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CDSOption

CDSOption instrument object

Since R2020a

Description

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

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

Syntax

CDSOptionObj = fininstrument(InstrumentType,'ExerciseDate',exercise_date,'Strike',strike_value,'CDS',cds_obj)

CDSOptionObj = fininstrument(___,Name,Value)

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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`InstrumentType` — Instrument type
string with value `"CDSoption"` | string array with values of `"CDSoption"` | character vector with value `'CDSoption'` | cell array of character vectors with values of `'CDSoption'`

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

Name-Value Arguments

Specify required and 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: 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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`ExerciseDate` — Option exercise date
datetime array | string array | date character vector

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

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

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

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

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` — `CDS` object
`CDS` object | vector of `CDS` objects

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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`OptionType` — Option type
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"` | character vector with value `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

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

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

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

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

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 CDSBlack Model and CDSBlack Pricer.

Data Types: double

`Name` — User-defined name for instrument
`" "` (default) | string | string array | character vector | cell array of character vectors

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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`ExerciseDate` — Option exercise date
datetime | vector of datetimes

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

Data Types: datetime

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

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

Data Types: double

`CDS` — `CDS` object
`CDS` object | vector of `CDS` objects

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

Data Types: object

`OptionType` — Definition of option
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"`

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

Data Types: string

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

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

Data Types: logical

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

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

`Name` — User-defined name for instrument
`" "` (default) | string | string array

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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Price `CDSOption` Instrument Using `CDSBlack` Model and `CDSBlack` Pricer

Open Live Script

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

Price Multiple `CDSOption` Instruments Using `CDSBlack` Model and `CDSBlack` Pricer

Open Live Script

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

Price CDS Index Options Using `CDSBlack` Model and `CDSBlack` Pricer

Open Live Script

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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Credit Default Swap Option

A credit default swap (CDS) option, or credit default swaption, is a contract that provides the option holder with the right, but not the obligation, to enter into a credit default swap in the future.

CDS options can be either payer swaptions or receiver swaptions. In a payer swaption, the option holder has the right to enter into a CDS in which they are paying premiums, and in a receiver swaption, the option holder is receiving premiums.

A CDS option can be a single-name CDS option or CDS index option. When pricing a CDS index option , use the optional name-value argument AdjustedForwardSpread. Unlike a single-name CDS, a CDS portfolio index contains multiple credits. When one or more of the credits default, the corresponding contingent payments are made to the protection buyer but the contract still continues with reduced coupon payments. Considering the fact that the CDS index option does not cancel when some of the underlying credits default before expiry, one might attempt to price CDS index options using the Black's model for non-knockout single-name CDS option. However, Black's model in this form is not appropriate for pricing CDS index options because it does not capture the exercise decision correctly when the strike spread (K) is very high, nor does it ensure put-call parity when (K) is not equal to the contractual spread (O'Kane, 2008).

However, with the appropriate modifications, Black's model for single-name CDS options used with a CDSOption instrument and CDSBlack pricer can provide a good approximation for CDS index options. While there are some variations in the way the Black's model is modified for CDS index options, they usually involve adjusting the forward spread F, the strike spread K, or both. Here we describe the approach of adjusting the forward spread only. In the Black's model for single-name CDS options, the forward spread F is defined as:

$F = S (t, t_{E}, T) = \frac{S (t, T) R P V 01 (t, T) - S (t, t_{E}) R P V 01 (t, t_{E})}{R P V 01 (t, t_{E}, T)}$

where

S is the spread.

RPV01 is the risky present value of a basis point (see cdsrpv01).

t is the valuation date.

t_E is the option expiry date.

T is the CDS maturity date.

To capture the exercise decision correctly for CDS index options, we use the knockout form of the Black's model and adjust the forward spread to incorporate the FEP (front end protection) as follows:

$F_{A d j} = F + \frac{F E P}{R P V 01 (t, t_{E}, T)}$

with FEP defined as

$F E P = (1 - R) Z (t, t_{E}) (1 - Q (t, t_{E}))$

where

R is the recovery rate.

Z is the discount factor.

Q is the survival probability.

In the CDSOption object, forward spread adjustment can be made with the AdjustedForwardSpread name-value argument. When computing the adjusted forward spread, you can compute the spreads using cdsspread and the RPV01s using cdsrpv01.

References

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

Version History

Introduced in R2020a

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R2022b: Serial date numbers not recommended

Although CDSOption 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.

