Fixed term loan

Term structure

The first loan type, called a fixed term loan, is used for lower levels of leverage (~1-40x on high market cap assets). The full interest needs to be paid upfront by the borrower, is non refundable and as such, is cheaper for borrowers.

The protocol will disburse the interest paid to the liquidity range lenders according to the maturity schedule. While the loan has a predetermined duration, borrowers can take profit on their trade at any point by swapping the borrowed assets back to their original token (eg. swapping ETH back to USDC in the original example).

Interest rate

Supposing that the pool price follows a geometric Brownian motion with no drift (ie. which is a martingale), then the fair value interest rate on a fixed term loan can be computed as:

$\frac{\lambda}{2qm^{q-\frac{1}{2}}-1}$ where $q = \sqrt{\frac{1}{4} + \frac{2\lambda}{v}}$

per day (times 100 in percentage terms).

• m is the ‘absolute’ moneyness (the distance between the pool price and the strike price), which is the maximum of $\frac{k}{p}$and $\frac{p}{k}$where p is the pool price and k is the strike price

• ν is the daily variance of the price, ie. quadratic variation of the logarithm of price over one day

• λ=ln(2) as previously defined