Pricing Open Repos: Overnight Renewal, Break Rights, and Optionality

# Pricing an open repurchase agreement


# Pricing an open repurchase agreement












I am wondering, how do you price a open-ended repo (when a maturity date is not set)?

I have done some research and have found no formula's or even an explanation of how to value such a repo. In fact, I have not found a pricing model for a term repo either.

I am considering the security as the object being lent or borrowed and the loan amount (money) as the collateral.

Edit:

By an open repo, I meant the one described by wikipedia:

> Open has no end date which has been fixed at conclusion. Depending on the contract, the maturity is either set until the next business day and the repo matures unless one party renews it for a variable number of business days. Alternatively it has no maturity date - but one or both parties have the option to terminate the transaction within a pre-agreed time frame.

## Answer by Lliane (score 1, accepted)

https://quant.stackexchange.com/a/35594

This is a bit too general, it really depends of the optionality of the contract : who can break the contract and when ?

The repo for a given maturity is just a market parameter, like spot, or interest rate, you don't price spot or interest rate, you take it for granted.

Thus, if the repo is open in the sense of one day tacit reconduction there is not much to price, it's just the 1-day repo rate. If it changes then you re-rate your repo and that's all.

For more complex structures such as evergreen (unilateral break with a notice period), pricing should be used in theory (using implied vol of the repo) but actually I have never seen these structures priced in a quantitative way. In the bulge bracket bank I used to work, this parameter didn't even exist (repo vol). Without sounding demeaning this area of finance is more about relationships, legal considerations and regulatory optimization than accurate pricing of repo volatility and structures to the third digit.

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/35532

There's no such thing as an undated repo. For example , what would happen if the underlying security matures?

Term repos of Treasuries of one week to one year are reasonably common. The pricing models incorporate some generic factors such as the shape of the Fed Funds curve, plus some security specific factors such as the likelihood of the underlying security going "special" during the repo (if a security becomes hard to borrow for some reason, the repo rate goes down).

To respond to your edit : If a repo is cancellable by either party on a given date, then it will theoretically terminate on that date (it must be advantageous for a party to do that , unless it is worth exactly zero). In this case the pricing is the same as a repo ending on that date.

If a repo is extendible or cancellable by one party only , we have a more complex situation. If the repo is a fixed rate repo, the party with the cancellation right owns an interest rate option so those types of models must be employed. If the repo is a floating rate repo, it depends how the floating rate is determined. Generally the option value will be less in this case.