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

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 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 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')