Definitions & Terminology

The "Definitions & Terminology" section serves as a comprehensive guide to the key terms, concepts, and constructs used within our automated trading platform. It is designed to empower developers by p

Trade Related

• Trade: A pair of buy and sell orders placed around a common reference price, positioned above and below it.

• Fluctuating Component: A signal or indicator that aligns and moves in response to market trends and patterns.

• Completion of an Order: The point at which an order is fully executed in the market.

• Completion of a Trade: The successful execution of all orders associated with a specific trade.

• Base Asset: The primary asset in a trading pair, such as BTC or ETH, representing the component being traded.

• Quote Asset: The secondary asset in a trading pair that is used to express the value of the base asset, such as USDT or BUSD.

• Open Trade: A trade that has only been partially completed, with at least one order executed.

• Pending Trade: A trade in which none of the associated orders have been executed.

• Pending Order: An order that has been placed but has not yet been executed.

---

Parameters & Variables

• $\text{total\_value}_{\text{init}}$ - Total initial asset value

• $\text{base\_amount}_{\text{init}}$ - Initial base asset amount

• $\text{base\_value}_{\text{init}}$ - Initial base asset value (in quote asset units)

• $p_{\text{init}}$ - Initial quote asset price

• $\text{quote\_value}_{\text{init}}$ - Initial quote asset value

• $\text{total\_value}_{\text{close}}$ - Total closing asset value

• $\text{base\_amount}_{\text{close}}$ - Closing base asset amount

• $\text{base\_value}_{\text{close}}$ - Closing base asset value (in quote asset units)

• $p_{\text{close}}$ - Closing quote asset price

• $\text{quote\_value}_{\text{close}}$ - Closing quote asset value

• $\text{mm\_gain}$ - Market-making gain (quote asset gain from completed trades → completed buy-sell pairs)

• $\Delta \text{quote\_value}$ - Quote asset difference

• $\Delta \text{base\_amount}$ - Base asset amount difference

• $\Delta \text{base\_value}$ - Base asset value difference (in quote asset units)

• $\Delta \text{total\_value}$ - Total asset value difference

• $\Delta p$ - Price difference ($p_{\text{close}} - p_{\text{init}}$)

• $\text{half\_buy\_amount}_{\text{base}}$ - Bought base asset amount of open trades (a trade with only the buy order has been executed)

• $\text{half\_buy\_spent}_{\text{quote}}$ - Spent quote asset value of open trades (a trade with only the buy order has been executed)

• $\text{half\_sell\_amount}_{\text{base}}$ - Sold base asset amount of open trades (a trade with only the sell order has been executed)

• $\text{half\_sell\_earned}_{\text{quote}}$ - Earned quote asset value of open trades (a trade with only the sell order has been executed)

• $\text{Fee}_{\text{maker}}$ - Maker fee

• $\text{Fee}_{\text{taker}}$ - Taker fee

---

Equations

Total initial and closing equity:

$$\text{total\_value}_{\text{init}} = \text{base\_value}_{\text{init}} + \text{quote\_value}_{\text{init}} \quad (1)$$

$$\text{total\_value}_{\text{close}} = \text{base\_value}_{\text{close}} + \text{quote\_value}_{\text{close}} \quad (2)$$

Initial base asset:

$$\text{base\_value}_{\text{init}} = \text{base\_amount}_{\text{init}} p_{\text{init}} \quad (3)$$

Closing base asset:

$$\text{base\_value}_{\text{close}} = \text{base\_amount}_{\text{close}} p_{\text{close}} \quad (4)$$

Since completed order pair will not add/remove a resultant base asset (buy_size = sell_size),

$$\text{base\_amount}_{\text{close}} = \text{base\_amount}_{\text{init}} + \text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}} \quad (5)$$

$$\text{base\_value}_{\text{close}} = \left(\text{base\_amount}_{\text{init}} + \text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}\right) p_{\text{close}} \quad (6)$$

