- Implied Base Correlation Mapping
The Mapping model serves the purpose of finding implied base correlations for a bespoke CDO trade from market quoted standard CDO indices Dow Jones CDX and iTraxx Europe. In this report, a CDO tranche is defined as bespoke if its reference portfolio composition is different from that of CDO indices.
2. Implied Correlation
The implied correlations for the CDO index tranches are the correlations backed out by the market quoted prices using CDO valuation models available in the credit library, namely, the Poisson model and the Normal Copula model.
3. Monte Carlo Acceleration
A new procedure is presented to accelerate the convergence of Monte Carlo simulations using the Default Correlation model. It is found that the modifications have been implemented correctly, and that the modifications result in a substantial improvement in the convergence rate of the Monte Carlo simulation models.
4. Credit Model Calibration
A calibration procedures of the Default Correlation model is presented. There are two principal modifications. The first is to change the manner in which asset correlations are converted into default correlations, the second is a small change in the algorithm by which the probability equations of the model are solved. These changes are considered appropriate, and are necessary for the model to be considered robust enough to underpin the structuring and trading of complex credit contingent instruments.
5. Credit Derivative Pricing
We propose default correlation model and four credit default derivative pricing models, namely, single name credit default swaps with counterparty risk, First-to-Default basket default swaps, FirstNofN basket default swaps, and FirstLoss trades.
6. Correlation MTM Process
The model for valuation of CDOs is well documented. An essential input into the model is the correlation between the obligors in the collateral pool. Historically, this correlation has been derived using a KMV based approach.
7. Forward Starting CDO Implementation
The forward starting CDO (FSCDO) valuation model serves the purpose of pricing FSCDO trades, which are defined as a forward agreement to enter into a CDO trade at some time in the future. Any obligor defaults before the forward starting date will be replaced by a risk free asset with the same notional amount.
8. Forward Starting CDO
The forward starting CDO (FSCDO) valuation model serves the purpose of pricing a forward starting CDO (FSCDO) tranche. An FSCDO trade is defined as an agreement to enter into a CDO trade at some time in the future. Unlike a usual forward starting instrument in the interest rate world, the obligors in the collateral pool of the FSCDO may default before the forward starting date, which makes the pricing of such trades complicated. Furthermore, the FSCDO involves the forward start date and the trade maturity; hence a pertinent valuation model
9. Deferred CDO Coupon Payment
The deferred CDO coupon payment valuation modelserves the purpose of valuing the accumulated coupon payments held in a non-interest-bearing reserve account for a CDO trade. It is a part of the valuation model for a non-vanilla CDO structure called “rated equity.”
10. Default Sensitivity
The default sensitivity test in Scenario Manager is implemented by setting the default time of the perturbed obligor to be the valuation date when the present value of each tranche is calculated, no matter when that obligor defaults in the generated Monte Carlo scenarios. Compared with other models, the implementation of Scenario Manager model is simple, direct, and efficient. However, the joint default events generated in the MC scenarios remain unchanged, which is an approximation of the realistic situation.
11 Credit Default Swap Index Curve
The methodology of credit default swap index (CDSI) curve adjustment serves the purpose of making adjustment to the credit spread curve of each reference name in the index portfolio such that the market price of the index can be reproduced using these constituent curves. The adjusted index constituent curves are then used to price the standard collateral debt obligation (CDO) tranches based on the index portfolio.
12. Credit Default Swap Option
The European credit default swap option (CDSO) valuation model is employed to price an option that grants its holder the right, but not the obligation, to enter into a Credit Default Swap (CDS) at some future point in time. The premium to be paid on this forward-start CDS is fixed in advance at some strike level. If the reference entity should default before the forward-start date, the contract is in null and no payments are made.
13. Hazard Rate Curve
The hazard rate curve defines the default probability of an obligor, serving as one of the fundamental components of all credit derivatives models. Within the current GSP credit derivatives modelling framework, the hazard rate curve is calibrated using the market information of the credit default swap (CDS).
14. Risk Equivalent CDO
Mapping CDO2 and CDO3 trades to risk equivalent CDO (RE-CDO) trades can be done by matching the b/e spread a RE-CDO is calculated and taken as the proxy of a target CDO2 or CDO3 trade. Then the MTM of the CDO2 or CDO3 trade can be calculated using the market observed correlations by finding the MTM of the proxy via index base correlations.
15. Credit Contingent Interest Rate Swap
A credit contingent interest rate swap is an option that grants its holder the right, but not the obligation, to enter into an interest rate swap (IRS) at the time when its reference obligor defaults. The premium to be paid on the underlying IRS is fixed in advance at some strike level. The notional amount of the swap is a function of a predetermined fixed amount and the recovery rate of the reference obligor. The model can also be employed to back out an implied correlation between the interest rate and the default arrival of an obligor.
16. Base Correlation Test
In general, there is still no market consensus on how to apply the market implied correlation information to bespoke tranches, in which the composition of the collateral pool is different from those indexes. Since the model was approved, there are several new developments in both modeling and market practice. There are three major changes to the GSP model:
17. Base Correlation Approach
To our best knowledge to date, there is no generally accepted methodology of applying base correlation to a non-index CDO trade. The proposed approach serves the purpose of finding an appropriate correlation to value a collateral debt obligation (CDO) tranche from market information via base correlations. The methodology involves four steps.
18. Base Correlation
The model serves the purpose of finding an appropriate correlation to value a collateral debt obligation (CDO) tranche from market information via base correlations.