In the financial system, the customers’ willingness to share their data is pivotal, because otherwise, banks and insurance companies are powerless to build on customer data. The key step now is to understand whether there is such willingness and what form it takes. In this study, we investigate how willing customers are to share various kinds of data (on physical health, home, driving style, travel, family, social networks) with their insurance company, in return for different rewards (customised products and services, reduced insurance claims risk and insurance premiums adjusted to personal habits and behaviour). Applying the privacy calculus framework to 1501 responses in a web-based survey, we found that rewards, especially when financial, such as insurance premium benefits, play a pivotal role in driving customer decisions about sharing data. Furthermore, customers associate the data they are asked to share with different levels of privacy, influencing their willingness to share. We also found that, when customers are asked to share various kinds of data in return for different rewards, their own personal innovativeness comes into play. Our findings suggest that, in the data-driven insurance business, different rewards offered in return for specific types of data could help companies minimise the “data acquisition cost” and maximise the data collected. In the era of open data, insurers can explore the many opportunities for segmentation, but new kinds of financial exclusion could emerge, resulting in potential biases and thus misinterpretations should analytics and artificial intelligence models be built upon these premises.