[](https://crates.io/crates/stochastic-rs)
[](https://codecov.io/gh/dancixx/stochastic-rs)
# stochastic-rs
A high-performance Rust library for stochastic process simulation,
quantitative finance, statistics, copulas, distributions, and
neural-network volatility surrogates. Generic over `f32` / `f64`, with
SIMD acceleration on CPU and CUDA / Metal / Accelerate / cubecl backends
where they pay off, and first-class Python bindings via PyO3.
## Documentation
📖 **[stochastic.rust-dd.com](https://stochastic.rust-dd.com)** —
full docs site (Fumadocs + Next.js, deployed on Vercel).
Local preview from source under [`website/`](website/):
```bash
cd website
bun install
bun run dev # http://localhost:3000
```
Highlights:
- **120+ stochastic processes** — diffusion, jump, fractional / rough,
short-rate, HJM, LMM, fBM, Hawkes, Lévy. Generic-precision
`ProcessExt<T>` impl, SIMD on CPU, optional CUDA / Metal for FGN /
fBM.
- **Pricing & calibration** — closed-form (BSM, Bachelier, Black76,
Bjerksund-Stensland, …), Fourier (Heston / Bates / Merton-jump / Kou
/ VG / CGMY / HKDE / double-Heston), Monte Carlo (basket, rainbow,
cliquet, autocallable, spread), finite difference, Bermudan LSM,
Heston SLV. Heston / SABR / SVJ / Lévy / rough Bergomi / double-Heston
/ Hull-White swaption-grid calibrators.
- **Statistics & risk** — Hurst (Fukasawa), MLE for 1-D diffusions
with 6 transition densities, ADF / KPSS / Phillips-Perron, realised
variance with BNHLS bandwidth, HMM, changepoint, particle filter, UKF.
VaR / CVaR / drawdown, Sharpe / Sortino / IR / Calmar.
- **Fixed income & credit** — yield-curve bootstrapping, Nelson-Siegel /
Svensson, multi-curve, IRS / inflation swaps, Vasicek / CIR /
Hull-White / G2++ short-rate engines, Merton structural model,
reduced-form survival curves, CDS pricing, JLT migration matrices.
- **Microstructure** — Almgren-Chriss, Kyle (1985), Bouchaud propagator,
full price-time priority order book.
- **Distributions & copulas** — 19 SIMD distributions with
closed-form pdf / cdf / cf / moments. Clayton / Frank / Gumbel /
Independence bivariate; Gaussian / vine multivariate.
- **Python bindings** — 210 entries (198 PyO3 classes + 12 functions)
spanning every sub-crate except AI surrogates. Numpy-in / numpy-out.
## Installation
### Rust
```toml
[dependencies]
stochastic-rs = "2.0.0"
```
```rust
use stochastic_rs::prelude::*;
use stochastic_rs::stochastic::diffusion::gbm::Gbm;
use stochastic_rs::quant::pricing::heston::HestonPricer;
```
For per-sub-crate (lean) builds, OpenBLAS / CUDA / Metal / cubecl /
Accelerate feature flags, native CPU optimisation, and SIMD details,
see the [installation guide](https://stochastic.rust-dd.com/docs/getting-started/installation-rust)
on the docs site.
### Python
```bash
pip install stochastic-rs
```
Source build (requires the Rust toolchain):
```bash
pip install maturin
maturin develop --release --manifest-path stochastic-rs-py/Cargo.toml
```
Linux (x86_64 / aarch64) and macOS (arm64 / x86_64) wheels ship with
the `openblas` feature on. The Windows wheel omits the 15
BLAS-backed classes; everything else (≈195 classes / 12 functions)
works identically. See the
[Python bindings page](https://stochastic.rust-dd.com/docs/python) for the parity
table and the source-build path with vcpkg.
