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CDSOption

CDSOption instrument object

Description

Create and price a CDSOption instrument object for one or more CDS Option instruments using this workflow:

  1. Use fininstrument to create a CDSOption instrument object for one or more CDS Option instruments. By default, this creates a single-name CDS option. You can create a CDS index option by specifying the optional name-value argument AdjustedForwardSpread.

  2. Use finmodel to specify a CDSBlack model for the CDSoption instrument object.

  3. Use finpricer to specify a CDSBlack pricing method for one or more CDSoption 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 using a CDSoption instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

CDSOptionObj = fininstrument(InstrumentType,'ExerciseDate',exercise_date,'Strike',strike_value,'CDS',cds_obj) creates a CDSOption object for one or more CDS Option instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments ExerciseDate, Strike, and CDS.

example

CDSOptionObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, CDSOptionObj = fininstrument("CDSoption",'ExerciseDate',datetime(2019,1,30),'Strike',500,'CDS',cds_object,'Name',"cdsoption_instrument") creates a CDSOption instrument for a single-name CDS option with a strike of 500. You can specify multiple name-value pair arguments.

Input Arguments

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

Data Types: char | cell | string

CDSOption 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: CDSOptionObj = fininstrument("CDSoption",'ExerciseDate',datetime(2019,1,30),'Strike',500,'CDS',cds_object,'Name',"cdsoption_instrument")
Required CDSOption Name-Value Pair Arguments

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Option exercise date, specified as the comma-separated pair consisting of 'ExerciseDate' 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 ExerciseDate property is stored as a datetime.

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

Option strike price, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative numeric or an NINST-by-1 vector of nonnegative numeric.

Data Types: double

CDS object, specified as the comma-separated pair consisting of 'CDS' and a scalar CDS object or an NINST-by-1 vector of CDS objects.

Data Types: object

Optional CDSOption Name-Value Pair Argument

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Option type, specified as the comma-separated pair consisting of 'OptionType' 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

Flag indicating if option is knockout type, specified as the comma-separated pair consisting of 'Knockout' and a scalar logical or an NINST-by-1 vector of logical values.

Data Types: logical

Adjusted forward spread (in basis points) for pricing a CDS index option, specified as the comma-separated pair consisting of 'AdjustedForwardSpread' and a scalar numeric or an NINST-by-1 numeric vector. For more information on using 'AdjustedForwardSpread' when pricing a CDS index option, see Price CDS Index Options Using CDS Black Model and CDS Black Pricer.

Data Types: double

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

Data Types: datetime

Option strike price, returned as a scalar nonnegative numeric or an NINST-by-1 vector of nonnegative numeric values.

Data Types: double

CDS object, returned as a scalar CDS object or an NINST-by-1 vector of CDS objects.

Data Types: object

Definition of option, returned as a scalar string or an NINST-by-1 string array with values of "call" or "put".

Data Types: string

Flag indicating if option is knockout type, returned as a scalar logical or an NINST-by-1 vector of logicals.

Data Types: logical

Adjusted forward spread (in basis points) for pricing a CDS index option, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

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

Data Types: string

Examples

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This example shows the workflow to price a CDSOption instrument for a single-name CDS option when you use a CDSBlack model and a CDSBlack pricing method.

Create CDS Instrument Object

Use fininstrument to create the underlying CDS instrument object.

CDSOpt = fininstrument("CDS",'Maturity',datetime(2021,9,15),'ContractSpread',150,'Notional',100,'Name',"CDS_option")
CDSOpt = 
  CDS with properties:

           ContractSpread: 150
                 Maturity: 15-Sep-2021
                   Period: 4
                    Basis: 2
             RecoveryRate: 0.4000
    BusinessDayConvention: "actual"
                 Holidays: NaT
        PayAccruedPremium: 1
                 Notional: 100
                     Name: "CDS_option"

Create defprobcurve Object

Create a defprobcurve object using defprobcurve.

