Abstract
This paper studies how recursive training on synthetic data affects the pricing of tail risk. Financial institutions and insurers commonly use risk models to estimate the probability of rare events, such as hurricanes or earthquakes. Given the lack of real observations of these events, these models have increasingly incorporated synthetic draws in recent years, including those produced by previous versions of the same model. Because the models tend to under-sample rare events, each round of training understates the tail slightly, and recursive training compounds these understatements. As a result, the estimated tail probability settles below the truth, with the largest proportional bias for the safest issuers. I also consider what happens when the number of defaults, and hence the amount of real data, depends in turn on the estimated tail probability. Since a lower estimate tightens spreads and reduces defaults, a long period of calm during which tail risks do not materialize can raise the share of synthetic data and tip the market into a persistent low-information state, which I call tail amnesia. Finally, I show that a policy requiring a minimum share of real data in training rules out this state and caps the bias.