💹 Simulations
Predator-Prey Model
Lotka–Volterra equations — the same differential equations that
describe supply and demand dynamics in markets.
Intermediate
SIR Spread Model
A contagion model analogous to financial panics and viral marketing.
Reproduction threshold R₀.
Intermediate
Travelling Salesman (TSP)
NP-hard optimisation corresponding to minimising transaction costs
in portfolio management.
Advanced
Stock Price — GBM
20 Geometric Brownian Motion trajectories: dS = μS·dt + σS·dW.
Adjust drift and volatility — watch bull/bear scenarios and the
lognormal price distribution.
Canvas 2D
Financial Bubble
Model boom-and-bust cycles using the Minsky-Kindleberger framework.
Watch price detach from fundamentals, fuel speculative mania, then
crash. Tune leverage, sentiment and fundamental value.
Canvas 2D
New
Options Pricing
Black-Scholes formula C = S·N(d₁) − K·e^(−rT)·N(d₂). Greeks: delta,
gamma, theta, vega — option sensitivity.
Canvas 2D
New
Bitcoin Mining
Proof-of-work and hash puzzle. Difficulty adjusts so a block is
found every 10 minutes regardless of hashrate.
Canvas 2D
New
Bank Run
Bank run in a fractional-reserve system. Linked banks and systemic
contagion risk during a crisis.
Canvas 2D
New
📐 Key Concepts
Geometric Brownian Motion
Stochastic differential equation dS = μS dt + σS dWt
models asset price. Solution: S(t) = S₀·exp((μ − σ²/2)t +
σWt). Foundation of Black-Scholes.
Black-Scholes Formula
Analytical call option pricing: C = S·N(d₁) − Ke^(−rT)·N(d₂).
Assumes GBM, no-arbitrage, and continuous hedging.
Nash Equilibrium
State in a game where no player can improve their outcome by
unilaterally deviating. Foundation of auction theory, cartel
analysis, and trade negotiations.
Value at Risk (VaR)
Maximum expected loss at confidence level α over time horizon T.
VaR₉₅% means: 95% chance of not losing more than X per day.
Efficient Market Hypothesis (EMH)
Prices reflect all available information. Weak (past prices),
semi-strong (public information), strong (insider) forms of market
efficiency.
Proof-of-Work
Finding nonce such that SHA256(block + nonce) starts with N zeros.
Difficulty N adjusts automatically every 2016 Bitcoin blocks.
📖 Learning Resources
🔗 Related Categories
💰 Financial simulations often use the same tools as
physical modelling — stochastic differential equations, Monte Carlo
methods, and agent-based models. Physicists Mandelbrot, Osborn, and
Black made enormous contributions to mathematical finance, transferring
physics methods to financial economics.
Key Concepts
Topics and algorithms you'll explore in this category
Interactive ModelReal-time browser simulation with live parameter controls
WebGL / Canvas 2DHardware-accelerated rendering in the browser
Mathematical FoundationDifferential equations and numerical integration
Open SourceMIT-licensed code — inspect, fork, and learn
No Install RequiredRuns directly in Chrome, Firefox, Safari, Edge
Educational FocusBuilt to explain the underlying science clearly
Frequently Asked Questions
Common questions about this simulation category
- Do these simulations require installation?
- No. Every simulation runs entirely in your web browser using WebGL and Canvas 2D. Nothing to install or download — open the page and the simulation starts immediately.
- Can I use these simulations for teaching?
- Yes — all simulations are designed to be educational and run without an account or login. They are widely used in university lectures, high-school science classes, and self-directed learning. Embed them via iframe or link directly.
- What devices do the simulations support?
- All simulations work on desktop browsers (Chrome, Firefox, Edge, Safari). Many work on mobile and tablets too, though some physics-heavy simulations benefit from the GPU performance of a desktop or laptop.