Work reduction in financial simulations

We investigate the possibility of efficiency gains from schemes that reduce the expected cost of a simulated path, which allows more paths given a fixed computational budget. Many such schemes impart bias, so we look at the bias-variance tradeoff in terms of mean squared error. The work reduction schemes we consider are fast numerical evaluation of functions, such as the exponential, as well as changes to simulation structure and sampling schemes. The latter include descriptive sampling, reducing the number of time steps, and dispensing with some factors in a multi-factor simulation. In simulations where computational budgets are tightly constrained, such as risk management and calibration of financial models, using cheaper, less accurate algorithms can reduce mean squared error.