Price Aggregator

The PriceAggregator contract serves as a sophisticated tool designed to compute the aggregated weighted average price of the crvUSD currency across a variety of liquidity pools, employing an advanced methodology that incorporates the exponential moving-average (EMA) of Total Value Locked (TVL) to ensure accurate and reliable pricing data.

The calculated price is primarily used as an oracle for calculating the interest rate, but also for PegKeepers to determine whether to mint and deposit or withdraw and burn.

Contract Source & Deployment

Source code is available on Github. Relevant contract deployments can be found here.

Calculations¶

The PriceAggregator contract calculates the weighted average price of crvUSD across multiple liquidity pools, considering only those pools with sufficient liquidity (MIN_LIQUIDITY = 100,000 * 10**18). This calculation is based on the exponential moving-average (EMA) of the Total Value Locked (TVL) for each pool, determining the liquidity considered in the price aggregation.

EMA TVL Calculation¶

The price calculation begins with determining the EMA of the TVL from different Curve Stableswap liquidity pools using the _ema_tvl function. This internal function computes the EMA TVLs based on the following formula, which adjusts for the time since the last update to smooth out short-term volatility in the TVL data, providing a more stable and representative average value over the specified time window (TVL_MA_TIME set to 50,000 seconds):

\[\alpha = \begin{cases} 1 & \text{if last_timestamp} = \text{current_timestamp}, \\ e^{-\frac{(\text{current_timestamp} - \text{last_timestamp}) * 10^{18}}{\text{TVL_MA_TIME}}} & \text{otherwise}. \end{cases} \]

\[\text{ema_tvl}_{i} = \frac{\text{new_tvl}_i * (10^{18} - \alpha) + \text{tvl}_i * \alpha}{10^{18}}\]

The code snippet provided illustrates the implementation of the above formula in the contract.

_ema_tvl

TVL_MA_TIME: public(constant(uint256)) = 50000  # s

@internal
@view
def _ema_tvl() -> DynArray[uint256, MAX_PAIRS]:
    tvls: DynArray[uint256, MAX_PAIRS] = []
    last_timestamp: uint256 = self.last_timestamp
    alpha: uint256 = 10**18
    if last_timestamp < block.timestamp:
        alpha = self.exp(- convert((block.timestamp - last_timestamp) * 10**18 / TVL_MA_TIME, int256))
    n_price_pairs: uint256 = self.n_price_pairs

    for i in range(MAX_PAIRS):
        if i == n_price_pairs:
            break
        tvl: uint256 = self.last_tvl[i]
        if alpha != 10**18:
            # alpha = 1.0 when dt = 0
            # alpha = 0.0 when dt = inf
            new_tvl: uint256 = self.price_pairs[i].pool.totalSupply()  # We don't do virtual price here to save on gas
            tvl = (new_tvl * (10**18 - alpha) + tvl * alpha) / 10**18
        tvls.append(tvl)

    return tvls

Aggregated Price Calculation¶

The _price function then uses these EMA TVLs to calculate the aggregated prices by considering the liquidity of each pool. A pool's liquidity must meet or exceed 100,000 * 10**18 to be included in the calculation. The function adjusts the price from the pool's price_oracle based on the position of crvUSD in the liquidity pair, ensuring consistent price representation across pools.

_price

@internal
@view
def _price(tvls: DynArray[uint256, MAX_PAIRS]) -> uint256:
    n: uint256 = self.n_price_pairs
    prices: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    D: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    Dsum: uint256 = 0
    DPsum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        price_pair: PricePair = self.price_pairs[i]
        pool_supply: uint256 = tvls[i]
        if pool_supply >= MIN_LIQUIDITY:
            p: uint256 = price_pair.pool.price_oracle()
            if price_pair.is_inverse:
                p = 10**36 / p
            prices[i] = p
            D[i] = pool_supply
            Dsum += pool_supply
            DPsum += pool_supply * p
    if Dsum == 0:
        return 10**18  # Placeholder for no active pools
    p_avg: uint256 = DPsum / Dsum
    e: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    e_min: uint256 = max_value(uint256)
    for i in range(MAX_PAIRS):
        if i == n:
            break
        p: uint256 = prices[i]
        e[i] = (max(p, p_avg) - min(p, p_avg))**2 / (SIGMA**2 / 10**18)
        e_min = min(e[i], e_min)
    wp_sum: uint256 = 0
    w_sum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        w: uint256 = D[i] * self.exp(-convert(e[i] - e_min, int256)) / 10**18
        w_sum += w
        wp_sum += w * prices[i]
    return wp_sum / w_sum

