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Parameters optimizing

Index

Overview

Some of crvUSD parameter research

dynamic_fee from 0.3% to 0.1%
N(band amount) N=4 vs N=5
A 100, 200, or 500
PNL of protocol —
loan_discount r=5%? 9%?

LLAMMA has two major pros:

  • better LTV ratio than MakerDao & Liquity (if users set N=4 to get the highest LTV=89.2%)
  • reversible liquidation means if the price comes back, the user's assets mostly come back mostly

cons:

  • intrinsically lossy or path-dependent
  • oracles' quality depending on the speed of value decay of users' collateral

LLAMMA uses an oracle to sell when the price is down and to buy when the price is up, which means that arbitrageurs' profits directly come from depositors' losses. Setting a higher dynamic_fee does protect users' positions from frequent arbitrage. However, a higher dynamic_fee means arbitrageurs are waiting for bigger price spreads between AMM and oracles to arbitrage, making users suffer more losses.

Setting dynamic _fee smaller

Let's take an example considering 0 gas and 0 profit for arbitrageurs. Set the dynamic _fee from 0.3% to 0.1% and see what would happen.

ETH price = 2000, N = 4, loan_discount = r = 9%. A=100.

Bob deposited 1 ETH at 2000 and got as many crvUSD as possible.

$$ Max\ LTV ratio = \frac{(1 - r)}{N} \cdot \sqrt{(A-1)A} \cdot (1-(\frac{A-1}{A})^N) $$

The number of crvUSD he got will be

2000*(1-9%)/4*((100-1)100)^0.5(1-(100-1)^4/100^4)=89.195%.

He would get 1783.9 crvUSD. If the price goes below 1783.9, the liquidation begins.

price_up price_down
band11 1820 1801.8
band12 1801.8 1783.782
band13 1783.782 1765.94418
band14 1765.94418 1748.28474

Bob's 1 ETH will be distributed to 4 bands, each with his 0.25 ETH. When the price comes down by 0.3% and is 1814.54 in band11.

$$ y_0 = \dfrac{(\dfrac{p\uparrow}{p_o}(A-1)x + \dfrac{p_o^2}{p\uparrow}Ay)+\sqrt{(\dfrac{p\uparrow}{p_o}(A-1)x + \dfrac{p_o^2}{p\uparrow}Ay)^2+4p_oA·xy}}{2p_oA} $$

  • dynamic_fee = 0.3%. After arbitraging 1 time, arbitrageurs' exchange avg price is 1802.13 profit rate = 0.6839%
  • dynamic_fee = 0.1%. After arbitraging 3 times, each time when the price falls by 0.1%, arbitrageurs' exchange avg price is 1802.13 profit rate = 0.2166%

Obviously, there are more losses if we set dynamic_fee to 0.3%. What will happen if we set dynamic_fee to 0.1% and even lower or 0?

Setting N=4 and N=5

Users get different Max LTV ratios and health and loss limits.

Setting parameters A to 100,200 or 500?

We found an exciting thing. If you set bigger A, arbitrageurs will get bigger $y_0$ which means arbitrageurs will get fewer assets and fewer losses for users. Of course, a bigger A will lead to many other problems like higher gas and less arbitrage. However, sometimes bigger A will lead p_out to jump out of active_band easier and cause more significant losses for users or profit for arbitrageurs.

What will Max-LTV-crvUSD borrowers experience?

From 2022-01-01 to 2023-04-20, Bob chose an arbitrary time to deposit his ETH, got max crvUSD, and held crvUSD for 30 days to get a payoff.

  • Maybe the ETH price went up; thus, after returning crvUSD, he will get a positive return because ETH jump。
  • Maybe ETH price dump after getting crvUSD, so his ETH cannot be returned, so he holds his crvUSD just like he had sold his ETH at a debt/collateral ratio.
  • Maybe ETH price dump and pump so liquidations or arbitrages happen frequently, or the price jumped too sharp, so your collateral ETH will be indeed discount liquidated with a 6% bonus for discount liquidators.

If every 15 minutes from 2022-01-01 to 2023-04-20, a user like Bob is using Max-LTV-crvUSD to sell his ETH. The probability distribution of his return is following.

figure

  • Chart 1 -last_pnl: crvUSD protocol's PNL. Assuming there is no discount liquidation—every user's PNL & probability of ETH put into the protocol. In most cases, positions stay at around 89%, and a minority of positions remain below 89%, which means Max-LTV-crvUSD borrowers will not likely cause damage to protocol because positions below 89% means protocol will start discount liquidation.
  • Chart 2-bench_pnl: In contrast to traditional collateral stablecoin protocols, Each user's collateral PNL.
  • Chart3-hold_loss_percent: Considering gas and profit, if the spreads between AMM price and oracle price is above 0.5%, the arbitrage happened—arbitrageurs' profit probability distribution of his returns.

Setting loan_discount to 5% or 9%?

figure

Mid price: 5 Min Candlestick Charts from Binance (high price + low price)/2

EMA price： EMA of Mid-price

Price movements between 30 days follow a normal distribution.

set loan_discount= r=5%. 60% dump will not exceed 6% and trigger arbitraging.

set loan_discount=r=9%. 90% dump will not exceed 9% and trigger arbitraging.