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Cheapest-to-Deliver Collateral Curves and Reference Papers

Article Quant Q&A · Author: vsa
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Summary

The document asks how cheapest-to-deliver collateral methodology handles agreements that permit collateral in multiple currencies. Its motivating concern is that choosing the most favorable collateral rate could cause discontinuities when the preferred rate switches, and it asks about smoothing those changes with an attenuation parameter. The question seeks an explanation of how that parameter is obtained and calibrated, but the response does not provide one.

Instead, the reply points to two articles by Vladimir Piterbarg on collateral, a collected volume on XVA, and a more recent paper on fast calculation of cheapest-to-deliver curves. These references offer places to pursue the methodology, but the document gives no derivation, calibration procedure, market example, or evidence comparing approaches. It is therefore most useful as a short reading guide for researchers studying collateral valuation and XVA, rather than as a standalone explanation of how to construct or calibrate a cheapest-to-deliver curve.

Key ideas

  • Cheapest-to-deliver collateral valuation considers the most favorable eligible collateral rate.
  • Switches between preferred rates may create discontinuities in valuation.
  • The question asks how an attenuation parameter is calibrated, but the response does not explain the process.
  • The answer identifies publications on collateral and cheapest-to-deliver curves for further reading.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Cheapest-to-Deliver (CTD) collateral methodology


# Cheapest-to-Deliver (CTD) collateral methodology












Do you know where can I find details about this methodology? Theoretically, in cases where the CSA allows collateral to be posted in different currencies, the counterparty will always choose the highest rate (cheapest bond).

However, as far as I understand, this can lead to discontinuities in the valuation when one rate is replaced by another and the general approach consists of using an attenuation parameter $\lambda$ between the rates.

Apparently, there is a famous paper from Piterbarg named 'Cooking with Collateral' providing details about all this, but I haven't been able to find it anywhere. Is there any way I can find this paper or a similar one explaining this attenuation concept? A short explanation of the methodology would be highly appreciated as well, how is this $\lambda$ obtained and calibrated?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/81920

I think you are looking for these 2 Piterbarg papers in Risk Magazine:

Vladimir V. Piterbarg. Cooking with collateral. Risk, August 2012.

Vladimir V. Piterbarg. Stuck with collateral. Risk, October 2013.

If you can't find it online, it's in this collection Landmarks in XVA: From Counterparty Risk to Funding Costs and Capital

The paper recently posted by Kemarsky, Van der Helm, Piterbarg at NatWest: Fast Calculation of Cheapest-to-Deliver Curves may suffice.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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