Markets

This document specifies nord’s market types and their respective behaviour, along with some implementation notes. It is designed to be readable by anyone with limited knowledge of financial markets, but with a strong technical background. Links to external resources are provided where appropriate.

Nord provides spot trading, perpetual futures trading, and spot lending. To limit risk, a margining system is defined to limit the risk a user may take on. To simplify margining, all prices are quoted (i.e. denominated) in the same asset, which we chose to be USDC. In the implementation, the first token, with token_id == 0, is the denominator.

Open questions

Do we need to define a dust threshold?

We can define a “dust threshold” for assets, where below a certain amount the asset is considered to have amount 0. We defined this in the past to deal with certain edge cases around bankruptcy, but don’t recall the rationale.

Do we need to define position open notional for spot markets?

This depends on if we want to limit open orders given a certain amount of assets and if we allow spot trades to create borrows.

Is it possible to pay and charge interest additively?

Multiplicative interest payments cause some amount of loss of precision. Granted, the difference is negligible, but may open a possible loss of funds vector.

Do we adjust margin fractions for small cap coins?

We can apply the following to deal with small market caps. Similarly for CMF, MMF.

Definitions

For the purposes of this document specific representations are used. Implementation may choose to diverge.

Position size

The number of owned contracts for a given perpetuals market. May be a fractional amount. A short position is defined as a negative position size.

Fill size

The size of the fill when orders are matched. The size is defined to be negative for the side selling.

Iverson bracket 

We sometimes use the Iverson bracket $\mathbb{I}[\cdot]$, where $\mathbb{I}[P] = 1$ if $P$ is true, and $0$ otherwise.

Tokens

Prior to trading, a user must first deposit tokens in the form of tokenized financial assets such as USDC and ETH. The token is deposited into the vault and the user’s token amount is increased by the same amount. Similarly for withdrawals.

Parameters

weight

A number in $(0, 1]$ defining the contribution of this token to the overall account value. The weight is used to deal with certain asset types having high volatility or low liquidity.

For example, suppose BTC has weight 0.9 and USD price 1000 USD/BTC. If a user deposits 1 BTC, then their account value increases by 0.9 * 1 BTC * 1000 BTC/USD = 900 USD.

token decimals

The decimal shift for the smallest possible denomination of this asset type. This allows deposit and withdrawals to be defined in terms of integers. The original value is recovered by dividing the amount by 10 ** token decimals.

For USDC, this might be set to 6. If a user wants to deposit 1 USDC, they would set the deposit amount to 1_000_000. Note that the shifted amount doesn’t have to be the fraction currency for the asset, such as cents for USD. For example, for ETH, we may choose a token decimals value of 8 instead of the intelligently chosen default of 18 to prevent overflows.

max rate

The maximum interest rate for borrows of this token.

optimal rate

The optimal interest rate, beyond which the rate sharply increases to the max rate.

optimal utilization

The optimal utilization, where utilization is the ratio of total borrow to total supply.

origination fee

Percentage fee charged for borrows. Suppose amount $x$ is borrowed. Then a fee of $y = x \cdot \text{origination fee}$ is moved to the accrued fee vault when the borrow occurs. The final borrowed amount is then $x - y$.

liq fee

Fee charged for having a spot borrow of this asset type be liquidated.

Borrowing

Tokens may also be borrowed against other, positive token. All positive token is implicitly lent and gains interest. Limits for borrows are defined by the margining system explained further below. Here, we define how lending and borrowing interest rates are computed. We first define the utilization $u$ as the fraction of borrows for the supply for a given token type. In other words,

Given the token metaparameters defined above, the yearly interest rate $\text{IR}$ is given by

The paid and charged interest are tracked lazily through the supply multiplier and borrow multiplier. Let $T = 3600 \cdot 24 \cdot 365$ be the period, $B_t$ the borrow multiplier at time $t$, and $S_t$ the supply multiplier at time $t$.

To apply the borrow and supply multipliers, the asset amounts by the borrow and supply multipliers to reflect the interest.

