QuantScenarioBench/qsb-black-scholes

QuantScenarioBench — Black-Scholes Benchmark Dataset

This dataset is a representative benchmark sample generated by [QuantScenarioBench](https://github.com/tim-nish/QuantScenarioBench), a JAX-native framework for reproducible stochastic market scenario generation.

It contains 10,000 independent asset-price paths simulated under the Black-Scholes (Geometric Brownian Motion) model over 252 daily time steps (1 year horizon).

Need a larger or custom dataset? This file is a fixed benchmark sample. To generate datasets at any scale — more paths, different parameters, non-uniform time grids, or other market models — use the QuantScenarioBench library directly: ``python pip install quantscenariobench `` See the GitHub project for full documentation and examples.

Model Description

The Black-Scholes model (Black & Scholes, 1973) describes the evolution of an asset price $S_t$ under Geometric Brownian Motion:

$$dSt = \mu\,St\,dt + \sigma\,St\,dWt$$

where $W_t$ is a standard Brownian motion. The model has constant drift $\mu$ and constant volatility $\sigma$.

This is the simplest and most widely used continuous-time model for equity prices. It produces log-normal returns with no volatility clustering or skew.

Parameters used for this dataset

The risk-neutral setting (mu=0) makes ATM option prices directly comparable across models in this benchmark suite.

Simulation Configuration

Column Schema

All QuantScenarioBench datasets share the same 12-column schema regardless of the market model used. This enables direct cross-model comparison by loading datasets with identical code.

Usage

from datasets import load_dataset
import numpy as np

ds = load_dataset("QuantScenarioBench/qsb-black-scholes", split="train")

# Each row is one simulated path
row = ds[0]
prices = np.array(row["observation"])   # shape (253,)
print(f"S0={prices[0]:.2f}  S_T={prices[-1]:.2f}")

# Stack all paths into a numpy array
all_paths = np.stack([ds[i]["observation"] for i in range(len(ds))])
print(all_paths.shape)   # (10000, 253)

Cross-model comparison

All three benchmark datasets share the same schema and time grid:

bs  = load_dataset("QuantScenarioBench/qsb-black-scholes",  split="train")
h   = load_dataset("QuantScenarioBench/qsb-heston",          split="train")
rb  = load_dataset("QuantScenarioBench/qsb-rough-bergomi",   split="train")

# Compare terminal distributions
import numpy as np
for name, ds in [("BS", bs), ("Heston", h), ("rBergomi", rb)]:
    terminals = np.array([ds[i]["observation"][-1] for i in range(len(ds))])
    print(f"{name:10s}  mean={terminals.mean():.2f}  std={terminals.std():.2f}")

Generate a custom dataset

from quantscenariobench.api import simulate
from quantscenariobench.export import export_parquet, publish_to_hub
from quantscenariobench.interface import TimeGrid
from quantscenariobench.models import BlackScholes
import jax.numpy as jnp

model    = BlackScholes(mu=0.0, sigma=0.3, S0=100.0)   # 30% vol
tg       = TimeGrid(jnp.linspace(0.0, 2.0, 505))       # 2-year horizon
scenario = simulate(model, tg, n_paths=100_000, seed=99)

export_parquet([scenario], "my_bs_dataset.parquet")
# or: publish_to_hub([scenario], "my-org/my-bs-dataset")

Reproducibility

Simulation paths are bit-identical across runs on the same computational backend when using the same seed, library_version, and model parameters.

Cross-backend bit-identity is not guaranteed. JAX floating-point operations may produce different bit patterns across hardware backends (CPU, GPU, TPU) even with identical inputs. The seed, prng_key_info, and library_version columns document full provenance so that any differences can be traced to backend changes rather than parameter or code drift.

Related Datasets

All three datasets use the same time grid, seed, and initial spot for direct cross-model comparison.

Citation

If you use this dataset or QuantScenarioBench in your research, please cite the GitHub repository.