4. Spot Price Calculation

The spot price is a theoretical or reference price based on the current state of the pool, including the weights and volumes of the tokens. It provides market participants with an indicative price that reflects the conditions under stable, non-transactional scenarios (infinitesimal swap).

The spot price is directly influenced by the volume of tokens in the pool, meaning it is affected by all past and current transactions conducted by Project Backers. Each time a $Token_{Traded}$ is exchanged for a $Token_{Anchor}$, the price of the $Token_{Traded}$ increases, highlighting the dynamic nature of the liquidity pool.

4.1. Mathematical Foundations

The weights of both Tokens adjust over time, directly affecting their pricing within the pool. Typically, as $Weight_{Traded}$ decreases, the price of $Token_{Traded}$ in terms of $Token_{Anchor}$ decreases.

This graph illustrates the evolution of the spot price over time within a Liquidity Bootstrapping Pool under the assumption that the volumes of the tokens ($Volume_{Traded}$ and $Volume_{Anchor}$) remain constant.

The spot price history serves as a guide for traders to anticipate price movements.

$SpotPrice_{Traded} = \frac{Volume_{Anchor}}{Volume_{Traded}} \times \frac{Weight_{Traded}}{Weight_{Anchor}}$

Where

• $SpotPrice_{Traded}$ : Spot price of $Token_{Traded}$ in terms of TokenAnchor.

• $Volume_{Traded}$​ : Current volume of $Token_{Traded}$ in the pool before the transaction.

• $Volume_{Anchor}$​ : Current volume of $Token_{Anchor}$ in the pool before the transaction.

• $Weight_{Traded}$​ : Current weight of $Token_{Traded}$ in the pool.

• $Weight_{Anchor}$​ : Current weight of $Token_{Anchor}$ in the pool.