Risk Parameters

This chapter describes how to choose the risk parameters that govern the perpetual futures exchange — the global Param fields and per-pair PairParam fields defined in the perps contract. The goal is a systematic, reproducible calibration workflow that balances capital efficiency against tail-risk protection.

1. Margin ratios

The initial margin ratio (IMR) sets maximum leverage ($1/\mathtt{imr}$). The maintenance margin ratio (MMR) sets the liquidation threshold. Both are per-pair.

1.1 Volatility-based derivation

Start from the asset’s historical daily return distribution:

1. Collect at least 1 year of daily log-returns.

2. Compute the 99.5th-percentile absolute daily return $r_{99.5}$.

3. Apply a liquidation-delay factor $k$ (typically 2–3) to account for the time between the price move and the liquidation execution:

   $$\mathtt{mmr}=r_{99.5}\times k$$

4. Set IMR as a multiple of MMR:

   $$\mathtt{imr}=\mathtt{mmr}\times m,m\in [1.5,4]$$

A higher $m$ gives more buffer between position entry and liquidation, reducing bad-debt risk at the cost of lower leverage.

1.2 Peer benchmarks

1.3 Invariants

The following must hold for every pair:

$$0<\mathtt{mmr}<\mathtt{imr}\le 1$$

$$\mathtt{liquidationFeeRate}\le \mathtt{mmr}-\mathrm{takerFeeRate}$$

The second constraint ensures a liquidated position can always cover the taker fee and liquidation fee from the maintenance margin cushion.

2. Fee rates

Three fee rates apply globally (not per-pair):

2.1 Sizing principles

• Taker fee should exceed the typical half-spread of the most liquid pair so the vault earns positive expected value on every fill against a taker.
• Maker fee can be zero or slightly positive. A zero maker fee attracts resting liquidity; a negative maker fee (rebate) is not currently supported.
• Liquidation fee must satisfy the invariant in §1.3. It should be large enough to fund the insurance pool but small enough that a liquidated user retains some margin when possible.

2.2 Industry benchmarks

3. Funding parameters

Funding anchors the perp price to the oracle. Two per-pair parameters and one global parameter control its behaviour (see Funding for mechanics):

3.1 Max funding rate

The max daily funding rate limits how much a position can be charged per day. A useful rule of thumb:

$$\mathtt{maxAbsFundingRat}{\mathtt{e}}_{\mathrm{daily}}\le \frac{\mathtt{imr}}{T_{\mathrm{liq}}}$$

where $T_{\mathrm{liq}}$ is the number of days it should take sustained max-rate funding to liquidate a fully leveraged position. For $T_{\mathrm{liq}}=3$ days and $\mathtt{imr}=5\%$:

$$\mathtt{maxRate}=\frac{0.05}{3}\approx 1.67\%\text{ per day}$$

3.2 Impact size

The impact_size determines how deep the order book is walked to compute the premium. Set it to a representative trade size — large enough that the premium reflects real depth, small enough that thin books don’t produce zero premiums too often. A good starting point is 1–5% of the target max OI.

4. Capacity parameters

4.1 Max open interest

The maximum OI per side caps the exchange’s aggregate exposure:

$$\mathtt{maxAbsOI}\le \frac{\mathtt{vaultEquity}\times w_{\mathrm{pair}}}{\mathtt{mmr}\times \mathtt{tailLossFactor}}$$

where $w_{\mathrm{pair}}$ is the pair’s weight fraction and $\mathtt{tailLossFactor}$ (2–5) is a safety multiplier reflecting how many times maintenance margin the vault could lose in a tail event.

Start conservatively — it is easy to raise OI caps but dangerous to lower them (existing positions above the cap cannot be force-closed).

4.2 Min order size

Prevents dust orders. Set to a notional value that covers at least 2× the gas cost of processing the order. Typical values: $10–$100.

4.3 Tick size

The minimum price increment. Too small increases book fragmentation; too large creates implicit spread. Rule of thumb:

$$\mathtt{tickSize}\approx \mathtt{oraclePrice}\times 10^{-4}\text{ to }10^{-3}$$

For BTC at $60,000: tick sizes of $1–$10 are reasonable.

5. Vault parameters

The vault’s market-making policy is controlled by three per-pair parameters and two global parameters (see Vault for mechanics):

5.1 Half-spread

The half-spread should be calibrated to short-term intraday volatility so the vault earns a positive edge:

$$\mathtt{halfSpread}\ge {\sigma }_{\mathtt{intraday}}+\mathtt{makerFeeRate}$$

where ${\sigma }_{intraday}$ is the standard deviation of intra-block price changes. A larger spread protects against adverse selection but reduces fill probability.

5.2 Max quote size

Caps the vault’s resting order size per side per pair. Should be consistent with max_abs_oi — the vault should not be able to accumulate more exposure than the system can handle:

$$\mathtt{maxQuoteSize}\le \mathtt{maxAbsOI}\times f,f\in [0.3,0.8]$$

5.3 Liquidity weight

Determines what fraction of total vault margin is allocated to each pair. Higher-volume, lower-risk pairs should receive higher weights. The sum of all weights equals vault_total_weight.

5.4 Cooldown period

Prevents LPs from front-running known losses. Should exceed the funding period and be long enough that vault positions cannot be manipulated by short-term deposit/withdraw cycles. Typical values: 7–14 days.

6. Operational limits

7. Calibration workflow

The following checklist produces a complete parameter set from scratch:

1. Collect data — Gather ≥ 1 year of daily and hourly OHLCV data for each asset.

2. Compute volatility — For each asset, compute $r_{99.5}$ (daily 99.5th percentile absolute return) and ${\sigma }_{intraday}$ (hourly return standard deviation).

3. Set margin ratios — Derive MMR from $r_{99.5}$ (§1.1), then IMR as a multiple of MMR. Cross-check against peer benchmarks (§1.2).

4. Set fees — Choose maker/taker/liquidation fee rates satisfying §2.1 and the invariant in §1.3.

5. Set funding — Pick funding_period, derive max_abs_funding_rate (§3.1), and calibrate impact_size (§3.2).

6. Size exposure — Set max_abs_oi from vault equity and tail-risk tolerance (§4.1).

7. Set order constraints — Choose min_order_size and tick_size (§4.2, §4.3).

8. Configure vault — Set vault_half_spread, vault_max_quote_size, and vault_liquidity_weight per pair (§5), and vault_cooldown_period globally.

9. Backtest — Replay historical price data through the parameter set. Verify:

   • Liquidations occur before bad debt in > 99% of cases.
   • Vault PnL is positive over the test period.
   • Funding rates do not hit the clamp for more than 5% of periods.

10. Deploy conservatively — Launch with the conservative profile (lower leverage, higher fees, lower OI caps). Tighten parameters toward the aggressive profile as the system proves stable and liquidity deepens.