CDSOption

Description

Creation

Syntax

Description

Input Arguments

`InstrumentType` — Instrument type
string with value `"CDSoption"` | string array with values of `"CDSoption"` | character vector with value `'CDSoption'` | cell array of character vectors with values of `'CDSoption'`

`ExerciseDate` — Option exercise date
datetime array | string array | date character vector

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

`CDS` — `CDS` object
`CDS` object | vector of `CDS` objects

`OptionType` — Option type
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"` | character vector with value `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

`Name` — User-defined name for instrument
`" "` (default) | string | string array | character vector | cell array of character vectors

Properties

`ExerciseDate` — Option exercise date
datetime | vector of datetimes

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

`CDS` — `CDS` object
`CDS` object | vector of `CDS` objects

`OptionType` — Definition of option
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"`

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

`Name` — User-defined name for instrument
`" "` (default) | string | string array

Examples

Price `CDSOption` Instrument Using `CDSBlack` Model and `CDSBlack` Pricer

Price Multiple `CDSOption` Instruments Using `CDSBlack` Model and `CDSBlack` Pricer

Price CDS Index Options Using `CDSBlack` Model and `CDSBlack` Pricer

More About

Credit Default Swap Option

References

Version History

R2022b: Serial date numbers not recommended

See Also

Functions

Topics

CDSOption

Description

Creation

Syntax

Description

Input Arguments

InstrumentType — Instrument type string with value "CDSoption" | string array with values of "CDSoption" | character vector with value 'CDSoption' | cell array of character vectors with values of 'CDSoption'

ExerciseDate — Option exercise date datetime array | string array | date character vector

Strike — Option strike price scalar nonnegative numeric | vector of nonnegative numeric

CDS — CDS object CDS object | vector of CDS objects

OptionType — Option type "call" (default) | string with value "call" or "put" | string array with values of "call" or "put" | character vector with value 'call' or 'put' | cell array of character vectors with values of 'call' or 'put'

Knockout — Flag indicating if option is knockout type false (default) | scalar logical with value true or false | vector of logicals with values of true or false

AdjustedForwardSpread — Adjusted forward spread (in basis points) for pricing CDS index option NaN (single-name CDS option) (default) | scalar numeric | numeric vector

Name — User-defined name for instrument " " (default) | string | string array | character vector | cell array of character vectors

Properties

ExerciseDate — Option exercise date datetime | vector of datetimes

Strike — Option strike price scalar nonnegative numeric | vector of nonnegative numeric

CDS — CDS object CDS object | vector of CDS objects

OptionType — Definition of option "call" (default) | string with value "call" or "put" | string array with values of "call" or "put"

Knockout — Flag indicating if option is knockout type false (default) | scalar logical with value true or false | vector of logicals with values of true or false

AdjustedForwardSpread — Adjusted forward spread (in basis points) for pricing CDS index option NaN (single-name CDS option) (default) | scalar numeric | numeric vector

Name — User-defined name for instrument " " (default) | string | string array

Examples

Price CDSOption Instrument Using CDSBlack Model and CDSBlack Pricer

Price Multiple CDSOption Instruments Using CDSBlack Model and CDSBlack Pricer

Price CDS Index Options Using CDSBlack Model and CDSBlack Pricer

More About

Credit Default Swap Option

References

Version History

R2022b: Serial date numbers not recommended

See Also

Functions

Topics

`InstrumentType` — Instrument type
string with value `"CDSoption"` | string array with values of `"CDSoption"` | character vector with value `'CDSoption'` | cell array of character vectors with values of `'CDSoption'`

`ExerciseDate` — Option exercise date
datetime array | string array | date character vector

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

`CDS` — `CDS` object
`CDS` object | vector of `CDS` objects

`OptionType` — Option type
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"` | character vector with value `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

`Name` — User-defined name for instrument
`" "` (default) | string | string array | character vector | cell array of character vectors

`ExerciseDate` — Option exercise date
datetime | vector of datetimes

`Strike` — Option strike price
scalar nonnegative numeric | vector of nonnegative numeric

`CDS` — `CDS` object
`CDS` object | vector of `CDS` objects

`OptionType` — Definition of option
`"call"` (default) | string with value `"call"` or `"put"` | string array with values of `"call"` or `"put"`

`Knockout` — Flag indicating if option is knockout type
`false` (default) | scalar logical with value `true` or `false` | vector of logicals with values of `true` or `false`

`AdjustedForwardSpread` — Adjusted forward spread (in basis points) for pricing CDS index option
`NaN` (single-name CDS option) (default) | scalar numeric | numeric vector

`Name` — User-defined name for instrument
`" "` (default) | string | string array

Price `CDSOption` Instrument Using `CDSBlack` Model and `CDSBlack` Pricer

Price Multiple `CDSOption` Instruments Using `CDSBlack` Model and `CDSBlack` Pricer

Price CDS Index Options Using `CDSBlack` Model and `CDSBlack` Pricer