Using FINCAD® XL CDO Tranche Workbook
Introduction
To view the CDS on Standard or Synthetic CDO tranche(s) workbook, contact a FINCAD Representative and download the latest trial version of FINCAD Analytics.
A CDO is a security that is backed by or linked to a diversified pool of credits. The credits can be assets, such as bonds or loans, or defaultable names such as companies. In general there are two types of CDOs: cash CDOs and synthetic CDOs. Cash CDOs, which are CDO notes backed by assets, such as bonds or loans, formed the greatest percentage of the CDO market. The payoff of a cash CDO comes from the actual cash flows of the assets in the pool.
Unlike a cash CDO, a synthetic CDO is linked to its reference entities by credit derivatives rather than backed by assets. The emergence of the synthetic CDO is largely due to the development of the credit default swap (CDS) market. Unlike a cash CDO, which gains exposure to credit risk of the underlying assets, a synthetic CDO gains exposure to credit risk by selling protection through CDSs. In other words, a cash CDO owns the physical bond, loan or security, while a synthetic CDO does not have to own the asset.
A common structure of CDOs involves tranching or slicing the credit risk of the reference pool into different risk levels. The risk of loss on the reference portfolio is divided into tranches of increasing seniority where the losses will first affect the equity (first loss) tranche, then the mezzanine tranches, and finally the senior and super senior tranches. The lower tranche boundary is called the attachment point, while the upper tranche boundary is called the detachment point. Based on their risk appetite, investors can take on exposure to a particular tranche by selling credit protection to the CDO issuer.
FINCAD's Single Tranche CDO Valuation
FINCAD's Synthetic CDO Single Tranche function(s) can be used to price CDO tranches for CDX (North America), Itraxx (Europe), or user-defined tranches.
The single tranche CDO valuation can be modelled by using the CDS on Standard or Synthetic CDO tranche(s) workbook. This workbook can be found by going to FINCAD XL → Workbooks (user data) → Credit Derivatives (CDS & Options) → CDS on Synthetic CDO Tranches. The workbook can be used to price anywhere from 1 to 5 tranches and with slight modifications to the workbook more than 5 tranches.
Below is a screenshot of where the workbook can be found in FINCAD XL.
There are two functions that can be used to price a single tranche CDO: aaCDO_ST_DS_std_p and the aaCDO_ST_DS_p. The former function should be used to price a synthetic CDO where a single notional, CDS spread, and recovery rate is used for each entity in the reference pool. The latter function allows for a varying notional, CDS spreads, and recovery rates for the entities in the reference pool. The workbook can be used to price a CDO tranche with flat parameters or varying parameters. The type of CDO to be priced can be set using the switch in cell C22 on the CDS on CDO Tranche(s) worksheet. Since the CDO tranche priced in this example uses a single notional, CDS spread, and recovery rate for each reference entity, the instrument was priced using aaCDO_ST_DS_p.
Below is a screenshot of the "CDO type" to "CDS spreads for all entities".
If the reference pool consisted of entities with varying notional, CDS spreads, and recovery rates, CDO type switch should be set to "synthetic" and the "Entity details for CDS on synthetic tranche" table on the Entity Details & Spread Curves worksheet should be populated for the reference entities. Even though the table is not used in this example, it has been set up for illustration purposes.
Below is a screenshot of the "Entity details for CDS on synthetic tranche" table from the Entity Details & Spread Curves worksheet.
For a comprehensive description of each input argument for the CDO functions please see the math document for CDO Tranches. This can be found by clicking on the "Math Reference" button on the CDS on CDO Tranche(s) worksheet. If you are unable to view the math reference contact a FINCAD Representative and download the latest trial version of FINCAD Analytics.
In this example, the "attachment/detachment levels" switch has been set to "user-input" and the tranche table is set up to price the one tranche. The attachment/detachment points and the base correlation for the tranche table can be found in the "calc info" portion of the Bloomberg Finance LP* screen and the coupon and the trade position in the tranche table correspond to the deal spread and buy/sell details found in the "deal information" portion of the Bloomberg Finance LP screen.