Settle = datetime(2020,9,20);
DefProbTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])];
DefaultProbabilities = [0.005 0.007 0.01 0.015 0.026 0.04 0.077 0.093 0.15 0.20]';
ProbDates = Settle + DefProbTimes;
DefaultProbCurve = defprobcurve(Settle,ProbDates,DefaultProbabilities,'Basis',5)
DefaultProbCurve = 
  defprobcurve with properties:

                  Settle: 20-Sep-2020
                   Basis: 5
                   Dates: [10x1 datetime]
    DefaultProbabilities: [10x1 double]

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2020,9,15);
Type = 'zero';
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create CDSOption Instrument Object

Use fininstrument to create a CDSOption instrument object for a single-name CDS option.

CDSOptionInst = fininstrument("CDSOption",'ExerciseDate',datetime(2021,8,15),'Strike',20,'CDS',CDSOpt,'OptionType',"put",'Knockout',true,'Name',"CDSOption_option")
CDSOptionInst = 
  CDSOption with properties:

               OptionType: "put"
                   Strike: 20
                 Knockout: 1
    AdjustedForwardSpread: NaN
             ExerciseDate: 15-Aug-2021
                      CDS: [1x1 fininstrument.CDS]
                     Name: "CDSOption_option"

Create CDSBlack Model Object

Use finmodel to create a CDSBlack model object.

CDSBlackModel = finmodel("CDSBlack",'SpreadVolatility',.2)
CDSBlackModel = 
  CDSBlack with properties:

    SpreadVolatility: 0.2000

Create CDSBlack Pricer Object

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

outPricer = finpricer("analytic",'Model',CDSBlackModel,'DefaultProbabilityCurve',DefaultProbCurve,'DiscountCurve',myRC)
outPricer = 
  CDSBlack with properties:

                      Model: [1x1 finmodel.CDSBlack]
              DiscountCurve: [1x1 ratecurve]
    DefaultProbabilityCurve: [1x1 defprobcurve]

Price CDSOption Instrument

Use price to compute the price for the CDSOption instrument for a single-name CDS option.

Price = price(outPricer,CDSOptionInst)
Price = 3.3016e-04

This example shows the workflow to price multiple CDSOption instruments when you use a CDSBlack model and a CDSBlack pricing method.

Create CDS Instrument Object

Use fininstrument to create the underlying CDS instrument object for three CDS Option instruments.

CDSOpt = fininstrument("CDS",'Maturity',datetime([2021,9,15 ; 2021,10,15 ; 2021,11,15]),'ContractSpread',150,'Notional',[10000 ; 20000 ; 30000],'Name',"CDS_option")
CDSOpt=3×1 object
  3x1 CDS array with properties:

    ContractSpread
    Maturity
    Period
    Basis
    RecoveryRate
    BusinessDayConvention
    Holidays
    PayAccruedPremium
    Notional
    Name

Create defprobcurve Object

Create a defprobcurve object using defprobcurve.

Settle = datetime(2020,9,20);
DefProbTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])];
DefaultProbabilities = [0.005 0.007 0.01 0.015 0.026 0.04 0.077 0.093 0.15 0.20]';
ProbDates = Settle + DefProbTimes;
DefaultProbCurve = defprobcurve(Settle,ProbDates,DefaultProbabilities,'Basis',5)
DefaultProbCurve = 
  defprobcurve with properties:

                  Settle: 20-Sep-2020
                   Basis: 5
                   Dates: [10x1 datetime]
    DefaultProbabilities: [10x1 double]

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2020,9,15);
Type = 'zero';
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create CDSOption Instrument Object

Use fininstrument to create a CDSOption instrument object for three single-name CDS options.

CDSOptionInst = fininstrument("CDSOption",'ExerciseDate',datetime(2021,8,15),'Strike',20,'CDS',CDSOpt,'OptionType',"put",'Knockout',true,'Name',"CDSOption_option")
CDSOptionInst=3×1 object
  3x1 CDSOption array with properties:

    OptionType
    Strike
    Knockout
    AdjustedForwardSpread
    ExerciseDate
    CDS
    Name

Create CDSBlack Model Object

Use finmodel to create a CDSBlack model object.

CDSBlackModel = finmodel("CDSBlack",'SpreadVolatility',.2)
CDSBlackModel = 
  CDSBlack with properties:

    SpreadVolatility: 0.2000

Create CDSBlack Pricer Object

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

outPricer = finpricer("analytic",'Model',CDSBlackModel,'DefaultProbabilityCurve',DefaultProbCurve,'DiscountCurve',myRC)
outPricer = 
  CDSBlack with properties:

                      Model: [1x1 finmodel.CDSBlack]
              DiscountCurve: [1x1 ratecurve]
    DefaultProbabilityCurve: [1x1 defprobcurve]

Price CDSOption Instruments

Use price to compute the prices for the three CDSOption instruments.

