Module RNG 

Normal draw generation for Monte Carlo pricing.

Two samplers:

• Seeded pseudo-random (PCG64): reproducible across runs, with antithetic pairing and moment matching as variance reduction.
• Low-discrepancy (1-D Sobol, i.e. the van der Corput base-2 sequence) mapped through the inverse normal CDF — near-O(1/n) convergence for terminal-value (single-dimension) simulation.

Multi-dimensional (path-wise) draws use the seeded pseudo-random generator; proper multi-dimensional Sobol with a Brownian bridge is future work.

Structs

BrownianBridge

Brownian bridge path construction: the first draw fixes the terminal value, subsequent draws fill midpoints by bisection, so low-discrepancy coordinates are spent on the dimensions that matter most. Weights are precomputed once per pricing call and shared across paths.

QmcSequence

Multi-dimensional low-discrepancy sequence: Halton with prime bases and a deterministic Cranley-Patterson rotation per dimension (derived from the seed), mapped to standard normals through the inverse CDF.

Functions

path_normals

Standard normal draws for one path from its own stream.

path_rng

Deterministic, independent RNG stream for one simulation path — the basis of parallel path generation (each path seeds its own generator, so results are identical regardless of thread scheduling).

pseudo_normal_matrix

paths x steps matrix of seeded pseudo-random standard normals for path-wise simulation. Deterministic per seed.

pseudo_normals

n seeded pseudo-random standard normals with antithetic pairing and moment matching (mean 0, variance 1 exactly). Deterministic per seed.

sobol_normals

n low-discrepancy standard normal draws (1-D Sobol through the inverse normal CDF). Deterministic.