The process involves:

Storing the price of crvUSD in a prices[i] array for each qualifying pool.
Recording each qualifying pool's supply (TVL) in D[i], adding this supply to Dsum, and accumulating the product of the crvUSD price and pool supply in DPsum.
Iterating over all price pairs to perform the above steps.

Finally, the contract:

Calculates an average price:

\[\text{average price} = \frac{\text{DPSum}}{\text{DSum}}\]
Computes a variance measure e for each pool's price relative to the average, adjusting by SIGMA to normalize:

\[\text{e}_i = \frac{(\max(p, p_{\text{avg}}) - \min(p, p_{\text{avg}}))^2}{\frac{\text{SIGMA}^2}{10^{18}}}\]

\[\text{e}_{min} = \min(\text{e}_i, \text{max_value(uint256)})\]
Applies an exponential decay based on these variance measures to weigh each pool's contribution to the final average price, reducing the influence of prices far from the minimum variance.

\[w = \frac{\text{D}_i * e^\left({\text{e}_i - e_{min}}\right)}{10^{18}}\]
Sums up all w to store it in w_sum and calculates the product of w * prices[i], which is stored in wp_sum.
Finally calculates the weighted average price as wp_sum / w_sum, with weights adjusted for both liquidity and price variance.

\[\text{final price} = \frac{\text{wp_sum}}{\text{w_sum}}\]

Prices¶

`price`¶

PriceAggregator.price() -> uint256:

Function to calculate the weighted price of crvUSD.

Returns: price (uint256).

Source code

PriceAggregator.vy

MAX_PAIRS: constant(uint256) = 20
MIN_LIQUIDITY: constant(uint256) = 100_000 * 10**18  # Only take into account pools with enough liquidity

STABLECOIN: immutable(address)
SIGMA: immutable(uint256)
price_pairs: public(PricePair[MAX_PAIRS])
n_price_pairs: uint256

@external
@view
def price() -> uint256:
    return self._price(self._ema_tvl())

@internal
@view
def _price(tvls: DynArray[uint256, MAX_PAIRS]) -> uint256:
    n: uint256 = self.n_price_pairs
    prices: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    D: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    Dsum: uint256 = 0
    DPsum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        price_pair: PricePair = self.price_pairs[i]
        pool_supply: uint256 = tvls[i]
        if pool_supply >= MIN_LIQUIDITY:
            p: uint256 = price_pair.pool.price_oracle()
            if price_pair.is_inverse:
                p = 10**36 / p
            prices[i] = p
            D[i] = pool_supply
            Dsum += pool_supply
            DPsum += pool_supply * p
    if Dsum == 0:
        return 10**18  # Placeholder for no active pools
    p_avg: uint256 = DPsum / Dsum
    e: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    e_min: uint256 = max_value(uint256)
    for i in range(MAX_PAIRS):
        if i == n:
            break
        p: uint256 = prices[i]
        e[i] = (max(p, p_avg) - min(p, p_avg))**2 / (SIGMA**2 / 10**18)
        e_min = min(e[i], e_min)
    wp_sum: uint256 = 0
    w_sum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        w: uint256 = D[i] * self.exp(-convert(e[i] - e_min, int256)) / 10**18
        w_sum += w
        wp_sum += w * prices[i]
    return wp_sum / w_sum

Example

>>> PriceAggregator.price()
999964013300395878

`last_price`¶

PriceAggregator.last_price() -> uint256: view

Getter for the last price. This variable was set to \(10^{18}\) (1.00) when initializing the contract and is now updated every time price_w is called.

