Token Offering Simulation

Token Offering Simulation

Interactive analysis of three pricing models: Linear Bonding Curve, Power-Law Bonding Curve, and CPMM

What is This Simulation?

This tool simulates an arbitrage-driven token purchase strategy across three competing pricing mechanisms. The simulation allocates capital intelligently by always purchasing from the cheapest available source at each step, mimicking rational market behavior where buyers seek the best price [web:1][web:5].

You can experiment with different parameters to see how bonding curve characteristics and liquidity pool settings affect token distribution, pricing dynamics, and capital allocation across the three models [web:6][web:9].

How to Use This Tool

  • Adjust Parameters: Use the sliders or input boxes on the left to modify curve parameters (A, B), initial pool reserves (S_pool_initial, T_pool_initial), starting price (P0), and purchase parameters (Step Size, Total SOL)
  • Observe Dynamics: Watch how the simulation distributes your capital across the three models by always choosing the cheapest option at each step
  • Analyze Results: Review the charts to understand token accumulation, SOL allocation, and price evolution across all three mechanisms
  • Experiment: Try extreme values to understand edge cases and how different curve shapes respond to buying pressure

Parameter Guide

A (Linear Curve Slope): Controls how aggressively price increases in Model 1. Higher values mean steeper price growth per SOL invested [web:5][web:7].

B (Power Curve Exponent): Shapes the price curve in Model 2. Values below 1 create sublinear growth (slower price increases), while values above 1 create superlinear growth [web:3][web:7].

S_pool_initial & T_pool_initial: Set the initial reserves in the CPMM liquidity pool. Their ratio determines the starting price in Model 3 [web:6][web:9].

P0 (Starting Price): The initial token price for Models 1 and 2, measured in SOL per token [web:1][web:4].

Step Size: The amount of SOL spent per purchase iteration. Smaller steps provide smoother simulation but take longer to complete.

Total SOL: The total capital to be deployed across all three models through the arbitrage strategy.

Model 1: Linear Bonding Curve

Price Function:
\( P(S) = P_0 + A \cdot S \)
Token Integration:
\( Q = \frac{1}{A} \ln\left(\frac{P_0 + A \cdot S_{new}}{P_0 + A \cdot S_{old}}\right) \)

A linear bonding curve increases price at a constant rate as cumulative SOL invested grows. The slope parameter A determines how quickly prices rise. This model is predictable and transparent, making it suitable for projects seeking steady, controlled price appreciation [web:5][web:7].

Where: P = price, P₀ = initial price, A = slope coefficient, S = cumulative SOL invested, Q = tokens received.

Model 2: Power-Law Bonding Curve

Price Function:
\( P(S) = P_0 \cdot S^B \)
Token Integration:
\( Q = \frac{1}{P_0} \cdot \frac{S_{new}^{1-B} - S_{old}^{1-B}}{1 - B} \)

The power-law curve uses an exponent B to create non-linear price dynamics. When B < 1, the curve exhibits sublinear growth (diminishing price increases), rewarding early participants while maintaining accessibility. When B > 1, prices accelerate rapidly [web:4][web:10].

Where: P = price, P₀ = base multiplier, B = power exponent, S = cumulative SOL invested, Q = tokens received.

Model 3: Constant Product Market Maker (CPMM)

Invariant:
\( S_{pool} \cdot T_{pool} = k \)
Price Function:
\( P = \frac{S_{pool}}{T_{pool}} \)
Token Output:
\( T_{out} = T_{pool} - \frac{k}{S_{pool} + \Delta S} \)

The CPMM (like Uniswap) maintains a constant product of reserves. Price is determined by the ratio of SOL to tokens in the pool. As traders remove tokens, the ratio shifts and price increases. This creates organic price discovery through supply and demand [web:6][web:9].

Where: Spool = SOL reserves, Tpool = token reserves, k = constant product, P = instantaneous price, Tout = tokens received, ΔS = SOL added.

Simulation Parameters

Controls price increase rate in Model 1

Controls price curve shape in Model 2

Initial SOL in liquidity pool

Initial tokens in liquidity pool

Initial token price in SOL

SOL amount per purchase step

Total SOL to invest

Results Summary

Cumulative Tokens Minted

SOL Allocation Across Models

Price Evolution