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Price Multiple CDS Option Instruments Using CDS Black Model and CDS Black Pricer

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This example shows the workflow to price multiple CDSOption instruments using a CDSBlack model and a CDSBlack pricer.

Create ratecurve Object

Create a ratecurve object using ratecurve. 

Settle = datetime(2021,9,20);
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;
ZeroCurve = ratecurve("zero", Settle, ZeroDates ,ZeroRates)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 20-Sep-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create defprobcurve Object

Create a defprobcurve object using defprobcurve. 

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)
DefaultProbCurve = 
  defprobcurve with properties:

                  Settle: 20-Sep-2021
                   Basis: 2
                   Dates: [10x1 datetime]
    DefaultProbabilities: [10x1 double]

Create CDS Instrument Object

Use fininstrument to create an underlying CDS instrument object. 

ContractSpreadBP = 0; % Contractual spread is determined on ExerciseDate
CDS = fininstrument("CDS",'Maturity',datetime(2027,9,20),'ContractSpread',ContractSpreadBP)
CDS = 
  CDS with properties:

           ContractSpread: 0
                 Maturity: 20-Sep-2027
                   Period: 4
                    Basis: 2
             RecoveryRate: 0.4000
    BusinessDayConvention: "actual"
                 Holidays: NaT
        PayAccruedPremium: 1
                 Notional: 10000000
                     Name: ""

Create CDSOption Instrument Objects

Use fininstrument to create multiple CDSOption instrument objects. 

ExerciseDate = datetime(2021, 12, 20);
Strikes = [30:2:90]';
PayerCDSOptions = fininstrument("CDSOption",'Strike',Strikes,'ExerciseDate',ExerciseDate,'OptionType',"call",'CDS',CDS)
PayerCDSOptions=31×1 object
  16x1 CDSOption array with properties:

    OptionType
    Strike
    Knockout
    AdjustedForwardSpread
    ExerciseDate
    CDS
    Name
      ⋮


ReceiverCDSOptions = fininstrument("CDSOption",'Strike',Strikes,'ExerciseDate',ExerciseDate,'OptionType',"put",'CDS',CDS)
ReceiverCDSOptions=31×1 object
  16x1 CDSOption array with properties:

    OptionType
    Strike
    Knockout
    AdjustedForwardSpread
    ExerciseDate
    CDS
    Name
      ⋮

Price CDSOption Instruments

Assuming a flat volatility structure across strikes, first use finmodel to create a CDSBlack model object. Then use finpricer to create a CDSBlack pricer object. Use price to compute the prices for the CDSOption instruments.

SpreadVolatility = 0.3;
CDSOptionModel = finmodel("CDSBlack",'SpreadVolatility',SpreadVolatility)
CDSOptionModel = 
  CDSBlack with properties:

    SpreadVolatility: 0.3000


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

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


PayerPrices = price(CDSOptionpricer,PayerCDSOptions)
PayerPrices = 31×1

  171.7269
  160.6802
  149.6346
  138.5931
  127.5648
  116.5716
  105.6576
   94.8983
   84.4061
   74.3266
      ⋮


ReceiverPrices = price(CDSOptionpricer,ReceiverCDSOptions)
ReceiverPrices = 31×1

    0.0000
    0.0003
    0.0016
    0.0070
    0.0256
    0.0794
    0.2123
    0.4999
    1.0547
    2.0221
      ⋮

Plot CDS Option Prices

Plot the payer and receiver CDS option prices.

figure;
plot(Strikes, PayerPrices, '--', Strikes, ReceiverPrices)
title('CDS Option Pricing')
xlabel('Option Strike (Basis Points)')
ylabel('Option Premium (Basis Points)')
legend('Payer CDS Options','Receiver CDS Options','Location','best')

Figure contains an axes object. The axes object with title CDS Option Pricing, xlabel Option Strike (Basis Points), ylabel Option Premium (Basis Points) contains 2 objects of type line. These objects represent Payer CDS Options, Receiver CDS Options.

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