Markets

Index price

Index price provided by oracle is not a single scalar value but rather a probabilistic one. Oracle collects prices for an asset from several values which leads to the final index price being expressed as median price Pm and confidence interval C, such that actual index price falls within [Pm-C; Pm+C] interval with 95% probability.
For more details, see Confidence intervals .

Computations which use index price prefer its “conservative” value, i.e. reduce positive values obtained with its use and increase negative ones. This way we’re more sure that we don’t overestimate factors like account health or funding rates.

Different kinds of index price are marked below as follows:

• median index price: $p_\text{index}$
• lower-bound index price: $p_\text{low index}$
• upper-bound index price: $p_\text{high index}$

Parameters

These definitions apply to both spot markets and perp markets.

size decimals

Similar to token decimals, but applied to sizes. Can be interpreted as the $log_{10}$ of the lot size of this market, where the lot size may only be a power of 10.

tick decimals

Similar to token decimals, but applied to all prices. Note that we use tick decimals and not a tick size, so tick sizes are limited to powers of 10.

example decimals

Let have 1 ETH. 1 ETH on balance represented by $10^{token\_decimals}$. 1 ETH on orderbook represented by $10^{size\_decimals}$.

So we if want to find out number representing same ETH amount on balance and on orderbook (or position), we will get:

which gives us way to convert one value into other.

Here is some examples of used conversions:

where amount is real number which humans usually expect to see

maker fee

Fee charged to an order maker on trades by the exchange. A typical value is 2 bps, or 0.02%.

taker fee

Fee charged to an order taker on trades by the exchange. A typical value is 5 bps, or 0.05%.

liq fee

Fee charged for having a position on this perp market be liquidated.

withdrawal fee

Withdrawing balance from app takes amount of token equivalent to amount configured in USDC. For token to be withdrawable it should have price to be available.

Spot

Spot trading can be used to trade non-USDC assets for USDC, and vice versa. Unlike perps, there isn’t a notion of reduce only orders nor of position. Trades only lead to user assets being swapped.

Perpetual futures

Perpetual Futures Fills

Users earns by trading taking and trading their positions. Let $S=\text{fill size} \cdot \text{position size}$. On trades we perform the following updates:

Notice that the total sum of PnL and position sizes must sum to zero, i.e. $\sum(\text{PnL}) = 0$ and $\sum(\text{position size}) = 0$. In practice, there may be a small non-zero amount, though this should always be in favour of the exchange to prevent a possible loss of funds vector. Updates to PnL is mutually exclusive with updates to open price and position size.

Funding

For a given perp market, we define the mark price $p_\text{mark}$ as

The “one sided multiplier” can be chosen arbitrarily and is used to incentivize placing orders on the empty side. We hardcode it to 1%. The mark price is kept close to the median index price through the use of funding. We define the funding rate $\text{FR}$ as

For notational simplicity, we define short positions as simply having a negative position and fill size of sell to be negative too, although implementations may choose to do so differently.

For perp market:

We define current funding index to be

The funding payment is done every hour (update interval), computed by

Unfortunately, iterating through all accounts to pay funding can be expensive. To alleviate this problem, we can pay funding lazily. We introduce the concept of unsettled funding to refer to funding that has not been paid out yet, and settled funding to denote the total amount of funding paid out so far.

The funding index is adjusted on funding rate updates. The user funding index updated on user funding payments and position updates.

When the position is closed, change to user position calculated as:

where $UFI$ use stored on last position update.

Funding index updated with:

Summary

• if $price_{mark} > price_{index}$ during update interval, $FR$ grows, lead to $FI$ grow, hence long positions pay short positions
• if $price_{mark} < price_{index}$ during update interval, shorts pay long
• funding rate is interest payed to incentivize mid point mark price to become close to index price
• all spot user’s unfilled positions and balances are collateral quoted in USD
• index price expressed in USDC, and relevant USD/USDC transformation is done to handle difference with risk
• if positive position size reduced toward 0, and price increased since open, user balance increased
• if negative position size increased toward zero, and price decreased since open, user balance increased

Margining

The margining system is defined to limit the amount of risk a given user can take on. Over-leveraged users are liquidated by the exchange, i.e. their orders are cancelled and positions are reduced, and possibly closed, until the user is aptly leveraged. This is to limit the exchange’s exposure to risk as a result of aggressive leverage. Liquidated users are charged a liquidation fee to disincentivize getting liquidated.

