# 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.

• In the body of the question, please try to use as little acronyms as possible. It makes the question clearer for general readers.
– SRKX
Apr 26, 2017 at 1:21
• Can you clarify what is in the SPV? What type of assets?
– dm63
Apr 26, 2017 at 10:37
• @dm63 added the assets and liabilities on SPV
– ash
Apr 26, 2017 at 11:19

## 1 Answer

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.

• is there consideration to consolidated nature of SPV on a bank balance sheet, esp where swap plus consolidating bank are one and same. @dm63
– rrg
May 24, 2018 at 10:39