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Bootstrapping a Default Probability Curve from Credit Default Swaps

This example shows how to bootstrap a default probability curve for CDS instruments.

Create a ratecurve Object for a Zero Curve

Create a ratecurve object using ratecurve.

Settle = datetime(2017,9,15);
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: 15-Sep-2017
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Market CDS Spreads and a Vector of Market CDS Instruments

Define the market CDS spreads and use fininstrument to create a vector of market CDS instrument objects.

SpreadTimes = [1 2 3 4 5 7 10 20 30]';
Spread = [140 175 210 265 310 360 410 460 490]';
MarketDates = datemnth(Settle,12*SpreadTimes);

NumMarketInst = length(MarketDates);
ContractSpreadBP = 50.*ones(NumMarketInst,1);

MarketCDSInstruments(NumMarketInst,1) = fininstrument("cds", ...
    'ContractSpread', ContractSpreadBP(end), 'Maturity', MarketDates(end));
for k = 1:NumMarketInst
    MarketCDSInstruments(k,1) = fininstrument("cds", ...
        'ContractSpread', ContractSpreadBP(k), 'Maturity', MarketDates(k));
end
MarketCDSInstruments
MarketCDSInstruments=9×1 object
  9x1 CDS array with properties:

    ContractSpread
    Maturity
    Period
    Basis
    RecoveryRate
    BusinessDayConvention
    Holidays
    PayAccruedPremium
    Notional
    Name

Bootstrap a Default Probability Curve

Use defprobstrip, hazardrates,and survprobs to analyse a default probability curve for the market CDS instruments.

DefaultProbCurve = defprobstrip(ZeroCurve, MarketCDSInstruments, Spread)
DefaultProbCurve = 
  defprobcurve with properties:

                  Settle: 15-Sep-2017
                   Basis: 2
                   Dates: [9x1 datetime]
    DefaultProbabilities: [9x1 double]

HazardRates = hazardrates(DefaultProbCurve)
HazardRates = 9×1

    0.0233
    0.0352
    0.0474
    0.0751
    0.0879
    0.0887
    0.1023
    0.1059
    0.2271

SurvivalProbabilities = survprobs(DefaultProbCurve, MarketDates)
SurvivalProbabilities = 9×1

    0.9766
    0.9424
    0.8981
    0.8322
    0.7612
    0.6358
    0.4658
    0.1590
    0.0159