Orderbook Mechanics

This page explains the math behind the ArcX orderbook. It covers:

• why the book is quoted in APR
• how ST and EPT prices are derived
• how order sizes are interpreted
• how same-asset and cross-asset matching works
• how market orders, slippage, partial fills, and cancels behave

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Core Setup

For all formulas below, let:

• APR = the annualized rate quoted in the book, written in decimal form for the formulas on this page (for example, 10% = 0.10)
• time remaining = time left until series maturity, measured in years
• rt = APR × time remaining

rt is the time-adjusted term used throughout the orderbook math.

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Why the Orderbook Is Quoted in APR

ST and EPT are both time-dependent claims. Even if the economic deal stays the same, the token amounts implied by that deal change as maturity approaches. If the book were quoted directly in token price, every resting order would appear to reprice over time. For example, imagine you want the same annualized ST deal for a series with 60 days left and then again with 10 days left.

• with 60 days left, that APR implies a larger ST amount per vToken
• with 10 days left, that same APR implies a smaller ST amount per vToken

If orders were quoted directly in token price, the same economic intention would have to be constantly repriced as maturity approached. APR is the stable quote unit. That is why the orderbook stores economic intent in APR and derives token prices and sizes from rt.

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Core Pricing Formulas

At a given rt, the implied prices in vToken terms are: $\text{Price(ST in vToken)} = \frac{1}{1 + rt}$ $\text{Price(EPT in vToken)} = \frac{rt}{1 + rt}$ The inverse “how much token do I get for 1 vToken?” views are: $\text{ST per vToken} = 1 + rt$ $\text{EPT per vToken} = \frac{1 + rt}{rt}$ These formulas already explain the directional intuition:

• higher APR lowers ST price and raises EPT price
• lower APR raises ST price and lowers EPT price

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Different Order Types

There are four native order types:

1. Buy ST
2. Sell ST
3. Buy EPT
4. Sell EPT

They are not all stored in the same raw unit, so it helps to reason in ST/EPT size.

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ST and EPT Have the Same Orderbook

Although ST and EPT may look like two different books in the UI, they are two views over the same underlying economic book. The core identity is: $$1 \text{ vToken} = 1 \text{ ST} + 1 \text{ EPT}$$ That means pricing either ST or EPT in vTokens automatically decides the price of the other side. Or in other words:

• 1 vToken can always be split into 1 ST + 1 EPT
• 1 ST + 1 EPT can always be combined back into 1 vToken

The core identities are:

• Buy ST is economically equivalent to Sell EPT
• Buy EPT is economically equivalent to Sell ST

For example, a Buy ST can match directly with a Sell ST. But it can also be satisfied by splitting vToken into ST + EPT and selling the EPT side. The same logic works in reverse on the EPT side too.

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How to Reason About APR

The practical direction table is: This table is just the pricing formulas above expressed in user-facing terms.

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APR Checks During Order Matching

Before two orders can match, their APRs must be compatible.

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Same asset

• Buy ST vs Sell ST: sell APR >= buy APR
• Buy EPT vs Sell EPT: buy APR >= sell APR

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Cross asset

• Buy EPT vs Buy ST: ept APR >= st APR
• Sell ST vs Sell EPT: st APR >= ept APR

The settlement APR is the maker APR, meaning the older resting order’s APR.

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Slippage

ArcX supports slippage protection on market orders. In the UI, users can set a slippage tolerance so their final market-order result does not drift too far from the quoted APR. If liquidity changes too much before execution, the order can fail instead of filling at a worse outcome than the user accepted.

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Partial Fills and Cancels

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Limit orders

Limit orders can be:

• OPEN
• PARTIAL
• FILLED
• CANCELLED

If a limit order is partially filled:

• only the matched portion settles
• the unmatched remainder stays resting

If you cancel:

• only the unmatched remainder is unlocked
• already matched amounts stay settled

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Market orders

Market orders do not leave a resting remainder. They either execute immediately as one bounded transaction or fail.

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Self-Match Prevention

Users cannot match against their own resting orders. This is enforced both in the UI quote and in on-chain contracts.

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Worked Examples

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Example 1: Buy ST

Suppose:

• raw size = 100 vToken
• APR = 10%
• time remaining = 1 year

Then: $rt = 0.10$ $\text{ST size} = 100 \times 1.10 = 110 \text{ ST}$ Interpretation:

• you pay 100 vToken
• you receive 110 ST

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Example 2: Buy EPT

Suppose:

• raw size = 100 vToken
• APR = 10%
• time remaining = 1 year

Then: $rt = 0.10$ $\text{EPT size} = 100 \times \frac{1.10}{0.10} = 1100 \text{ EPT}$ Interpretation:

• you pay 100 vToken
• you receive 1100 EPT

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Related Reading

• Orderbook Guide for user-facing order intuition
• EPT Pricing for returns framing on the points side
• Credit Mathematics for how credits translate into points