What is a credit default swap?
A credit default swap (CDS) is a contract that provides protection against credit loss on an underlying reference asset as a result of a specific credit event. A credit event is usually a default of the asset issuer or, possibly, a credit downgrade. The reference asset may be a bond, a loan, a trade receivable, or some other type of liability. The buyer of a default swap pays a premium to the writer or seller in exchange for the right to receive a payment should a credit event occur. In essence, the buyer is purchasing insurance.
Using FINCAD Analytics Suite to Value a CDS (Single Asset)
A single asset credit default swap, where the asset is any asset that has a fixed principal and the default swap protects this principal, can be valued by using the CDS (Single Asset) workbook. This workbook can be found by clicking on the FINCAD Analytics Suite menu → Workbooks (user data) → Credit Derivatives (CDS & Options) → CDS (Single Asset).
To download the latest trial version of FINCAD Analytics Suite, contact a FINCAD Representative.
The user can enter the curve in the Default Probability/Density Curve table:
If a calculated default probability curve is used to value the CDS, the default probability curve can be calculated on the Probability Curve tab by using aaCredit_DfltProb_DSSprd. This function will generate a default probability curve for a given par default swap spread curve.
The following screenshots from the CDS (Single Asset) workbook display the inputs of an example CDS deal and the par default swap spreads used to generate a default probability curve.
When a user uses FINCAD Analytics Suite to generate a valuation that is comparable to Bloomberg Finance LP's valuation the user should use the following tables as a guide for entering arguments in FINCAD Analytics Suite as compared to Bloomberg Finance LP* for a CDS valuation.
Table 1: Swap Calculator Tab Inputs (aaCredit_DS)
FINCAD Analytics Suite  Bloomberg Finance LP® 
Value Date  Valuation Date (from Calculator section) 
Effective Date  Effective Date 
Terminating Date  Maturity Date 
Date of First Coupon (optional) Note: If the date generation method selected in Bloomberg Finance LP is "backward", do not enter the date of the first coupon.  First Cpn 
Date of Next to Last Coupon (optional) Note: If the date generation method selected in Bloomberg Finance LP is "backward", only enter the date of next to last coupon.  Last Cpn 
Notional Principal Amount  Notional 
Premium Coupon Rate (in %)  Deal Spread (in bps) 
Premium Payment Frequency  Payment Frequency 
Type of Premium Accrued Interest Premium:

Pay Accrued:

Accrual Method  Day Count (from deal information section) 
Business Day Convention  Business Day Adj 
Default Probability Curve (see Table 2) Note: Default probability source (set this switch to "use calculated probabilities")  
Interpolation Method of Probability Curve  
Recovery Rate  Recovery Rate 
Payoff Type (if the pay accrued argument in Bloomberg Finance LP is set to True use "pay at default")  
Holidays  Business Days (from Deal Information section) 
Discount Factor Curve (risk free) Note: Discount Factor Curve can be generated on the Zero Curve tab. Select the curve that is used in the "Spreads" section of the CDSW screen. Use the appropriate rates for the curve (i.e. Ask, Bid, or Mid Curve).  
Interpolation Method  
Trade Position: (1 for a long position, 2 for a short position)  Trade Position is set by selecting B for Buy (equivalent to a long osition) or S for Sell (equivalent for a short position). 
Calculation Type:

Model Type:

Table 2: Default Probability Curve (Probability Calculator tab: aaCredit_DfltProb_DSSprd)
FINCAD Analytics Suite  Bloomberg Finance LP® 
Value Date  Valuation Date (from Calculator section) 
Par Default Swap Spread Table Note: Table with the following column headings (effective date, maturity date, CDS par spread, type of accrued interest payment, recovery rate)  Recovery Rate (from Spreads section) 
Premium Payment Frequency  Frequency (from Spreads section) 
Accrual Method  Day Count (from Spreads section) 
Business Day Convention  
Discount Factor Curve Note: Note: Discount Factor Curve can be generated on the Zero Curve tab. Select the curve that is used in the "Spreads" section of the CDSW screen. Use the appropriate rates for the curve (i.e. Ask, Bid, or Mid Curve).  
Interpolation Method  
Time Points (in years) at which Default Probabilities are Forecasted  
Interpolation Method of Probability Curve  
Holiday List  Business Days (from the Deal Information tab) 
There is a related function aaCredit_DS_SPV01, which calculates PV01 (basis point value) based on the details of the CDS and a par default swap spread table. The PV01 value found on the Probability Calculator tab can be used to replicate the Sprd DV01 value in the Calculator section of the CDSW screen.
Steps to valuing a CDS
To value a credit default swap we first start with our market data assumptions. We need to calculate a riskfree curve, which can be done using the Fincad function aaSwap_crv2 using quoted deposit, futures, and/or par swap rates. The CDS (Single Asset) workbook has a tab called Zero Curve, which can be used to automate this process.
Then given a series of quoted par default quotes (see example above), we can create a table for input into the aaCredit_DfltProb_DSSprd function.
time length (in years)  CDS par spread in bps  recovery rate 
0.5  480.12  39.67% 
1  1002.34  39.67% 
2  1741.31  39.67% 
3  2372.68  39.67% 
4  2807.36  39.67% 
5  3158.55  39.67% 
7  3871.72  39.67% 
10  5798.15  39.67% 
For the quotes above, we would first convert them into a format that conforms to the input 'par default swap spread table' as shown below:
Now the risk free curve (discount factor curve) and the converted quotes from the par default swap spread information can be used to calculate a default probability curve with aaCredit_DfltProb_DSSprd as shown below:
term in years  probability value 
0.5  0.0390 
1  0.1553 
2  0.4681 
3  0.7865 
4  0.8266 
5  0.8547 
7  0.9108 
10  0.9949 
The default probability curve can then be used to generate the CDS valuation on the Swap Calculator tab.
Additional functions for Single Asset Credit Default Swaps
FINCAD Analytics Suite has over 60 functions related to various credit derivatives including basket credit default swaps, total return swaps, spreads, and many utility functions.
Below is a listing of additional functions related to Single Asset Credit Default Swaps. The following functions use the methodology shown in Hull J. and A. White, "Valuing Credit Default Swaps I, No Counterparty Default Risk", The Journal of Derivatives, 8 (1), (Fall 2000), p. 2940.
Calculating the expected payoff based on the probability of default
aaCredit_Dpayoff  Calculate fair value for the payoff of a default swap on a bond 
aaCredit_Dpayoff_bin  Calculate fair value for the payoff of a binary default swap using a discount factor curve 
aaCredit_Dpayoff_bin_crv  Calculate fair value for the payoff of a binary default swap using a discount factor curve 
aaCredit_Dpayoff_crv  Calculate fair value for the payoff of a default swap on a bond using a discount factor curve 
aaCredit_Dpayoff_fs  Calculate fair value for the payoff of a default swap on a userdefined loan 
aaCredit_Dpayoff_fs_crv  Calculate fair value for the payoff of a default swap on a userdefined loan using a discount factor curve 
Calculating the premium by calculating the fair value of the stream of coupons paid for the protection.
aaCredit_Dpremium  Calculate the fair value for premium payments of a default swap 
aaCredit_Dpremium_crv  Calculate the fair value for premium payments of a default swap using a discount factor curve 
aaCredit_Dpremium_fs  Calculate the fair value for freestyle premium payments of a default swap 
aaCredit_Dpremium_fs_crv  Calculate the fair value for freestyle premium payments of a default swap using a discount factor curve 
Calculating Spreads
aaCredit_Dswap_bin_spread  Calculate the spread (premium rate) of a binary default swap on a bond 
aaCredit_Dswap_bin_spread_crv  Calculate the spread (premium rate) of a binary default swap on a bond swap using a discount factor curve 
aaCredit_Dswap_spread  Calculate the spread (premium rate) of a default swap on a bond 
Calculating Swaps
aaCredit_Dswap  Calculate the fair value of a default swap on a bond 
aaCredit_Dswap_bin  Calculate the fair value of a binary default swap on a bond 
aaCredit_Dswap_bin_crv  Calculate the fair value of a binary default swap on a bond swap using a discount factor curve 
aaCredit_Dswap_bin_fs  Calculate the fair value of a binary default swap on a loan 
aaCredit_Dswap_bin_fs_crv  Calculate the fair value of a binary default swap on a loan swap using a discount factor curve 
aaCredit_Dswap_crv  Calculate the fair value of a default swap on a bond swap using a discount factor curve 
aaCredit_Dswap_fs  Calculate the fair value of a default swap on a userdefined loan 
aaCredit_Dswap_fs_crv  Calculate the fair value of a default swap on a userdefined loan swap using a discount factor curve 
aaCredit_Dswap_spread_crv  Calculate the spread (premium rate) of a default swap on a bond swap using a discount factor curve 
Disclaimer
Your use of the information in this article is at your own risk. The information in this article is provided on an "as is" basis and without any representation, obligation, or warranty from FINCAD of any kind, whether express or implied. We hope that such information will assist you, but it should not be used or relied upon as a substitute for your own independent research.
For more information or a customized demonstration of the software, contact a FINCAD Representative.
* Bloomberg is a trademark of Bloomberg Finance LP. FINCAD is not associated in any way with Bloomberg Finance LP.