Price = price(outPricer,CDSOptionInst)
Price = 3×1

    0.0003
    0.0384
    0.5941

This example shows the workflow to use a CDSOption instrument to price CDS index options when you use a CDSBlack model and a CDSBlack pricing method.

Set Up Data for CDS Index

% CDS index and option data
Recovery = .4;
Basis = 2;
Period = 4;
CDSMaturity = datetime(2017, 6, 20);
ContractSpread = 100;
IndexSpread = 140;
BusDayConvention = 'follow';
Settle = datetime(2012, 4, 13);
OptionMaturity = datetime(2012, 6, 20);
OptionStrike = 140;
SpreadVolatility = .69;

Create ratecurve Object for Zero Curve Using irbootstrap

Create ratecurve object for a zero curve using irbootstrap.

% Zero curve data
DepRates = [0.004111 0.00563 0.00757 0.01053]';
DepTimes = calmonths([1 2 3 6]');
DepDates = Settle + DepTimes;
nDeposits = length(DepTimes);

SwapRates = [0.01387 0.01035 0.01145 0.01318 0.01508 0.01700 0.01868 ...
    0.02012 0.02132 0.02237 0.02408 0.02564 0.02612 0.02524]';
SwapTimes = calyears([1 2 3 4 5 6 7 8 9 10 12 15 20 30]');
SwapDates = Settle + SwapTimes;
nSwaps = length(SwapTimes);

nInst = nDeposits + nSwaps;

BootInstruments(nInst,1) = fininstrument.FinInstrument;
for ii=1:length(DepDates)
    BootInstruments(ii) = fininstrument("deposit","Maturity",DepDates(ii),"Rate",DepRates(ii));
end

for ii=1:length(SwapDates)
    BootInstruments(ii+nDeposits) = fininstrument("swap","Maturity",SwapDates(ii),"LegRate",[SwapRates(ii) 0]);
end

ZeroCurve = irbootstrap(BootInstruments,Settle)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [18x1 datetime]
                Rates: [18x1 double]
               Settle: 13-Apr-2012
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Bootstrap Default Probability Curve

Use defprobstrip to bootstrap default probability curve assuming a flat index spread.

ProbDates = datemnth(OptionMaturity,(0:5*12)');
MarketCDSInstruments = fininstrument("cds", ...
    'ContractSpread', ContractSpread, 'Maturity', CDSMaturity);
DefaultProbCurve = defprobstrip(ZeroCurve, MarketCDSInstruments, IndexSpread, 'ProbDates', ProbDates)
DefaultProbCurve = 
  defprobcurve with properties:

                  Settle: 13-Apr-2012
                   Basis: 2
                   Dates: [61x1 datetime]
    DefaultProbabilities: [61x1 double]

Compute Spot and Forward RPV01s

Compute the spot and forward RPV01s using cdsrpv01.

ProbData = [datenum(DefaultProbCurve.Dates) DefaultProbCurve.DefaultProbabilities];

% RPV01(t,T)
RPV01_CDSMaturity = cdsrpv01(ZeroCurve,ProbData,Settle,CDSMaturity)
RPV01_CDSMaturity = 4.7853
% RPV01(t,t_E,T)
RPV01_OptionExpiryForward = cdsrpv01(ZeroCurve,ProbData,Settle,CDSMaturity,...
    'StartDate',OptionMaturity)
RPV01_OptionExpiryForward = 4.5972
% RPV01(t,t_E) = RPV01(t,T) - RPV01(t,t_E,T)
RPV01_OptionExpiry = RPV01_CDSMaturity - RPV01_OptionExpiryForward
RPV01_OptionExpiry = 0.1882

Compute Spot Spreads

Compute the spot spreads using cdsspread.

