# Revolving loan

## Term structure

The second loan type, called a revolving loan, is used for higher levels of leverage (~40-1000x or more on high market cap assets). It is more expensive for borrowers as it offers them more optionality.

The revolving loan matures according to the same schedule as the fixed term loan. However, unlike fixed term loans, a revolving loan can be closed out anytime, in which case it effectively matures immediately. By closing out the loan, the borrower returns the liquidity range to the pool (so that the liquidity ranges are available again to lend or provide liquidity), and no longer owes further interest payments.

Revolving loan’s interest is not paid upfront, instead borrowers can post collateral incrementally to cover future interest payments. In the case the borrower closes out their loan, they will get back any unspent collateral. For example, if a borrower posts enough collateral for a 1 hour loan, but closes out their position after 30 minutes, they will get back ~50% of their collateral. This is what makes it possible to achieve higher ratios of amount borrowed to capital provided (ie. higher leverage ratios).

In other words, the high levels of leverage generated by revolving loans come from the multiplication of two factors. The first factor comes from using the typical leverage mechanism used for fixed term loans (~1-40x leverage). The second factor comes from the ability to pay interest incrementally.

Using the exponential maturity function we can determine what fraction of the interest is due over a given time period. For example, the interest due for 15 minutes of the loan is 1/139 of the total due. If you then multiply the maximum leverage available normally (40x) by the amount of interest you need to provide for 15m of that loan instead of the full duration (139), you get access to extremely high leverage (5560x).

Borrowers can pay the interest by depositing one of the two pool tokens (or a mix of both) and choosing a deadline from under 12 minutes to over 1 day. Beyond a 1 day deadline most of the total interest is already required (as the loan has a half-life of one day). Borrowers can either extend the deadline for their loan by depositing additional tokens, or the loan will be closed out automatically after the deadline is passed.

## Interest rate

Supposing again that the pool price follows a geometric Brownian motion with no drift, then the fair value interest rate on a revolving loan on a per day basis (times 100 in percentage terms) can be computed as:

$\frac{\lambda}{(q+\frac{1}{2})m^{q-\frac{1}{2}}-(q-\frac{1}{2})m^{-q-\frac{1}{2}}-1}$ where q, m are defined as previously.

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