## Quickstart
```rust
use stochastic_rs::prelude::*;
use stochastic_rs::stochastic::diffusion::ou::Ou;
use stochastic_rs::quant::pricing::heston::HestonPricer;
use stochastic_rs::quant::types::OptionType;
fn main() {
// Mean-reverting OU path
let p = Ou::<f64>::new(2.0, 0.0, 1.0, 1_000, Some(0.0), Some(1.0));
let path = p.sample();
// Heston European call with first- and second-order Greeks
let pricer = HestonPricer::<f64>::new(
100.0, 100.0, 1.0, 0.03, 0.0,
0.04, 2.0, 0.04, 0.3, -0.5,
);
let price = pricer.price(OptionType::Call);
let greeks = pricer.greeks(OptionType::Call);
println!("call={:.4}, delta={:.4}, vega={:.4}", price, greeks.delta, greeks.vega);
}
```
```python
import stochastic_rs as srs
# Mean-reverting OU path
p = srs.Ou(theta=2.0, mu=0.0, sigma=1.0, n=1000, x0=0.0, t=1.0)
path = p.sample() # numpy.ndarray, shape (1000,)
# Heston European call
pricer = srs.HestonPricer(
s0=100, k=100, tau=1.0, r=0.03, q=0.0,
v0=0.04, kappa=2.0, theta=0.04, sigma=0.3, rho=-0.5,
)
print("call =", pricer.price("call"))
g = pricer.greeks("call")
print(f"delta={g.delta:.4f}, vega={g.vega:.4f}")
```
More end-to-end recipes (Heston calibration, fBM Hurst estimation,
vol-surface from quotes, Python interop) live in the
[tutorials section](https://stochastic.rust-dd.com/docs/tutorials).
## Benchmarks
### FGN — CPU vs CUDA native (`f32`, H = 0.7)
```bash
cargo bench --features cuda-native --bench fgn_cuda_native
```
Single path:
| 1,024 | 8.1 µs | 46 µs| 0.18× |
| 4,096 | 35 µs | 84 µs| 0.42× |
| 16,384 | 147 µs | 110 µs| **1.3×** |
| 65,536 | 850 µs | 227 µs| **3.7×** |
Batch:
| 4,096, 32 | 147 µs | 117 µs | **1.3×** |
| 4,096, 512 | 1.78 ms | 2.37 ms | 0.75× |
| 65,536, 128 | 12.6 ms | 10.5 ms | **1.2×** |
| 65,536, 1 k | 102 ms | 93 ms | **1.1×** |
CUDA wins for large `n` (≥ 16 k); CPU rayon dominates for medium `n`
because of the GPU launch / transfer overhead.
### Distribution sampling — multicore (`cargo bench --bench dist_multicore`)
`sample_matrix`, 1-thread vs 14-thread rayon. `f64` continuous, integer
discrete. Most distributions: `1024 × 1024`; heavy discrete: `512 × 512`.
| Normal | 1.78 | 0.34 | 5.28× |
| Cauchy | 6.23 | 0.90 | 6.96× |
| LogNormal | 5.07 | 0.81 | 6.25× |
| Gamma | 5.20 | 0.72 | 7.19× |
| StudentT | 7.89 | 1.89 | 4.18× |
| Beta | 11.85 | 1.68 | 7.04× |
| Weibull | 13.17 | 1.73 | 7.59× |
| AlphaStable | 42.52 | 5.36 | 7.94× |
| Poisson | 2.28 | 0.42 | 5.40× |
| Hypergeo (512²) | 20.99 | 2.76 | 7.60× |
(Full table — 18 distributions — on the
[benchmarks page](https://stochastic.rust-dd.com/docs/benchmarks).)
`Normal` single-thread `fill_slice` vs the upstream `rand_distr` baseline:
- vs `rand_distr + SimdRng` — ≈ **1.21×** to **1.35×**
- vs `rand_distr + rand::rng()` — ≈ **4.09×** to **4.61×**
## Contributing
Contributions are welcome — bug reports, feature suggestions, or PRs.
Open an issue or start a discussion on GitHub. Per-feature recipes
(`add-diffusion-process`, `adding-distribution`, `calibration-pattern`,
`docs-writing`, …) live under [`.claude/skills/`](.claude/skills/).
## License
MIT — see [LICENSE](https://github.com/dancixx/stochastic-rs/blob/main/LICENSE).