During periods of high volatility, it is possible a user is not liquidated before their account value goes negative. In this case, the liquidation is is tokenized by the exchange’s insurance fund. If the insurance fund is depleted, losses are socialized among users proportional to leverage of profitable accounts.

To summarise the margining system, when opening a position or borrowing, the user must first provide an initial margin in the form of token, proportional to their position. Then, they must maintain their token above a maintenance margin. Otherwise, the user’s liquidated until back above the maintenance margin.

Due to the mark price being unreliable during liquidity shortages, we use the index price in risk calculations to avoid undeserved liquidation cascades.

position notional $PN$ and position open notional $PON$

Note on index price: Since PN/PON are considered risk/borrow values, they’re maximized, usually by picking $\text{p}_{high index}$, in order to consider the worst case risk of the account.

Perp

The position notional is the value of a given user’s position. For perp markets, we define it as

The position open notional is the maximum position notional achievable by filling all the user’s open orders. This is used to limit how much risk a user is exposed to through their open orders.

We define the position open notional as

Spot

Spot positions refer to borrowed assets, which we define as having a negative balance. Thus the position taken on by a trader for a negative balance scales with the amount borrowed. Only negative balances are counted towards the position, while positive balances count instead as collateral. See the account value definition for more info. Currently, we set for borrows:

and

To sum it up, We can compute user’s total position notional and total position open notional as $\sum_{markets}\text{PN}$ and $\sum_{markets}\text{PON}$ respectively.

account value $AV$

The account value is computed by summing the unrealized profit and loss (PnL) of the user’s positions, the token, and the borrows. We define unrealized PnL as PnL that hasn’t currently been reflected in the user’s balances by closing the position. We say PnL is realized when a position is closed.

To compute this, we define $p_\text{open}$ as the price at which the position was opened at, corresponding to the purchase or sell price of the position. In practice, a user’s position will have been opened at different prices by purchasing or selling contracts at different prices. To simplify implementation, it’s sufficient to reweight the open price accordingly. For example, suppose a user purchases 5 contracts at price 20, and 10 contracts at price 30. Then,

The open price must be reweighted after each fill, for both makers and takers. Now, recall that the position size is defined to be negative for short positions. We can now define unrealized PnL as

Note on index price: since it’s assets value, we use higher-bound index price for negative position size and lower-bound for positive one

$\text{TV}$ is a total value of weighted user’s tokens normalized by index price:

Note on index price: since it’s positive assets value, lower-bound index price is used

To compute the value of assets, we weigh positive token with the asset and subtract the borrows. To represent this succinctly, token corresponds to a positive amount and borrows correspond to a negative amount. Amount includes unsettled funding payments. With this, we have our final account value calculation.

denominated in token_id = 0. Essentially, $\text{TV}$ corresponds to the user’s collateral, whereas $\text{AV}$ also discounts borrows and includes the current PnL. This is to ensure that borrows are capped by the collateral to prevent exploits.

Margin fraction

These fractions define initial and maintenance leverage permitted by the exchange, before a user is liquidated. Each market has a different base fraction, typically depending on the risk or volatility of the underlying asset.

margin fraction $MF$

Calculated per user as:

open margin fraction $OMF$

Approximately ratio for all user assets (positions, balances, PnL) to user possible risk(debt, derivatives. open orders).

Note the amount includes unsettled funding.

initial margin fraction $IMF$

Defines the initial margin to open a position or borrow assets. After opening a position or borrowing an asset, we must have $\text{OMF}_user > \text{IMF}_user$. First, we first define a per-market or per-asset base IMF.

where

• $\text{max leverage}$ is the maximum leverage multiplier for specific market; implementation may operate with market’s $\text{imf}$ value, in which case

• $\text{weight}$ is the weight of spot market’s base token

Note that in practice, we need only store the market IMF and token IMF. The leverage is implied from this value. Then we have the user’s IMF.

