Credit Derivative Valuation

  1. Weighted Monte Carlo Simulation

A regular Monte Carlo (MC) simulation algorithm assigns each simulation scenario, or path, an identical probability weight. A weighted Monte Carlo (WMC), however,  allows a different probability to be assigned to each simulation path.  For example, we can choose the probabilities of each path in a manner such that the simulation is guaranteed to reproduce the prices of “benchmark” securities, whose prices are known from market data.  A simulation thus calibrated to benchmarks will then price off-market securities in a realistic manner.

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Github mc

Github simulation

2. Model Reserves

Parameters risks are encompassed under correlation and recovery ratios reserves.  Correlation reserves are computed at 0.15 for first to default baskets and 0.20 for other transactions that are not subject to EITF 02-03.  Recovery ratios are randomly simulated for each obligor with a beta distribution and reserves are set to a 25-percentile loss on a portfolio.

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Github model

Core model

3. Credit Delta VaR

Discuss credit delta (PV01) and credit VaR measurements.

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Github credit

Archive dgv

4. Repo Curve

A repo curve calibration methodology is presented to bring it more consistent with market quotation. Instead of a fixed term structure for an issuer, the repo curve in essence becomes a “repo factor collection” in which a constant repo factor is stored with respect to each outstanding bond of the issuer. 

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Github repo

Github curve

5. Index Tranches and Bespoke CDOs

The purpose of the model is to calculate the credit spread sensitivity, correlation sensitivity, and default sensitivity via analytic methods for index CDO trades and bespoke CDO trades.

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Github tranche

Github mapping

6. FNM and CDO2&3 Trades

The purpose of the submitted model is to calculate the risk measures for FirstNofM trade (FNM) trades and CDO2&3 trades. They are bucketed credit spread sensitivities for FNM trades; bucketed credit spread sensitivities for CDO2&3 trades; default sensitivities and correlation sensitivities for CDO2&3 trades.

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Github fnm

7. CDS Basis Adjustment

The model serves the purpose of computing basis adjustments for credit spread curves of the constituent obligors of the indexes such that the market price of the index can be repriced exactly. These adjusted index constituent curves are then used to compute index base correlations and mapped base correlations for bespoke trades, price the standard index CDO tranches, and calculate risks for constituent obligors. 

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Github base

Github cds

8. Weighted Monte Carlo Sensitivity

The model is a non-parametric approach to value complex CDO structures that need to be priced using the market information on tranche losses at multiple points of time. Currently, the model is being used for the valuation of forward starting CDO trades (FSCDO) and loss-trigger leverage super senior tranches (LT-LSS).

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Github sensitivity

Gitbook mc

9. Variable Maturity Giant First Loss

A variable maturity GiantFirstLoss trade has a non-vanilla collateral debt obligation (CDO) structure, in which the maturities of the obligors in the underlying collateral pool can be different from the trade maturity.

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Zenodo variable maturity loss pdf

Github loss

10. Variable Maturity CDO

The model serves the purpose of pricing a non-vanilla synthetic CDO trade, where the maturities of the underlying synthetic assets in the collateral pool can be different from the trade maturity.

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Github cdo

Github impl

11. Basket Default Swap

A pricing model is presented to calculate Mark-to-Market (MTM) and all sensitivities for basket default swaps and Collateral Debt Obligations (CDOs) (FirstNofM, GiantFirstLoss, GiantFirstLossPayEnd, Caribou, and Reindeer). It is composed of the credit library, BulkCurveGenerator, five outstanding pricing templates, and Scenario Manager.

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Github basket

Github default

12. Giant First Loss

Compared to the standard first loss model with the same collateral pool and tranche structure, the new model predicts smaller B/E spreads for each tranche. Further, it is more sensible to the interest rate and the sensitivity to the interest rate term structure changes dramatically. The B/E spreads for each tranche calculated by both models converge when the hazard rates of the obligors become very small.

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Github first loss

Github expect

13. Credit Derivative

The credit derivative model serves the purpose of pricing and calculating sensitivities for the credit derivative products which are Credit Default Swaps (CDSs), First-to-Default swaps (FTDs), FirstNofM basket default swaps (FNMs), all level Collateral Debt Obligations (CDOs, CDO2s, and CDO3s), and forward starting CDOs.

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Github credit derivatives

Core credit

14. Normal Copula

As a well known default correlation model, the normal copula provides an alternative method to the Poisson model in generating correlated default events of a collateral pool. It is implemented using the Monte Carlo (MC) simulation.  The testing was conducted by implementing an independent test model using the MC simulation. The results of two sample trades, generated by the test model and the model, respectively, were compared. The MC implementation was also verified by the closed form solutions and the Poisson model.

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Github copula

15. MezzMezzMezz Trade

The MezzMezzMezz trade model is a synthetic Collateral Debt Obligation (CDO) structure in which the collateral pool is composed of tranches issued under MezzOfMezz or Caribou structures. Each participating MezzOfMezz tranche is a CDO mezz tranche defined by a threshold and a principal. Several such MezzOfMezz tranches are aggregated and tranched into MezzMezzMezz tranches. Within the existing modelling framework the model is implemented by adding a layer of CDO structure to the MezzOfMezz model.

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Github mezz

Github forward

16. Loss Trigger Leveraged Super Senior Tranche

The loss trigger leveraged super senior tranche (LT-LSS) valuation model is presented. A leveraged super senior tranche trade is a credit linked note, which provides investors with a leveraged exposure to the super senior tranche in a synthetic CDO transaction. The note holder earns the risk premium associated with selling protection on the entire senior exposure when the protection it provides is limited to only the funded principal amount which is just a fraction of the entire exposure.

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Github trigger

Zenodo trigger