Temporal aggregation of equity return time-series models

With large volatility observed in stock markets around the world over the last few years, many actuaries are now being urged to employ stochastic models to measure the solvency risk generated from insurance products with equity-linked guarantees. There are a large number of potential stochastic models for equity returns. Insurance regulators, both in Europe and North America, normally do not restrict the use of any stochastic model that reasonably fits the historical baseline data. However, in the U.S. and Canada, the final model must be calibrated to some specified distribution percentiles. The emphasis of the calibration process remains on the tails of the equity return distribution over different holding periods. In this paper, we examine the effect of temporal aggregation on classes of stochastic equity return models that are commonly used in actuarial practice. The advantages of choosing a closed (under temporal aggregation) class of processes for modelling asset returns and equity-linked guarantees are discussed. Actuarial applications of temporal aggregation using S&P500 data are given.