Estimating catastrophic harms from frontier AI is hindered by deep ambiguity: many of its risks are not only unobserved but unanticipated by analysts. The central limitation of current risk analysis is the inability to populate the $\textit{catastrophic event space}$, or the set of potential large-scale harms to which probabilities might be assigned. This intractability is worsened by the $\textit{Lucretius problem}$, or the tendency to infer future risks only from past experience. We propose a process of $\textit{dark speculation}$, in which systematically generating and refining catastrophic scenarios ("qualitative" work) is coupled with estimating their likelihoods and associated damages (quantitative underwriting analysis). The idea is neither to predict the future nor to enable insurance for its own sake, but to use narrative and underwriting tools together to generate probability distributions over outcomes. We formalize this process using a simplified catastrophic Lévy stochastic framework and propose an iterative institutional design in which (1) speculation (including scenario planning) generates detailed catastrophic event narratives, (2) insurance underwriters assign probabilistic and financial parameters to these narratives, and (3) decision-makers synthesize the results into summary statistics to inform judgment. Analysis of the model reveals the value of (a) maintaining independence between speculation and underwriting, (b) analyzing multiple risk categories in parallel, and (c) generating "thick" catastrophic narrative rich in causal (counterfactual) and mitigative detail. While the approach cannot eliminate deep ambiguity, it offers a systematic approach to reason about extreme, low-probability events in frontier AI, tempering complacency and overreaction. The framework is adaptable for iterative use and can be further augmented with AI systems.