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Using FINCAD Analytics Suite's Single Asset Credit Default Swap Functions

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.

FINCAD Analytics Suite's Function Finder

The user can enter the curve in the Default Probability/Density Curve table:

Default probability and density curve screenshot

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.

Probability Calculator

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.

Single Asset Default Swap - Vanilla Screenshot

 

Probability Calculator

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 interest upon default
  • pay no accrued interest upon default
Pay Accrued:
  • True
  • False
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:
  • Simplified calculation method
Model Type:
  • JPMorgan

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 risk-free 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:

par default swap spread table

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.

Single Asset Default Swap - Vanilla Screenshot

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. 29-40.

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 user-defined loan
aaCredit_Dpayoff_fs_crv Calculate fair value for the payoff of a default swap on a user-defined 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 free-style premium payments of a default swap
aaCredit_Dpremium_fs_crv Calculate the fair value for free-style 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 user-defined loan
aaCredit_Dswap_fs_crv Calculate the fair value of a default swap on a user-defined 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.