Pricing a Single-Name CDS Option
This example shows how to price a single-name CDS option using
cdsoptprice. The function
cdsoptprice is based on the Black's model as described in O'Kane (2008). The optional
knockout argument for
cdsoptprice supports two variations of the mechanics of a CDS option. CDS options can be knockout or non-knockout options.
A knockout option cancels with no payments if there is a credit event before the option expiry date.
A non-knockout option does not cancel if there is a credit event before the option expiry date. In this case, the option holder of a non-knockout payer swaption can take delivery of the underlying long protection CDS on the option expiry date and exercise the protection, delivering a defaulted obligation in return for par. This portion of protection from option initiation to option expiry is known as the front-end protection (FEP). While this distinction does not affect the receiver swaption, the price of a non-knockout payer swaption is obtained by adding the value of the FEP to the knockout payer swaption price.
Define the CDS instrument.
Settle = datenum('12-Jun-2012'); OptionMaturity = datenum('20-Sep-2012'); CDSMaturity = datenum('20-Sep-2017'); OptionStrike = 200; SpreadVolatility = .4;
Define the zero rate.
Zero_Time = [.5 1 2 3 4 5]'; Zero_Rate = [.5 .75 1.5 1.7 1.9 2.2]'/100; Zero_Dates = daysadd(Settle,360*Zero_Time,1); ZeroData = [Zero_Dates Zero_Rate]
ZeroData = 6×2 105 × 7.3521 0.0000 7.3540 0.0000 7.3576 0.0000 7.3613 0.0000 7.3649 0.0000 7.3686 0.0000
Define the market data.
Market_Time = [1 2 3 5 7 10]'; Market_Rate = [100 120 145 220 245 270]'; Market_Dates = daysadd(Settle,360*Market_Time,1); MarketData = [Market_Dates Market_Rate]; ProbData = cdsbootstrap(ZeroData, MarketData, Settle)
ProbData = 6×2 105 × 7.3540 0.0000 7.3576 0.0000 7.3613 0.0000 7.3686 0.0000 7.3759 0.0000 7.3868 0.0000
Define the CDS option.
[Payer,Receiver] = cdsoptprice(ZeroData, ProbData, Settle, OptionMaturity, ... CDSMaturity, OptionStrike, SpreadVolatility, 'Knockout', true); fprintf(' Payer: %.0f Receiver: %.0f (Knockout)\n',Payer,Receiver);
Payer: 196 Receiver: 23 (Knockout)
[Payer,Receiver] = cdsoptprice(ZeroData, ProbData, Settle, OptionMaturity, ... CDSMaturity, OptionStrike, SpreadVolatility, 'Knockout', false); fprintf(' Payer: %.0f Receiver: %.0f (Non-Knockout)\n',Payer,Receiver);
Payer: 224 Receiver: 23 (Non-Knockout)