Linear Congruential Generators for Monte Carlo Simulation
Summary
The document explains how to separate random number generation from Monte Carlo pricing code through an abstract generator interface. It describes exposing seed controls, draw dimensionality, integer generation, and uniform samples so that downstream distribution classes can transform uniforms into Gaussian or other variates. This design supports reproducibility, multiple independent streams, and substitution of different generator types.
It then introduces the linear congruential generator (LCG), which updates a seed through a modular recurrence and scales the resulting integers into uniform draws. The example produces values in the open unit interval, illustrating the transformation. The article also notes that LCGs are periodic pseudorandom sequences and points to limitations and pitfalls in basic implementations. They may be useful for learning or simple simulation setups, but the discussion does not establish suitability for demanding production or high-quality Monte Carlo work; more advanced generators and sampling methods are mentioned as extensions.
Key ideas
- A shared generator interface can decouple uniform number production from Monte Carlo solvers and distribution transforms.
- Seed access and reset methods make runs reproducible and allow independent random streams.
- An LCG updates its state with a modular recurrence and maps integer outputs to uniform values.
- LCGs are periodic pseudorandom generators, so their statistical limitations should be considered.
- The article presents architecture and an example rather than a detailed quality assessment of the generator.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.