Returns: last price of crvUSD (uint256).

Source code

PriceAggregator.vy

last_price: public(uint256)

@external
def __init__(stablecoin: address, sigma: uint256, admin: address):
    STABLECOIN = stablecoin
    SIGMA = sigma  # The change is so rare that we can change the whole thing altogether
    self.admin = admin
    self.last_price = 10**18
    self.last_timestamp = block.timestamp

@external
def price_w() -> uint256:
    if self.last_timestamp == block.timestamp:
        return self.last_price
    else:
        ema_tvl: DynArray[uint256, MAX_PAIRS] = self._ema_tvl()
        self.last_timestamp = block.timestamp
        for i in range(MAX_PAIRS):
            if i == len(ema_tvl):
                break
            self.last_tvl[i] = ema_tvl[i]
        p: uint256 = self._price(ema_tvl)
        self.last_price = p
        return p

Example

>>> PriceAggregator.last_price()
999385898759491513

`ema_tvl`¶

PriceAggregator.ema_tvl() -> DynArray[uint256, MAX_PAIRS]

Getter for the exponential moving-average of the TVL in price_pairs.

Returns: array of ema tvls (DynArray[uint256, MAX_PAIRS]).

Source code

PriceAggregator.vy

TVL_MA_TIME: public(constant(uint256)) = 50000  # s

last_tvl: public(uint256[MAX_PAIRS])

@external
@view
def ema_tvl() -> DynArray[uint256, MAX_PAIRS]:
    return self._ema_tvl()

@internal
@view
def _ema_tvl() -> DynArray[uint256, MAX_PAIRS]:
    tvls: DynArray[uint256, MAX_PAIRS] = []
    last_timestamp: uint256 = self.last_timestamp
    alpha: uint256 = 10**18
    if last_timestamp < block.timestamp:
        alpha = self.exp(- convert((block.timestamp - last_timestamp) * 10**18 / TVL_MA_TIME, int256))
    n_price_pairs: uint256 = self.n_price_pairs

    for i in range(MAX_PAIRS):
        if i == n_price_pairs:
            break
        tvl: uint256 = self.last_tvl[i]
        if alpha != 10**18:
            # alpha = 1.0 when dt = 0
            # alpha = 0.0 when dt = inf
            new_tvl: uint256 = self.price_pairs[i].pool.totalSupply()  # We don't do virtual price here to save on gas
            tvl = (new_tvl * (10**18 - alpha) + tvl * alpha) / 10**18
        tvls.append(tvl)

    return tvls

Example

>>> PriceAggregator.ema_tvl()
59321570154325618129121893, 42600769394518064802429328, 8535901977675585449164114, 4775645754381802242168047

`last_tvl`¶

PriceAggregator.last_tvl(arg0: uint256) -> uint256:

Getter for the total value locked of price pair (pool).

Returns: total value locked (uint256).

Input	Type	Description
`arg0`	`uint256`	Index of the price pair

Source code

PriceAggregator.vy

last_tvl: public(uint256[MAX_PAIRS])

Example

>>> PriceAggregator.last_tvl()
1689448067

`price_w`¶

PriceAggregator.price_w() -> uint256:

Function to calculate and write the price. If called successfully, updates last_tvl, last_price and last_timestamp.

Returns: price (uint256).

Source code

PriceAggregator.vy

@external
def price_w() -> uint256:
    if self.last_timestamp == block.timestamp:
        return self.last_price
    else:
        ema_tvl: DynArray[uint256, MAX_PAIRS] = self._ema_tvl()
        self.last_timestamp = block.timestamp
        for i in range(MAX_PAIRS):
            if i == len(ema_tvl):
                break
            self.last_tvl[i] = ema_tvl[i]
        p: uint256 = self._price(ema_tvl)
        self.last_price = p
        return p

