Resampling a time-series process: a method of estimating the probabilities associated with alternative plans for protecting pensions against inflation

Any pension protection formula that falls short of complete compensation for inflation has associated with it a time-series of probability distributions of future purchasing power losses. A method of estimating those distributions is proposed and applied. The method is based on the idea of representing inflation as a multivariate time-series process and using a model fitted to historical data to generate a large artificial sample of `realized' inflation sequences by means of a bootstrapping procedure. The purchasing power losses under a given protection plan can then be simulated for each inflation sequence and the sample distributions calculated.