,1);
Rate = 0.1;

ZeroCurve = ratecurve('zero',StartDate,EndDate,Rate,'Compounding',-1,'Basis',1)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2015
                Rates: 0.1000
               Settle: 01-Jan-2014
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create FiniteDifference Pricer Object

Use finpricer to create a FiniteDifference pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

outPricer = finpricer("FiniteDifference",'Model',BSModel,'SpotPrice',AssetPrice,'DiscountCurve',ZeroCurve)
outPricer = 
  FiniteDifference with properties:

     DiscountCurve: [1x1 ratecurve]
             Model: [1x1 finmodel.BlackScholes]
         SpotPrice: 50
    GridProperties: [1x1 struct]
      DividendType: "continuous"
     DividendValue: 0

Price ConvertibleBond Instruments

Use price to compute the prices and sensitivities for the ConvertibleBond instruments.

[Price, outPR] = price(outPricer,ConvBond,"all")
Price = 3×1

  104.3812
  198.3288
  298.3014

outPR=3×1 object
  3x1 priceresult array with properties:

    Results
    PricerData

outPR.Results
ans=1×7 table
    Price     Delta      Gamma     Lambda      Theta       Rho       Vega 
    ______    ______    _______    _______    _______    _______    ______

    104.38    1.3012    0.04195    0.62329    0.72984    -21.883    17.947

ans=1×7 table
    Price     Delta      Gamma       Lambda    Theta        Rho           Vega   
    ______    _____    __________    ______    ______    __________    __________

    198.33      4      1.7053e-13    1.0084    300.82    2.8422e-10    2.8422e-10

ans=1×7 table
    Price    Delta       Gamma       Lambda    Theta         Rho           Vega    
    _____    _____    ___________    ______    ______    ___________    ___________

    298.3      6      -1.7053e-13    1.0057    277.96    -1.7053e-09    -5.6843e-10

More About

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Tips

After creating a ConvertibleBond object, you can modify the CallSchedule and CallExerciseStyle using setCallExercisePolicy. You can modify the PutSchedule and PutExerciseStyle values using setPutExercisePolicy.

Introduced in R2021a