Explore real-time simulations of stochastic processes used in quantitative finance. Watch price paths evolve as they stream from our simulation engine.
Constant volatility diffusion models with continuous price paths; analytically tractable but empirically limited.
Models where volatility itself is a random process, capturing volatility clustering and the leverage effect.
Models volatility as a mean-reverting stochastic process correlated with returns. Captures volatility clustering (high v...
Learn more →Rough volatility model where variance follows a fractional Volterra integral equation with Hurst exponent H < 0.5. The k...
Learn more →A Markov-modulated Heston model where all parameters evolve according to a hidden Markov chain representing market regim...
Learn more →Models with finite jump arrivals that extend GBM by allowing discontinuous price moves and event risk.
Extends GBM with compound Poisson jumps to capture sudden price movements from earnings announcements, market shocks, or...
Learn more →Uses asymmetric double-exponential distribution for jump sizes, allowing different characteristics for upward rallies vs...
Learn more →Combines Heston stochastic volatility with Merton-style jumps, providing the most realistic single-asset dynamics. Captu...
Learn more →The most comprehensive model: combines stochastic volatility with state-dependent jump intensity. Higher variance leads ...
Learn more →Pure-jump Lévy processes with infinite activity, capturing heavy tails and return asymmetry without a diffusion component.
A pure-jump Lévy process constructed via time-changed Brownian motion. Unlike Merton/Kou which add finite jumps to diffu...
Learn more →A pure-jump Lévy process constructed by subordinating Brownian motion with an Inverse Gaussian process. NIG provides sem...
Learn more →The most general tempered stable Lévy process, introduced by Carr, Geman, Madan, and Yor (2002). CGMY generalizes both V...
Learn more →Deterministic volatility models constructed to reproduce observed option prices; calibration-perfect but dynamically fragile.
A deterministic volatility model where the instantaneous volatility depends on both spot price and time: σ_loc(S, t). Un...
Learn more →A binomial tree model calibrated to match an implied volatility surface exactly at each node. Uses forward induction to ...
Learn more →Projects any stochastic volatility model to an equivalent local volatility surface using Gyöngy's lemma. The projected l...
Learn more →Combines local volatility with stochastic variance for the best of both worlds: exact fit to the implied volatility surf...
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Disclaimer: These simulations are for educational purposes only. They demonstrate the behavior of mathematical models and should not be used for trading decisions. Real market dynamics are significantly more complex than any single stochastic model can capture.