Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. As the resulting liabilities are very long-lived, it is a desired feature of an ESG to replicate equity returns over such horizons. However, the short-term performance of the assets backing these liabilities may also trigger significant losses and in turn affect the financial stability of the insurer or plan. Therefore, the ESG must replicate both short- and long-term stock price dynamics consistently.

We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using the generalized method of moments (GMM), we find that simple jump-diffusion models or regime-switching models (with at least three regimes) have an excellent fit for various moments observed at different time scales. Finally, we investigate three typical actuarial applications.