@internal
@view
def _price(tvls: DynArray[uint256, MAX_PAIRS]) -> uint256:
    n: uint256 = self.n_price_pairs
    prices: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    D: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    Dsum: uint256 = 0
    DPsum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        price_pair: PricePair = self.price_pairs[i]
        pool_supply: uint256 = tvls[i]
        if pool_supply >= MIN_LIQUIDITY:
            p: uint256 = price_pair.pool.price_oracle()
            if price_pair.is_inverse:
                p = 10**36 / p
            prices[i] = p
            D[i] = pool_supply
            Dsum += pool_supply
            DPsum += pool_supply * p
    if Dsum == 0:
        return 10**18  # Placeholder for no active pools
    p_avg: uint256 = DPsum / Dsum
    e: uint256[MAX_PAIRS] = empty(uint256[MAX_PAIRS])
    e_min: uint256 = max_value(uint256)
    for i in range(MAX_PAIRS):
        if i == n:
            break
        p: uint256 = prices[i]
        e[i] = (max(p, p_avg) - min(p, p_avg))**2 / (SIGMA**2 / 10**18)
        e_min = min(e[i], e_min)
    wp_sum: uint256 = 0
    w_sum: uint256 = 0
    for i in range(MAX_PAIRS):
        if i == n:
            break
        w: uint256 = D[i] * self.exp(-convert(e[i] - e_min, int256)) / 10**18
        w_sum += w
        wp_sum += w * prices[i]
    return wp_sum / w_sum

Example

>>> PriceAggregator.price_w()
999385898759491513

Adding and Removing Price Pairs¶

All price pairs added to the contract are considered when calculating the price of crvUSD. Adding or removing price pairs can only be done by the admin of the contract, which is the Curve DAO.

`price_pairs`¶

PriceAggregator.price_pairs(arg0: uint256) -> tuple: view

Getter for the price pair at index arg0 and whether the price pair is inverse.

Returns: price pair (address) and true or false (bool).

Input	Type	Description
`arg0`	`uint256`	Index of the price pair

Source code

PriceAggregator.vy

price_pairs: public(PricePair[MAX_PAIRS])

Example

>>> PriceAggregator.price_pairs(0)
'0x4DEcE678ceceb27446b35C672dC7d61F30bAD69E, false'

`add_price_pair`¶

PriceAggregator.add_price_pair(_pool: Stableswap):

Guarded Method

This function is only callable by the admin of the contract.

Function to add a price pair to the PriceAggregator.

Emits: AddPricePair

Input	Type	Description
`_pool`	`address`	Price pair to add

Source code

PriceAggregator.vy

event AddPricePair:
    n: uint256
    pool: Stableswap
    is_inverse: bool

@external
def add_price_pair(_pool: Stableswap):
    assert msg.sender == self.admin
    price_pair: PricePair = empty(PricePair)
    price_pair.pool = _pool
    coins: address[2] = [_pool.coins(0), _pool.coins(1)]
    if coins[0] == STABLECOIN:
        price_pair.is_inverse = True
    else:
        assert coins[1] == STABLECOIN
    n: uint256 = self.n_price_pairs
    self.price_pairs[n] = price_pair  # Should revert if too many pairs
    self.last_tvl[n] = _pool.totalSupply()
    self.n_price_pairs = n + 1
    log AddPricePair(n, _pool, price_pair.is_inverse)

Example

>>> PriceAggregator.add_price_pair("0x0cd6f267b2086bea681e922e19d40512511be538")

`remove_price_pair`¶

PriceAggregator.remove_price_pair(n: uint256):

Guarded Method

This function is only callable by the admin of the contract.

Function to remove a price pair from the contract. If a prior pool than the latest added one gets removed, the function will move the latest added price pair to the removed pair pairs index to not mess up price_pairs.

Emits: RemovePricePair and possibly MovePricePair

Input	Type	Description
`n`	`uint256`	Index of the price pair to remove

Source code

PriceAggregator.vy

event RemovePricePair:
    n: uint256

event MovePricePair:
    n_from: uint256
    n_to: uint256

@external
def remove_price_pair(n: uint256):
    assert msg.sender == self.admin
    n_max: uint256 = self.n_price_pairs - 1
    assert n <= n_max

    if n < n_max:
        self.price_pairs[n] = self.price_pairs[n_max]
        log MovePricePair(n_max, n)
    self.n_price_pairs = n_max
    log RemovePricePair(n)

Example

>>> PriceAggregator.remove_price_pair("0x4DEcE678ceceb27446b35C672dC7d61F30bAD69E")

Admin Ownership¶

`admin`¶

PriceAggregator.admin() -> address: view

Getter for the admin of the contract, which is the Curve DAO OwnershipAgent.

