Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. Because the resulting liabilities are very long-lived and the short-term performance of the assets backing these liabilities may trigger important losses, it is thus a desired feature of an ESG to replicate equity returns over such horizons. In light of this horizon duality, we investigate the relevance of jumps in ESGs to replicate dynamics over different horizons and compare their performance to popular models in actuarial science. We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using a generalized method of moments–based approach, however, we find that simple jump-diffusion models have an excellent fit overall (moments and the entire distribution) at different timescales. We also investigate three typical applications: the value of $1 accumulated with no intermediate monitoring, a solvency analysis with frequent monitoring, and a dynamic portfolio problem. We find that jumps have long-lasting effects that are difficult to replicate otherwise, so, yes, jumps do matter in the long term.

股票的经济情景生成器 (ESG) 是人寿保险和养老金计划估值和风险管理过程的重要组成部分。由于由此产生的负债是长期存在的，并且支持这些负债的资产的短期表现可能会引发重大损失，因此在这些期限内复制股权回报是 ESG 的理想特征。鉴于这种视野二元性，我们研究了 ESG 跳跃与在不同视野中复制动态的相关性，并将其性能与精算科学中的流行模型进行比较。我们表明，如果以最大似然估计，跳跃扩散模型无法复制更高的矩。然而，使用基于矩的方法的广义方法，我们发现简单的跳跃扩散模型在不同的时间尺度上具有很好的整体拟合（矩和整个分布）。我们还研究了三个典型应用：没有中间监控的累积 1 美元的价值、频繁监控的偿付能力分析和动态投资组合问题。我们发现跳跃具有难以复制的长期影响，因此，是的，跳跃从长远来看确实很重要。