Increasing international trade has exacerbated the risks of ecological damage due to invasive pests and diseases. For extreme events such as invasions of damaging exotic species or natural catastrophes, there are no or very few directly relevant data, so expert opinion must be relied on heavily. Expert opinion must be as fully informed and calibrated as possible – by available data, by other experts, and by the reasoned opinions of stakeholders. We survey a number of quantitative and non-quantitative methods that have shown promise for improving extreme risk analysis, particularly for assessing the risks of invasive pests and pathogens associated with international trade. We describe the legally inspired regulatory regime for banks, where these methods have been brought to bear on extreme ‘operational risks’. We argue that an ‘advocacy model’ similar to that used in the Basel II compliance regime for bank operational risks and to a lesser extent in biosecurity import risk analyses is ideal for permitting the diversity of relevant evidence about invasive species to be presented and soundly evaluated. We recommend that the process be enhanced in ways that enable invasion ecology to make more explicit use of the methods found successful in banking.