Simulation parameters
Monte Carlo Sandbox
Running…
The adaptive and fixed monitors receive the same number of samples on every path. The experiment therefore compares sample placement—not computational cost.
How the Monte Carlo comparison works
- Simulate: generate independent GBM or Merton jump-diffusion price paths on a fine grid.
- Mark events: record each path's first lower- and upper-barrier crossing.
- Allocate samples: adaptive intervals shrink near the closest barrier; the fixed monitor receives the same sample count, spaced uniformly.
- Score: an event is detected when a sampled price remains beyond the barrier within the selected deadline.
The headline compares detections and mean lag under an equal sample budget. The miss budget ε is a local diffusion-model design parameter, not a global guarantee.
Raw result JSON
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How to read it
- Open cyan circles
- Adaptive observations. The interval shrinks quadratically as the log-price approaches the nearer barrier.
- Grey dots
- An equal-budget fixed sampler with the same number of observations on each path, spaced uniformly.
- Red × and green ▲
- The first lower- and upper-barrier events on the fine reference grid.
- Headline
- Same paths and the same sample budget. Compare how many events each schedule confirms before the deadline.
Research demo caveat
The adaptive law is derived from a continuous diffusion model. Discrete grids, estimated volatility, latency, and jumps weaken any literal miss-probability guarantee.
How this works
The app simulates price paths, marks first barrier crossings, and compares two observation schedules on exactly the same paths.
Adaptive intervals use a Brownian-bridge proxy and shrink with squared distance to the nearest barrier. Fixed observations are either equal-budget or independently spaced at a chosen cadence.