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Estimating SPV Credit Risk for Swap CVA

Article Quant Q&A · Author: ash
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Summary

The document outlines a practitioner approach to estimating credit value adjustment for an uncollateralized swap with a special purpose vehicle. When the SPV’s only asset is a corporate loan, the answer suggests using the borrower’s credit default swap market information to estimate default probability and loss given default. It assumes the SPV defaults if and only if that loan defaults, linking the loan’s credit risk to the SPV’s.

The exposure loss then depends on the swap’s seniority relative to the SPV’s bank borrowing. A senior claim may incur loss only when the loan’s value falls below swap exposure; a junior claim may be modeled with no recovery, while pari passu treatment falls between those cases. This is a simplified structural view, not a complete CVA procedure. It assumes the SPV has a single asset and that its default is fully tied to the borrower’s; it does not detail calibration, discounting, or exposure modeling beyond the stated EPE context.

Key ideas

  • For an SPV whose only asset is a corporate loan, the borrower’s CDS market can inform estimates of default probability and loss given default.
  • The suggested approach assumes the SPV defaults exactly when its loan borrower defaults.
  • Swap seniority relative to the SPV’s borrowing determines how much recovery may be available.
  • The treatment is a simplified practitioner framework and does not fully specify CVA calibration or calculation.

Tags

Fixed incomeDerivatives pricing
Full text
# How to compute the CVA on a swap with SPV?


# How to compute the CVA on a swap with SPV?












If we have a swap with a bank and Special Purpose Vehicle (SPV), and the swap is un-collateralized , how do we estimate Credit Value Adjustment on the swap?

I will be able to get the Expected Positive Exposure (EPE) profile but I need to know the Loss Given Default (LGD) and probability of default (essentially a credit curve).

Therefore my question is, what are some real world ways to estimate a credible credit curve for an SPV ?

I am only looking at it from a practitioners perspective.

This SPV borrows EUR from a bank , does cross currency swap with swap counter party and lends USD to a corporate client. The banks and swap counterparty is A rate and corporate client is BBB+ rate.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/33903

The assets of the SPV constitute a single corporate loan. Therefore the probability of default and LGD of the bond can be estimated from the CDS market for that corporate. Now the SPV defaults if and only if the bond defaults, so you have the probability of the SPV defaulting. Next you need to compute your exposure in a default situation. What matters is whether you are senior to, pari passu, or junior to the EUR loan taken by the SPV. If you are senior , you would only lose money if bond value< swap exposure, which is a very low probability since most recovery assumptions are in the 40pct area and you are ok unless the currency has moved by 40pct. If you are junior, you can assume zero recovery on the swap. The pari passu case is in between. Hope that helps.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.