Closing quote assets: Mm_gain is the profit by completing an order pair,

$$\text{quote\_value}_{\text{close}} = \text{quote\_value}_{\text{init}} - \text{half\_buy\_spent}_{\text{quote}} + \text{half\_sell\_earned}_{\text{quote}} + \text{mm\_gain} \quad (7)$$

Base Asset Gain:

$$\text{gain}_{\text{base}} = \text{base\_value}_{\text{close}} - \text{base\_value}_{\text{init}} \quad (8)$$

From (8), (6), (3),

$$\text{gain}_{\text{base}} = (\text{base\_amount}_{\text{init}} + \text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}) p_{\text{close}} - \text{base\_amount}_{\text{init}} p_{\text{init}} \quad (9)$$

$$\text{gain}_{\text{base}} = \text{base\_amount}_{\text{init}} (p_{\text{close}} - p_{\text{init}}) + (\text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}) p_{\text{close}} \quad (10)$$

Quote Asset Gain:

$$\text{gain}_{\text{quote}} = \text{quote\_value}_{\text{close}} - \text{quote\_value}_{\text{init}} \quad (11)$$

From (11), (7),

$$\text{gain}_{\text{quote}} = (\text{quote\_value}_{\text{init}} - \text{half\_buy\_spent}_{\text{quote}} + \text{half\_sell\_earned}_{\text{quote}} + \text{mm\_gain}) - \text{quote\_value}_{\text{init}} \quad (12)$$

$$\text{gain}_{\text{quote}} = \text{mm\_gain} + \text{half\_sell\_earned}_{\text{quote}} - \text{half\_buy\_spent}_{\text{quote}} \quad (13)$$

Equity Gain:

$$\text{gain}_{\text{total}} = \text{gain}_{\text{base}} + \text{gain}_{\text{quote}} \quad (14)$$

From (10), (13),

$$\text{gain}_{\text{total}} = \text{base\_amount}_{\text{init}} (p_{\text{close}} - p_{\text{init}}) + (\text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}) p_{\text{close}} + (\text{half\_sell\_earned}_{\text{quote}} - \text{half\_buy\_spent}_{\text{quote}}) + \text{mm\_gain} \quad (15)$$

• $\text{gain1} = \text{base\_amount}_{\text{init}} (p_{\text{close}} - p_{\text{init}})$ - gain/loss due to the holding of the base asset

• $\text{gain2} = (\text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}) p_{\text{close}}$ - base asset mismatch due to open trades/pending orders

• $\text{gain3} = (\text{half\_sell\_earned}_{\text{quote}} - \text{half\_buy\_spent}_{\text{quote}})$ - quote asset mismatch due to open trades/pending orders

• $\text{gain4} = \text{mm\_gain}$ - market-making gain from completed trades

$$\text{gain}_{\text{total}} = \text{holding\_cost} + \text{pending\_component} + \text{mm\_gain} \quad (16)$$

Gain1 - Holding Cost

• Definition: Represents gains or losses resulting from holding the base asset.

• Market Impact:

  • Bullish Conditions: Gains are realized when the value of the base asset increases.

  • Bearish Conditions: Losses occur when the value of the base asset decreases.

• Significance: This is the first component contributing to inventory risk, as fluctuations in the base asset's value directly affect overall asset performance.

Gain2 and Gain3 - Pending Component

• Definition: Refers to the impact of pending orders or open trades on asset valuation.

• Resultant Effect: Often leads to a loss due to unresolved trades.

• Inventory Risk: This is the second major component contributing to inventory risk.

Gain2 - Base Asset Mismatch Due to Open Trades

• Description: Represents changes caused by open trades involving the base asset.

  • Buy Order Execution: If only the buy order is executed, this term increases as more base assets are acquired.

  • Sell Order Execution: If only the sell order is executed, this term decreases as base assets are sold off.

• Significance: This component contributes to the pending component by highlighting the imbalance in base asset positions during open trades.

Gain3 - Quote Asset Mismatch Due to Open Trades

• Description: Reflects changes related to open trades involving the quote asset.

  • Buy Order Execution: If only the buy order is executed, this term decreases since quote assets are spent.

