Pricnig 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.

The asset substitution option is implemented. If an asset matures before both the trade maturity and the substitution termination date, it is substituted by an appropriate asset.

The model is implemented upon the Oscar/Fritz credit library platform, which is more computational efficient.

The sensitivity computation via Weighted Monte Carlo (WMC) approximation is replaced by a direct full Monte Carlo simulation of the perturbed scenarios. The new method is in line with the outstanding one for vanilla CDO trades.

To our best knowledge to date, there is no generally accepted methodology of modelling the asset substitution option. The choice of substitution asset has to follow the contractual portfolio management guideline, which is contingent upon the outcome of various portfolio statistics performed at the maturity of the substituted asset. From a mathematical modelling viewpoint, the value of this option cannot be fully determined unless a dynamic process of the portfolio is modelled. Furthermore, it is almost impossible to get the pertinent market information to calibrate such a process.

Instead of attempting to solve this complicated modelling problem, a simple and flexible approach is adopted in the submitted model. Although it is unpredictable how the portfolio will evolve over time and what the substitution asset would be, it is expected that the substitution asset should have certain probability of default before the trade maturity. In a MC scenario in which the substituted asset survives beyond its maturity, a default time of the substitution asset is then simulated by assuming that it is forward starting at the time of substitution. The uncertainty in modelling the asset substitution is cushioned by an appropriate model risk reserve

An upgraded version of variable maturity synthetic CDO (VMS-CDO) trade valuation is presented. A VMS-CDO trade has a non-vanilla structure, in which the maturities of the underlying obligors could be different from that of the CDO trade.

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