Returns: admin (address).

Source code

PriceAggregator.vy

admin: public(address)

@external
def __init__(stablecoin: address, sigma: uint256, admin: address):
    STABLECOIN = stablecoin
    SIGMA = sigma  # The change is so rare that we can change the whole thing altogether
    self.admin = admin

Example

>>> PriceAggregator.admin()
'0x40907540d8a6C65c637785e8f8B742ae6b0b9968'

`set_admin`¶

PriceAggregator.set_admin(_admin: address):

Guarded Method

This function is only callable by the admin of the contract.

Function to set a new admin.

Emits: SetAdmin

Input	Type	Description
`_admin`	`address`	new admin address

Source code

PriceAggregator.vy

event SetAdmin:
    admin: address

admin: public(address)

@external
def set_admin(_admin: address):
    # We are not doing commit / apply because the owner will be a voting DAO anyway
    # which has vote delays
    assert msg.sender == self.admin
    self.admin = _admin
    log SetAdmin(_admin)

Example

>>> PriceAggregator.set_admin("0xd8dA6BF26964aF9D7eEd9e03E53415D37aA96045")

Contract Info Methods¶

`SIGMA`¶

PriceAggregator.SIGMA() -> uint256: view

Getter for the sigma value. SIGMA is a predefined constant that influences the adjustment of price deviations, affecting how variations in individual stablecoin prices contribute to the overall average stablecoin price.

Returns: sigma (uint256).

Source code

PriceAggregator.vy

SIGMA: immutable(uint256)

@external
@view
def sigma() -> uint256:
    return SIGMA

Example

>>> PriceAggregator.SIGMA()
1000000000000000

`STABLECOIN`¶

PriceAggregator.STABLECOIN() -> address: view

Getter for the stablecoin contract address.

Returns: crvUSD contract (address).

Source code

PriceAggregator.vy

STABLECOIN: immutable(address)

@external
@view
def stablecoin() -> address:
    return STABLECOIN

Example

>>> PriceAggregator.STABLECOIN()
'0xf939E0A03FB07F59A73314E73794Be0E57ac1b4E'

`last_timestamp`¶

PriceAggregator.last_timestamp() -> uint256:

Getter for the latest timestamp. Variable is updated when price_w is called.

Returns: timestamp (uint256).

Source code

PriceAggregator.vy

last_timestamp: public(uint256)

Example

>>> PriceAggregator.last_timestamp()
1689448067

`TVL_MA_TIME`¶

PriceAggregator.TVL_MA_TIME() -> uint256: view

Getter for the time period for the calculation of the EMA prices.

Returns: timestamp (uint256).

Source code

PriceAggregator.vy

TVL_MA_TIME: public(constant(uint256)) = 50000  # s

Example

>>> PriceAggregator.TVL_MA_TIME()
50000

Price Aggregator

Calculations¶

EMA TVL Calculation¶

Aggregated Price Calculation¶

Prices¶

price¶

last_price¶

ema_tvl¶

last_tvl¶

price_w¶

Adding and Removing Price Pairs¶

price_pairs¶

add_price_pair¶

remove_price_pair¶

Admin Ownership¶

admin¶

set_admin¶

Contract Info Methods¶

SIGMA¶

STABLECOIN¶

last_timestamp¶

TVL_MA_TIME¶

`price`¶

`last_price`¶

`ema_tvl`¶

`last_tvl`¶

`price_w`¶

`price_pairs`¶

`add_price_pair`¶

`remove_price_pair`¶

`admin`¶

`set_admin`¶

`SIGMA`¶

`STABLECOIN`¶

`last_timestamp`¶

`TVL_MA_TIME`¶