Write an SDE, discretize it, and see the distribution of its solutions and their sensitivities.

About sItô

sItô compiles parametric stochastic differential equations into fast Monte Carlo simulations. You write the drift and the diffusion of a system of Itô or Stratonovich equations, in one or several dimensions, and choose what to look at: fans of paths over time, the distribution of the final values, averages, quantiles, and their sensitivities to the parameters (the Greeks). You also select from five discretization schemes.

To start, pick one of the pre-defined models, or Your own; choose the statistics you want to see; press Run simulation. This is a demo with limits on size and cost; the demo limit badges beside the fields list them.

Read more about sItô. Made by .

All models

Pick one: it fills the form, ready to run.

Finance

Equity and FX

Rates and bonds

Commodities

Path-dependent options and credit

Physics

Biology

Demo limits

These are the restrictions of this demo. They keep each request cheap on a shared server.

Paths
250 to 10000
Time steps
100 to 4000, and paths × steps at most 1,000,000: a run costs about the same time for the same product, whatever the horizon.
Horizon T
1, 2, 5, 10, 20, 40. The time step is T / steps: a coarse step is yours to judge, with a hint when it is large for Euler.
Trajectory run
When every statistics line is a Path of two or three expressions: 5 paths and 1000, 2000, 4000 steps, without sensitivities.
State variables
up to 3
Noise terms
up to 3 (the columns of the diffusion matrix)
Parameters
up to 8
Statistics
up to 4 lines
Size of a formula
500 characters per field and 200 operations per expression
Cost and memory
a request whose estimated memory is above 300 MB, or whose cost is too high, is refused with the figures
Queue
one simulation at a time for each visitor and a queue of 5; a simulation is stopped after 30 s
Model
Set initial values and parameters
Initial state
Parameters
Transform the process with Itô's lemma
Statistics
Statistics you can use
  • every path, drawn as a distribution
  • the value at the final time, one per path
  • two states against each other: a few paths in the plane
  • two final values together: their joint distribution
  • ∂average over paths, per time
  • ∂variance over paths, per time
  • ∂standard deviation over paths
  • ∂a quantile over paths
  • ∂a single number
  • running maximum of each path
  • running minimum of each path
  • time integral along each path
  • time each path first meets a condition
  • ∂share of paths meeting a condition

supports sensitivities

Simulation
10K
100
1

Precision
Hardware

Model loaded from the link. Press Run simulation to see its results.

Model loaded from the link. Press Run simulation to see the results.