  • Sell Order Execution: If only the sell order is executed, this term increases as quote assets are received.

• Significance: Like Gain2, this component contributes to the pending component by capturing the mismatch in quote asset holdings during open trades.

$$\text{pending\_component} = (\text{half\_buy\_amount}_{\text{base}} - \text{half\_sell\_amount}_{\text{base}}) p_{\text{close}} + (\text{half\_sell\_earned}_{\text{quote}} - \text{half\_buy\_spent}_{\text{quote}}) \quad (17)$$

Rearranging (17),

$$\text{pending\_component} = (\text{half\_buy\_amount}_{\text{base}} p_{\text{close}} - \text{half\_buy\_spent}_{\text{quote}}) + (\text{half\_sell\_earned}_{\text{quote}} - \text{half\_sell\_amount}_{\text{base}} p_{\text{close}}) \quad (18)$$

If pending buy orders get accumulated (only the sell part of trades gets executed more often),

Gain4 - Market-Making Gain (mm_gain)

• Definition: Represents gains earned through market-making activities from completed trades.

• Mechanism: Involves placing a buy-sell order pair of the same size, with the buy price set lower than the sell price. This approach ensures a profit is generated through the difference (spread) between the buy and sell prices when both orders are successfully executed.

• Significance: This gain highlights the profitability of market-making strategies and reflects the effectiveness of capturing spreads between orders as a key component of trading performance.

Rearranged Aggregated Gain Components: Here, we have rearranged some of the aforementioned components for the sake of representation and ease.

$$\text{half\_buy\_component} = (\text{half\_buy\_amount}_{\text{base}} p_{\text{close}} - \text{half\_buy\_spent}_{\text{quote}}) \quad (19)$$

$$\text{half\_sell\_component} = (\text{half\_sell\_earned}_{\text{quote}} - \text{half\_sell\_amount}_{\text{base}} p_{\text{close}}) \quad (20)$$

$$\text{pending\_component} = \text{half\_buy\_component} + \text{half\_sell\_component} \quad (21)$$

$$\text{net\_mm\_gain} = \text{pending\_component} + \text{mm\_gain} \quad (22)$$

$$\text{resultant\_gain} = \text{holding\_component} + \text{net\_mm\_gain} \quad (23)$$

$$\text{big\_bulls\_mm\_gain} = \text{half\_sell\_component} + \text{mm\_gain} \quad (24)$$

Note: \text{big_bulls_mm_gain} is a measure favoring long-term bullish behavior in the market. Therefore, we ignore the \text{half_buy_component} from the \text{net_mm_gain} equation since having extra base asset (BTC) in hand will benefit in long-term bullish conditions.

---

Different Market Confitions and Behaviours

Factors Reducing Total Equity Value:

• Pending Component: When the majority of pending orders or open trades are positioned against the direction of market profit.

  • Bearish Market Impact: The value of the base asset declines, resulting in reduced equity value.

Bear Markets:

• Objective: Aim to accumulate more quote assets.

• Impact on Holding Cost:

  • The decline in base asset prices turns the holding cost into a loss.

• Trade Behavior:

  • More sell orders remain pending while buy orders get executed frequently, leading to an accumulation of base assets and a reduction in quote assets.

  • Result: Loss

• Market-Making Impact:

  • Expected gains from market-making activities are reduced due to pending orders, leading to a loss.

Bull Markets:

• Objective: Aim to accumulate more base assets.

• Impact on Holding Cost:

  • The increase in base asset prices turns the holding cost into a gain.

• Trade Behavior:

  • More buy orders remain pending while sell orders get executed frequently, resulting in the accumulation of quote assets and a reduction in base assets.

  • Result: Loss

• Market-Making Impact:

  • Expected gains from market-making activities are reduced due to pending orders, leading to a loss.

Ranging Markets:

• Holding Cost:

  • This component does not dominate the overall behavior, resulting in a neutral effect.

• Pending Orders:

  • Minimal pending orders, with trades getting completed more frequently, leading to a neutral effect.

• Market-Making Gains:

  • Maximized gains from market-making activities.