Generating Correlated Gaussian Paths with Cholesky for Monte Carlo Pricing

Summary

This article explains how to generate correlated standard-normal draws for simulating multiple asset paths. Its motivating application is the Heston stochastic-volatility model, where the asset and variance processes are driven by Brownian motions with a specified correlation. The basic construction combines an independent normal draw with a draw from another series, weighted by the target correlation and its complementary scale. For multiple assets, the corresponding matrix operation is a Cholesky factorization of the correlation matrix.

A C++ example derives one correlated stream from an existing stream and demonstrates paired draws at a stated correlation of 0.5. The article also notes that a production implementation would centralize random-number generation and use an efficient matrix routine with a precomputed Cholesky factor. The code illustrates the two-series case rather than a general robust simulation framework; the article does not validate distributional accuracy statistically or present option-pricing results. Its purpose is to establish a building block for later Monte Carlo work, including Heston simulations.

Key ideas

• Correlated stochastic drivers are needed to simulate the asset and variance processes in the Heston model.
• A second standard-normal stream can be formed by mixing an independent stream with a reference stream according to the target correlation.
• For several assets, Cholesky factorization maps independent normal draws through the correlation structure.
• The C++ demonstration uses a two-series example and identifies matrix-based implementation as a more scalable approach.
• The example presents simulation mechanics but does not report pricing validation or strategy performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.