Brownian Bridge: Simulating Non-Linear Stochastic Differential Equations
Document ID: 2008-297 (previously Issue 1)
Published on: 30th June 2008
Author: Graeme Lawson
Within the ESG, we currently have a number of non-linear models that require sampling at a time-step that is often significantly smaller than the time-step permitted by the ESG. Examples include the local volatility equity model, and Cox-Ingersoll-Ross (CIR) model which is used to model both credit risk premiums, and to model volatility (variance) stochastically in the Stochastic Volatility Jump Diffusion Model (SVJD). (The SVJD is an equity model that is currently being developed for a future release of the ESG.) Sampling at a typical ESG time-step i.e. monthly or annual, can introduce non-trivial errors. These non-trivial errors imply that we will not generate the correct marginal distributions for the CIR, local volatility, and SVJD models
