Free lesson · DeFi models

Concentrated liquidity and range boundaries

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Concentrated liquidity deploys inventory only within a selected price interval. Narrow ranges create greater exposure changes and can become entirely one asset.

Define quote-per-base price p and bounds a

The formulas here describe one idealized range position using liquidity L and continuous prices. Actual token decimals, discrete ticks and rounding must be applied for a protocol implementation.

Apply it in a strategy

• Compare range width, inventory concentration and the cash cost of moving a range after price changes.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Leaving the range can stop fee participation while retaining a one-sided asset exposure.

Research deliverable

Build and explain a concentrated liquidity and range boundaries worksheet. Compare range width, inventory concentration and the cash cost of moving a range after price changes.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
from math import sqrt
def range_inventory(liquidity,price,lower,upper):
    if liquidity<0 or not 0<lower<upper or price<=0: raise ValueError("Invalid range")
    p=min(upper,max(lower,price))
    return liquidity*(1/sqrt(p)-1/sqrt(upper)),liquidity*(sqrt(p)-sqrt(lower))

print(range_inventory(100,4,1,9))