# Summary

We are proposing the implementation of a price impact mechanism on Jupiter to enhance market stability and protect liquidity providers. This mechanism introduces dynamic fees that adjust based on the imbalance of open positions within short time intervals (e.g., one minute). The primary goals of this proposal are to:

**Promote Fair Trading Practices**: Discourage the rapid accumulation of large, one-sided positions that can disrupt market equilibrium.**Enhance Market Stability**: Mitigate risks associated with sharp price movements by compensating for the added exposure faced by liquidity providers during periods of significant market imbalance.**Minimize Impact on Regular Trading**: Ensure that typical trading activities remain largely unaffected, with additional fees applied primarily during periods of extreme market imbalance.

By calibrating specific parameters for each assetâ€”such as the base fee rate, delta imbalance thresholds, and maximum feesâ€”we aim to implement a system that is both effective in risk mitigation and fair to all traders. This approach seeks to strengthen the resilience of Jupiterâ€™s markets without imposing undue burdens on legitimate trading activities.

# Price Impact as a Function of Delta Imbalance in a Time Window

We propose introducing a price impact fee based on the delta imbalance created in each market within a specific time window, such as a 1-minute interval. This approach addresses several key issues:

**Informed Trading:**Traders with strong signals on price movements (e.g., the trader in the SOL market) will not benefit from splitting positions across different trades or addresses, as positions must be opened quickly before their alpha decays.**Sharp Price Movements:**During sharp price movements, traders taking numerous one-sided positions will incur higher costs for opening their positions. This compensates for the undesirable delta imposed on the JLP.**High Volume Periods:**During periods of high trading volume in both directions, the imbalance difference will be minimal due to offsetting buy and sell trades. Thus, a high price impact fee will not be imposed, and overall volume and utilization should remain unaffected.

**Suggested Mechanism:**

For each market, we calculate the open interest imbalance (the sum of long open interest minus the sum of short open interest) after the current trade and subtract the open interest imbalance from one minute earlier (approximated by block numbers). This gives us the delta imbalance.

We then define the price impact fee as a function of the delta imbalance:

\text{price impact fee}=\text{base fee}+\text{factor}\times{\text{abs(delta imbalance)}^{exp}}

Where `factor`

and `exp`

are parameters that must be calibrated.

This method presents a trade-off between mitigating potential manipulation, which could lead to losses for liquidity providers (LPs), and imposing unnecessarily high fees on legitimate traders. We will optimize the methodâ€™s parameters to strike a balance between these two concerns.

Price impact will apply to both open and close trades but will not trigger or apply to liquidations. Forcing liquidations due to large price impact fees (e.g., a 1% maximum price impact) is undesirable and leads to poor user experience.

Additionally, traders could exploit the system by opening interleaved positions below the delta imbalance threshold, using a hedge on the opposite side, and gradually reaching their desired position. They could then close the unnecessary side just before executing a manipulation, effectively bypassing the price impact. To address this, we must also apply price impact on position closures to prevent such tactics.

For a factor of 5e-10 and an exp of 2, the fee will be 10 bps for a 2M$ delta imbalance and 20 bps for a $4M delta imbalance. If the max price impact is set to 0.5%, i.e., trades as of $10M and above delta imbalance, will pay a price impact of 0.5% and not more.

## Impact on Innocent Traders

To examine instances where high fees are incurred in percentage terms and test their correlation with price changes, we analyzed the median fee percentage over 1-minute windows for the SOL market. We observed a low correlation between the median fee percentage and price change, with a correlation of 1.6% for the 1-minute period. Below, we present the median fee percentage versus price over a 1-minute window, highlighting the impact of the suggested price impact fee method.

## Parameter Specification

The suggested method requires specifying five parameters for each asset:

**Base Rate**: A fixed fee expressed as a percentage of the trade size.**Exp**: The exponent to which the absolute value of delta imbalance is raised.**Factor**: A multiplier applied to abs(delta imbalance)exp.**Delta Imbalance Threshold**: A threshold for the absolute value of delta imbalance. When exceeded, additional price impact fees are applied. This prevents high fees during periods of low delta imbalance, which is not the methodâ€™s target.**Max Fee**: The maximum total fee, expressed as a percentage of the trade size, to prevent excessively high fees.

The following simulations used live trade data from Jupiter from 10 August to 9 September 2024.

### SOL

**Benchmark**:

- All Users: Paid $8,520,454 in open/close fees and price impact.

Below, we present the total fees paid for each configuration combination. The heat maps use an exponent (exp) of 2 and fine-tune the factor, delta imbalance threshold, and max fee parameters.

We recommend a maximum fee of 0.5%, a delta imbalance threshold of $1.5M, and a factor of 5e-10. This configuration results in $6.7 million in total fees for all traders, a 22% decrease compared to the benchmark. Below, we provide the fee distribution and explain why this decrease in fees is justified.

The $1.5M delta imbalance threshold was chosen because it actively charges price impact when needed, and should help reduce the risk of large positions being opened simultaneously. At the same time, it imposes fewer fees on regular users, reducing the likelihood of negative community feedback. This threshold was preferred over a $1M threshold with the same factor, which would generate more fees but could be seen as more punitive.

Alternatively, a delta imbalance threshold of $2M would lead to $6.3 million in price impact fees, a 26% decrease, and would only apply price impact in 0.7% of trades, compared to 1% for the $1.5M threshold. Therefore, a $2M threshold could also be considered.

As can be seen, the impact on traders is minimalâ€”99% of trades only incur the base rate.

### BTC

**Benchmark -** All Users Paid $1,649,758 in open/close fees and price impact.

We recommend a delta imbalance threshold of $5,000,000, with a factor of 5e-11 and a max fee of 0.5%. This approach ensures we do not impose unnecessary limitations on the BTC market, either now or unintentionally, if the market grows. These values will currently keep the feature inactive, only triggering it if a strong one-sided volume occurs in a short period on Jupiter. As a result, they will reduce price impact for the BTC market by ~11%, from $1,649,758 to $1,472,101.

### ETH

**Benchmark -** All Users Paid $656,604 in open/close fees and price impact.

We recommend a delta imbalance threshold of $5,000,000, with a factor of 5e-11 and a max fee of 0.5%. As with BTC, this approach ensures we do not impose unnecessary limitations on the ETH market as it grows. These values will keep the feature inactive, only triggering it if a strong one-sided volume occurs in a short period on Jupiter. As a result, they will reduce price impact for the current ETH market by ~16%, from $656,604 to $554,954.

# Recommendations

Asset | base rate | factor | exp | delta_imbalance_thr | max_fee |
---|---|---|---|---|---|

SOL | 6 bps | 5e-10 | 2 | 1,500,000 | 0.5% |

BTC | 6 bps | 5e-11 | 2 | 5,000,000 | 0.5% |

ETH | 6 bps | 5e-11 | 2 | 5,000,000 | 0.5% |