Generating Correlated Synthetic Asset Paths with Cholesky Decomposition
Summary
The document describes a framework for generating synthetic correlated asset-price paths by combining a correlation-matrix generator with individual time-series models. Independent standard normal shocks are transformed using a matrix factorization so that each asset’s shocks retain standard normal marginal distributions while reflecting the selected cross-asset correlation structure. The correlated shocks are then supplied to each model to produce paths, with the generated correlation matrix returned for diagnostics.
If Cholesky factorization fails, the implementation falls back to an eigenvalue decomposition and adjusts negative eigenvalues to create a usable matrix square root. The article also outlines extensible classes that allow different correlation structures and time-series models to be mixed, and illustrates paths from geometric Brownian motion and jump-diffusion examples. This is a synthetic-data and simulation method, not evidence that the generated paths reproduce real market behavior. The fallback adjustment can alter the intended correlations, and the realism of outputs depends on the chosen models and input correlation matrix.
Key ideas
- Multiplying independent normal shocks by a Cholesky factor imposes a specified correlation structure.
- Each asset can use a different time-series model while sharing a generated cross-asset shock structure.
- An eigenvalue-based matrix square root provides a fallback when Cholesky factorization fails.
- The generated paths and correlation matrix can be inspected together for diagnostics.
- Synthetic paths depend on the assumed correlation generator and asset models, so they do not establish real-market validity.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.