% S(t,t_E)
Spread_OptionExpiry = cdsspread(ZeroCurve,ProbData,Settle,OptionMaturity,...
    'Period',Period,'Basis',Basis,'BusDayConvention',BusDayConvention,...
    'PayAccruedPremium',true,'recoveryrate',Recovery)
Spread_OptionExpiry = 139.8995
% S(t,T)
Spread_CDSMaturity = cdsspread(ZeroCurve,ProbData,Settle,CDSMaturity,...
    'Period',Period,'Basis',Basis,'BusDayConvention',BusDayConvention,...
    'PayAccruedPremium',true,'recoveryrate',Recovery)
Spread_CDSMaturity = 139.9999

Compute Forward Spread

Compute the forward spread using the spot spreads and RPV01s.

% F = S(t,t_E,T)
ForwardSpread = (Spread_CDSMaturity.*RPV01_CDSMaturity - Spread_OptionExpiry.*RPV01_OptionExpiry)./RPV01_OptionExpiryForward
ForwardSpread = 140.0040

Compute Front-End Protection

Compute the front-end protection (FEP).

FEP = 10000*(1-Recovery)*ZeroCurve.discountfactors(OptionMaturity)*DefaultProbCurve.DefaultProbabilities(1)
FEP = 26.3108

Compute Adjusted Forward Spread

Compute the adjusted forward spread to use when creating an CDSOption instrument.

AdjustedForwardSpread = ForwardSpread + FEP./RPV01_OptionExpiryForward
AdjustedForwardSpread = 145.7273

Compute CDS Option Prices with Adjusted Forward Spread

Use fininstrument to create the underlying CDS instrument object for the two CDS Option instruments.

CDS = fininstrument("cds",'ContractSpread', ContractSpread, 'Maturity', CDSMaturity)
CDS = 
  CDS with properties:

           ContractSpread: 100
                 Maturity: 20-Jun-2017
                   Period: 4
                    Basis: 2
             RecoveryRate: 0.4000
    BusinessDayConvention: "actual"
                 Holidays: NaT
        PayAccruedPremium: 1
                 Notional: 10000000
                     Name: ""

Use fininstrument to create a CDSOption instrument for two CDS index option instruments.

CDSCallOption = fininstrument("cdsoption", 'Strike', OptionStrike, ...
    'ExerciseDate', OptionMaturity, 'OptionType', 'call', 'CDS', CDS, ...
    'Knockout',true, 'AdjustedForwardSpread', AdjustedForwardSpread)
CDSCallOption = 
  CDSOption with properties:

               OptionType: "call"
                   Strike: 140
                 Knockout: 1
    AdjustedForwardSpread: 145.7273
             ExerciseDate: 20-Jun-2012
                      CDS: [1x1 fininstrument.CDS]
                     Name: ""

CDSPutOption = fininstrument("cdsoption", 'Strike', OptionStrike, ...
    'ExerciseDate', OptionMaturity, 'OptionType', 'put', 'CDS', CDS, ...
    'Knockout',true, 'AdjustedForwardSpread', AdjustedForwardSpread)
CDSPutOption = 
  CDSOption with properties:

               OptionType: "put"
                   Strike: 140
                 Knockout: 1
    AdjustedForwardSpread: 145.7273
             ExerciseDate: 20-Jun-2012
                      CDS: [1x1 fininstrument.CDS]
                     Name: ""

Create CDSBlack Model Object

Use finmodel to create a CDSBlack model object.

CDSOptionModel = finmodel("cdsblack",'SpreadVolatility',SpreadVolatility)
CDSOptionModel = 
  CDSBlack with properties:

    SpreadVolatility: 0.6900

Create CDSBlack Pricer Object

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

CDSOptionpricer = finpricer("analytic",'Model',CDSOptionModel,'DiscountCurve',ZeroCurve,'DefaultProbabilityCurve',DefaultProbCurve)
CDSOptionpricer = 
  CDSBlack with properties:

                      Model: [1x1 finmodel.CDSBlack]
              DiscountCurve: [1x1 ratecurve]
    DefaultProbabilityCurve: [1x1 defprobcurve]

Price CDS Index Options

Use price to compute the price for the two CDS index options.

outPrice = price(CDSOptionpricer, [CDSCallOption;CDSPutOption]);
fprintf('    Payer: %.0f   Receiver: %.0f  \n',outPrice(1),outPrice(2));
    Payer: 92   Receiver: 66  

More About

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References

[1] O'Kane, D. Modelling Single-name and Multi-name Credit Derivatives. Wiley, 2008, pp. 156–169.

Introduced in R2020a