What uncertainty are you trying to disturb?
A Monte Carlo procedure should begin with a specific uncertainty question: sequence order, trade sampling, parameter uncertainty, data-generation uncertainty, or another clearly defined source. Different procedures answer different questions even when every output is called “Monte Carlo.”
A simulation is a rule, repeated.
- Define the observed object and statistic you care about.
- Choose a randomization, resampling, or generative rule that represents the uncertainty being studied.
- Generate many alternative synthetic realizations under that rule.
- Recompute the statistic on every realization.
- Inspect the resulting distribution, including center, dispersion, tails, and failure regions.
Changing the resampling scheme changes the question.
Independent resampling
Sampling observations independently is simple, but it can remove sequence dependence that exists in the original data.
Block resampling
Sampling contiguous blocks can retain local ordering within each block. Block length becomes an assumption: blocks that are too short can erase dependence, while very long blocks reduce the number of effectively different rearrangements.
Permutation or shuffle tests
Shuffling can be useful when exchangeability under a null hypothesis is defensible. It is not a generic substitute for every time-series uncertainty question.
The main risk is pretending the simulation is assumption-free.
- Dependence: decide what serial or cross-sectional structure the procedure should preserve.
- Stationarity: decide whether the resampled history is treated as representative of the process being simulated.
- Block length / sampling unit: the unit being shuffled or resampled changes what information survives.
- Costs and constraints: simulated paths are not economically meaningful if material costs or constraints are omitted from the measured object.
- Selection: a Monte Carlo result performed after many candidate choices can inherit the selection process unless that process is included in the experiment.
Read the distribution as conditional evidence.
A percentile describes where an outcome sits inside the distribution generated by the chosen procedure. It is not, by itself, a probability that the future market will produce that outcome. Useful interpretation asks what assumptions were held fixed, what was randomized, and whether the failure region changes a research decision.
Common ways the picture becomes more confident than the evidence.
- Destroying meaningful dependence with an inappropriate shuffle.
- Using too few distinct observations or blocks and mistaking replicate count for information.
- Reporting only favorable percentiles while hiding the full distribution or failure tail.
- Choosing the simulation rule after seeing which rule gives the preferred result.
- Ignoring selection, costs, or constraints that materially shaped the original result.
One starting point, many illustrative paths.
The Research Lab path field begins every synthetic path from the same zero level and varies the generated increments. The resulting terminal distribution is useful for visualizing path uncertainty, but it intentionally does not claim to reproduce a market or a TraderCockpit result.
Open the synthetic path field →