Why Is the Constant Sum Formula Considered a "Linear" Pricing Model? ⎊ Path

Why Is the Constant Sum Formula Considered a “Linear” Pricing Model?

The constant sum formula (x+y=k) is considered a linear pricing model because it creates a straight-line pricing curve. The price of one asset in terms of the other is constant, regardless of the trade size.

This is because the formula dictates that for every one unit of asset x that is added to the pool, one unit of asset y must be removed to maintain the constant sum. This results in a 1:1 trading ratio, which is ideal for assets that are expected to have a perfectly stable price relationship, such as two stablecoins pegged to the same currency.

What Role Does the “K” Constant Play in the Constant Product Market Maker Formula?

How Does a Constant Sum Market Maker (X+y=k) Differ from a Constant Product AMM?

How Do Different AMM Formulas, like Constant Sum, Affect the Severity of Impermanent Loss?

How Do Hybrid AMM Models, like Curve’s StableSwap Invariant, Improve upon the Constant Product Formula for Stablecoin Trading?

Why Is a Futures Contract Considered a Linear Derivative While an Option Is Non-Linear?

What Is the Constant Sum Formula (X+y=k) and Why Is It Not Used Alone?

How Do Different AMM Models, like Balancer or Curve, Modify the Constant Product Formula?

How Does Market Sentiment Influence the Shape of the Cryptocurrency Futures Curve?

Glossar

Pricing Model

Model ⎊ A pricing model is a mathematical framework used to calculate the theoretical fair value of financial instruments, most notably options contracts.

Constant Sum Formula

Mechanism ⎊ The Constant Sum Formula, sometimes employed in specialized stablecoin AMMs, dictates that the sum of the reserves ($x + y = k$) remains fixed, implying a constant marginal price of one-to-one regardless of the trade size.