Collateral, Repo, and Unsecured Funding Rates in Derivatives Pricing

Summary

The document asks how collateral remuneration, repo, and unsecured bank funding rates relate in post-crisis derivatives pricing, referring to a paper by Vladimir Piterbarg. It defines the collateral rate as the rate paid on posted collateral, the repo rate as secured borrowing against the underlying asset, and the funding rate as unsecured bank borrowing. The quoted relationship in the paper is that the collateral rate is expected to be no greater than the repo rate, which in turn is no greater than unsecured funding.

The author accepts the intuition that secured repo funding should generally be cheaper than unsecured borrowing, but questions why the collateral rate would be lower than repo and why it would differ from a bank’s other funding costs. They note that Fed Funds has been treated as unsecured overnight interbank lending and ask how the risk distinctions apply. The document contains no reply or resolution, so it identifies conceptual questions rather than supplying a pricing derivation. It does not establish that the ordering holds in every market or circumstance.

Key ideas

• The document distinguishes collateral remuneration, secured repo borrowing, and unsecured bank funding rates.
• It presents an expected ordering in which the collateral rate is below repo and repo is below unsecured funding.
• The author questions how an unsecured interbank collateral rate can be below secured repo funding.
• The text also asks why collateral remuneration and a bank’s unsecured funding costs can differ.
• No explanation or general proof of the rate ordering is provided.

Tags

# Collateral rate vs. funding rate vs. repo rate in derivatives pricing post-GFC


# Collateral rate vs. funding rate vs. repo rate in derivatives pricing post-GFC












I am reading Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing by V. Piterbarg.

Now I have a question about the relation of the different funding rates in the paper.

- $r_C$ is the short rate paid on collateral, e.g. Fed Funds (before the move to SOFR)

- $r_R$ is the short rate for a repo transaction with the underlying asset, e.g. a stock as collateral

- $r_F$ is the short rate for unsecured bank funding

In the paper, Piterbarg states that one expects that $r_C \leq r_R \leq r_F$ and that the existence of non-zero spreads between short rates based on different collateral can be recast in the language of credit risk.

It is clear that $r_R \leq r_F$ should hold since a repo corresponds to secured funding whereas $r_F$ is unsecured funding. However, there are two things I don't understand:

1.) Why should the collateral rate, which also corresponds to unsecured funding (one bank gives cash to another bank and gets it back the next day + interest) be lower than the repo rate, which corresponds to secured funding? For example, the Fed Funds rate is the interest rate banks charge each other for unsecured overnight funding.

2.) Why would the collateral rate and the funding rate be different ($r_C \leq r_F$)? Both should reflect the credit risk of the counterparty? I know that bank funding comes from various sources like deposits, issued bonds, etc. and that there is a spread for credit risk, but why would a counterparty not charge for this the same way for cash given to the bank via a collateral agreement.

I hope my question is clear.

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