goosefx-amm-sdk/src/gfx/cpmm/curve/fee.ts

SDK for the GooseFx AMM

import BN from "bn.js";
import { CpmmObservationState, CpmmObservation } from "../type";
import Decimal from "decimal.js-light";
import { checkedCeilDiv, saturatingSub } from "./common";

export const ONE_BASIS_POINT = new BN(100);
export const FEE_RATE_DENOMINATOR_VALUE = new BN(1_000_000);
const OBSERVATION_LEN = 100;
// Volatility-based fee constants
// const MAX_FEE_VOLATILITY = new BN(10000); // 1% max fee
const VOLATILITY_WINDOW = new BN(3600); // 1 hour window for volatility calculation

const MAX_FEE = new BN(100000); // 10% max fee
const DEFAULT_VOLATILITY_FACTOR = new BN(300000); // Adjust based on desired sensitivity

type PriceRange = {
  minPrice: BN;
  maxPrice: BN;
  twapPrice: BN;
};

type FeeType = "volatility";

export class DynamicFee {
  static calculateDynamicFee(
    amount: BN,
    blockTimestamp: BN,
    observationState: CpmmObservationState,
    feeType: FeeType,
    baseFees: BN,
    poolVolatilityFactor: BN,
    isInvokedWithSignedSegmenter: boolean,
  ): BN {
    const feeRate = this.calculateDynamicFeeRate(
      blockTimestamp,
      observationState,
      feeType,
      baseFees,
      poolVolatilityFactor,
      isInvokedWithSignedSegmenter,
    );

    const [dynamicFee, _feeRateDenominator] = checkedCeilDiv(amount.mul(feeRate), FEE_RATE_DENOMINATOR_VALUE);
    return dynamicFee;
  }

  static calculatePreDynamicFee(
    amount: BN,
    blockTimestamp: BN,
    observationState: CpmmObservationState,
    feeType: FeeType,
    baseFees: BN,
    poolVolatilityFactor: BN,
    isInvokedWithSignedSegmenter: boolean,
  ): BN {
    const feeRate = this.calculateDynamicFeeRate(
      blockTimestamp,
      observationState,
      feeType,
      baseFees,
      poolVolatilityFactor,
      isInvokedWithSignedSegmenter,
    );

    if (feeRate.isZero()) {
      return amount; // No fee, pre-fee amount = post-fee amount
    }

    const denominator = FEE_RATE_DENOMINATOR_VALUE.sub(feeRate);
    if (denominator.isZero()) {
      throw new Error("Fee rate equals denominator, causing division by zero");
    }

    // x = (y * D + (D - r) - 1) / (D - r)
    const numerator = amount.mul(FEE_RATE_DENOMINATOR_VALUE);
    const result = numerator.add(denominator).sub(new BN(1)).div(denominator);

    return result;
  }

  static calculateDynamicFeeRate(
    blockTimestamp: BN,
    observationState: CpmmObservationState,
    feeType: FeeType,
    baseFees: BN,
    poolVolatilityFactor: BN,
    isInvokedWithSignedSegmenter: boolean,
  ): BN {
    switch (feeType) {
      case "volatility": {
        return this.calculateVolatileFee(
          blockTimestamp,
          observationState,
          baseFees,
          poolVolatilityFactor,
          isInvokedWithSignedSegmenter,
        );
      }
    }
  }

  static calculateVolatileFee(
    blockTimestamp: BN,
    observationState: CpmmObservationState,
    baseFees: BN,
    poolSpecifiedVolatilityFactor: BN,
    isInvokedWithSignedSegmenter: boolean,
  ): BN {
    const { minPrice, maxPrice, twapPrice } = this.getPriceRange(observationState, blockTimestamp, VOLATILITY_WINDOW);
    if (minPrice.eqn(0) || maxPrice.eqn(0) || twapPrice.eqn(0) || twapPrice.eqn(1)) {
      return baseFees;
    }

    const logMaxPrice = new Decimal(maxPrice.toString()).ln();
    const logMinPrice = new Decimal(minPrice.toString()).ln();
    const logTwapPrice = new Decimal(twapPrice.toString()).ln();

    const numerator = logMaxPrice.sub(logMinPrice);
    const denominator = logTwapPrice.abs();

