Covariance - Preserving SDE Transformations with Implications for ESG Simulation
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Document ID: 2006-615 (previously 2006/017)
Published on: 1st September 2006
Various ESG submodels can be described using (one or more) stochastic differential equations. A system of such equations can be formulated in more than one way. One formulation, involving correlated processes, is more relevant for model-building. Another formulation, involving independent Brownian motions, is more relevant for Monte Carlo simulation. This note shows how to relate the two representations by a suitable change of model coefficients. This note should be seen as an extension of a previous technical note (Tech Note 2006/16) since it merely allows for a scaling of the stochastic terms in the financial model.