Listed below is a comparison of the CDO tranche valuation:
FINCAD |
Bloomberg Finance LP |
||
| Fair Value less accrued | 1,355,031.74 | Principal | 1,355,090.81 |
| Accrued Interest | -98.96 | Accrued | -98.96 |
| Fair Value | 1,355,130.70 | Market Value | 1,355,189.77 |
| Value of Payoff | 1,508,953.00 | Default PV | 1,509,792.59 |
Using CDS Spreads to Price Credit Instruments
One major enhancement worth noting in FINCAD XL v9 is the introduction of the ability to use CDS spreads to price a credit instrument. This is highlighted by the CDS spread curves on the "Entity Details & Spread Curves" worksheet. Prior to version 9, a default probability curve was required for each entity in the reference pool.
Below is a screenshot of the "CDS Spread Curves" table from the Entity Details & Spread Curves worksheet
Related CDO Functions
CDO valuation given tranche or base correlations
| aaCDO_ST_DS_std_p | Calculates the fair values and other statistics of a credit default swap on standardized CDO tranches using a one-factor Gaussian copula model. The correlation can be either a tranche or a base correlation. Multiple tranches can be valued simultaneously. |
| aaCDO_ST_DS_std_prem_cf | Calculates expected cash flows and their present values of a credit default swap on standardized CDO tranches using a one-factor Gaussian copula model. The correlation can be either a tranche or a base correlation. |
| aaCDO_ST_DS_p | Calculates the fair values and other statistics of a credit default swap on synthetic CDO tranches using a one-factor Gaussian copula model. The correlation can be either a tranche or a base correlation. Multiple tranches can be valued simultaneously. |
| aaCDO_ST_DS_prem_cf | Calculates expected cash flows and their present values of a credit default swap on synthetic CDO tranches using the one-factor Gaussian copula model. The correlation can be either a tranche or a base correlation. |
CDO valuation given factor loadings
| aaCDO_ST_DS_fl_p | Calculates the fair values and other statistics of a credit default swap on synthetic CDO tranches using a one-factor copula model. Different reference entities can have different factor loadings. Multiple tranches can be valued simultaneously. |
| aaCDO_ST_DS_fl_prem_cf | Calculates the fair values and other statistics of a credit default swap on synthetic CDO tranches using a one-factor copula model. Different reference entities can have different factor loadings. Multiple tranches can be valued simultaneously. |
| aaCDO_ST_DS_dgen_fl_p | Calculate the fair values and other statistics of a credit default swap on synthetic CDO tranches using a one-factor Gaussian copula model. Different reference entities can have different factor loadings and the premium leg can have variable notionals and coupons. Multiple tranches can be valued simultaneously. |
| aaCDO_ST_DS_dgen_fl_prem_cf | Calculates expected premium cash flows and their present values of synthetic CDO tranches using a one-factor Gaussian copula model. Different reference entities can have different factor loadings and the premium leg can have variable notionals and coupons. |
Calculation of sensitivities with respect to individual entities
| aaCDO_ST_DS_risk | Calculates for each entity the credit spread and other sensitivities of credit default swaps on synthetic CDO tranches. A one-factor Gaussian copula model with either a tranche or a base correlation is used in CDO modeling. |
| aaCDO_ST_DS_fl_risk | Calculates for each name the credit spread and other sensitivities of credit default swaps on synthetic CDO tranches. A one-factor Gaussian copula model with variable factor loadings is used in CDO modeling. |
| aaCDO_ST_DS_dgen_fl_risk | Calculates for each name the credit spread and other sensitivities of credit default swaps on synthetic CDO tranches that have variable notionals and coupons. A one-factor Gaussian copula model with variable factor loadings is used in CDO modeling. |
Calibration of base correlations
| aaCDO_ST_DS_base_ic | Given par spreads of a credit default swap of synthetic CDO tranches calculates the base correlations of the tranches. |
| aaCDO_ST_DS_std_base_ic | Given par spreads of a credit default swap of standardized CDO tranches calculates the base correlations of the tranches. |
Calculation of loss distributions
| aaCredit_loss_prob_cum | Calculates the cumulative loss distribution of a basket of defaultable entities using a one-factor Gaussian copula model. |
| aaCredit_loss_prob_cum | Calculates the loss distribution at discrete loss points of a basket of defaultable entities using a one-factor Gaussian copula model. |
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.