    if (denominator.eq(0)) {
      return baseFees;
    }

    const volatility = numerator.div(denominator);
    const volatilityFactor = poolSpecifiedVolatilityFactor.eqn(0)
      ? DEFAULT_VOLATILITY_FACTOR
      : poolSpecifiedVolatilityFactor;
    const volatilityComponent = new Decimal(volatilityFactor.toString()).mul(volatility);

    const dynamicFee = new Decimal(baseFees.toString()).add(volatilityComponent);
    const finalFee = new BN(
      dynamicFee.lessThan(new Decimal(MAX_FEE.toString())) ? dynamicFee.toString() : MAX_FEE.toString(),
    );
    if (isInvokedWithSignedSegmenter) {
      const discountedFee = saturatingSub(finalFee, ONE_BASIS_POINT);
      return baseFees.gt(discountedFee) ? baseFees : discountedFee;
    } else {
      return finalFee;
    }
  }

  static getPriceRange(observationState: CpmmObservationState, currentTime: BN, window: BN): PriceRange {
    let minPrice = new BN(1).ushln(128).subn(1);
    let maxPrice = new BN(0);

    let descendingObservations = observationState.observations
      .map((observation, idx) => ({ observation, idx }))
      .filter(({ observation }) => {
        observation.blockTimestamp.eqn(0) &&
          !observation.cumulativeToken0PriceX32.eqn(0) &&
          !observation.cumulativeToken1PriceX32.eqn(0) &&
          currentTime.sub(observation.blockTimestamp) <= window;
      })
      .map(({ observation, idx }) => {
        return {
          index: idx,
          observation,
        };
      });

    if (descendingObservations.length < 2) {
      return {
        minPrice: new BN(0),
        maxPrice: new BN(0),
        twapPrice: new BN(0),
      };
    }

    descendingObservations.sort((a, b) => b.observation.blockTimestamp.cmp(a.observation.blockTimestamp));

    const newestObs = descendingObservations[0];
    const oldestObs = descendingObservations[descendingObservations.length - 1];

    const totalTimeDelta = saturatingSub(newestObs.observation.blockTimestamp, oldestObs.observation.blockTimestamp);
    if (totalTimeDelta.eqn(0)) {
      return {
        minPrice: new BN(0),
        maxPrice: new BN(0),
        twapPrice: new BN(0),
      };
    }

    const twapPrice = newestObs.observation.cumulativeToken0PriceX32
      .sub(oldestObs.observation.cumulativeToken0PriceX32)
      .div(totalTimeDelta);

    for (const indexedObservation of descendingObservations) {
      let lastObservation: CpmmObservation;
      if (indexedObservation.index == 0) {
        lastObservation = observationState.observations[OBSERVATION_LEN - 1];
      } else {
        lastObservation = observationState.observations[indexedObservation.index - 1];
      }

      if (lastObservation.blockTimestamp.eqn(0)) {
        continue;
      }

      if (lastObservation.blockTimestamp > indexedObservation.observation.blockTimestamp) {
        break;
      }

      const nextObservation = indexedObservation.observation;
      const timeDelta = saturatingSub(nextObservation.blockTimestamp, lastObservation.blockTimestamp);

      if (timeDelta.eqn(0)) {
        continue;
      }

      const price = nextObservation.cumulativeToken0PriceX32
        .sub(lastObservation.cumulativeToken0PriceX32)
        .div(timeDelta);

      minPrice = BN.min(minPrice, price);
      maxPrice = BN.max(maxPrice, price);
    }

    return {
      minPrice,
      maxPrice,
      twapPrice,
    };
  }

  static calculatePreFeeAmount(
    blockTimestamp: BN,
    postFeeAmount: BN,
    observationState: CpmmObservationState,
    feeType: FeeType,
    baseFees: BN,
    poolVolatilityFactor: BN,
    isInvokedWithSignedSegmenter: boolean,
  ): BN {
    const dynamicFeeRate = this.calculateDynamicFeeRate(
      blockTimestamp,
      observationState,
      feeType,
      baseFees,
      poolVolatilityFactor,
      isInvokedWithSignedSegmenter,
    );
    if (dynamicFeeRate.eqn(0)) {
      return postFeeAmount;
    } else {
      const numerator = postFeeAmount.mul(FEE_RATE_DENOMINATOR_VALUE);
      const denominator = FEE_RATE_DENOMINATOR_VALUE.sub(dynamicFeeRate);

      return numerator.add(denominator).subn(1).div(denominator);
    }
  }
}