Note that for tokens, $\text{IMF}_\text{base}$ is only defined if the token is borrowable.

For $\text{OMF} > \text{IMF}$ condition we can observe that sides have same denominator, which allows to simplify it to:

Let use $AB = \min\{\text{AV}, \text{TV}\}$.

cancel margin fraction $CMF$

The $OMF$ below which open orders that extend the user’s current position are cancelled. Defined similarly to IMF.

maintenance margin fraction $MMF$

The $MF$ below which the user’s positions are closed and borrows unlent until the $MF$ is back above the $MMF$ .

Liquidations

Notice that, by definition,

and from that if $MF < MMF$ implies $CMF < OMF$($CMF < OMF$ will happen before $MF < MMF$) (but not necessarily the other way around) because:

which implies, with gradual change of values, cancelling orders will happen not later than reducing positions.

$MF <= 0$ implies $AV < 0$. $\text{AV} < 0$ is bankruptcy

Action is successful and changes market and account state, or fails - in this case no changes retain. Batch is tuple of actions, in case of successful all action are successful, in case of any action fail - all actions fail.

So we can summarize next actions which can be taken by liquidators and users depending on conditions. If conditions are not met, actions cannot be executed.

Let $m$ indicated specific market on which action is executed. Table is per user:

User always act as liquidator.

It is possible that user cannot open orders nor liquidator can cancel existing, which helps to avoid jitter of user open/liquidator cancel.

A liquidation fee is charged to the liquidated user in case action was performed by liquidator. In case of bankruptcy no fees are payed.

All orders when user is subject to liquidation are Fill-or-Kill(FoK, executed within single action, flash).

User can execute any allowed action in any order. Liquidator can execute next actions in table only if previous are not possible. For example, cancelling orders taking priority over closing positions.

Batch is allowed to compensate remaining negative balances from insurance fund.

Orders

Ideal means amount which makes $OMF = IMF$ exactly.

So fee is payed only only for part of order which had to be eliminated to get factors healthy.

Perpetuals

Perp positions are liquidated by reducing the user’s position.

Ideal position is $MF = IMF$. Let ideal balance fraction be $IBF$, ideal position fraction $IPF$, real balance fraction $RBF$.

So:

So reward is:

So liquidating more than needed to get $OMF$ up to $IMF$ will not give liquidator more fee.

Liquidator fee calculated after taker fee taken as long as account is not in bankruptcy.

Action can be executed iff all orders increasing position canceled. Action collects $PnL$ during reduction.

Borrows

Borrows are liquidated by reducing a borrower’s debt by liquidating a positive supply token, at the choice of the liquidator.

The borrow the liquidator takes is defined by:

Sells

In order to reduce perpetual position or repay borrow, sometimes need to get other token than user have. In this case fee is not taken.

Bankruptcy

An account is said to be in bankruptcy if $\text{AV} < 0$.

Liquidator detects bankrupt account(liquidatee) and:

• cancels all account orders
• transfers all, negative and positive, balances to insurance fund
• distributes all accounts’s positions and debt to using the closing mechanism described below
• account is cleared and may be used again

Closing mechanism

1. Applies negative debt or perp position PnL to liquidator(s) account.
2. The liquidator(s) will be compensated for the borrowed debt or negative perp PnL amount in USDC by the insurance fund. 2.1. Insurance funds will be sold for USDC as needed 2.2. Negative balances of tokens in insurance vault are reduced
3. If the insurance fund is depleted (bankruptcy of protocol), the loss will be socialized according to socializing mechanism

Socializing mechanism

Through the supply APY.

Withdrawals $W$ are penalized per token as long as there is debt of it on insurance funds (for perps USDC).

Difference is used to reduce $debt$

Price bands

Reject place order requests with a limit price too far from the index price for the perpetual market to band B to reduce price manipulation on small markets. $p_\text{low index} \cdot (1 - B)$ for smallest price and $p_\text{high index} \cdot (1 - B)$ for highest price possible, and $B=0.1$.