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As climate change poses new and more unpredictable challenges to society, insurance is an essential avenue to protect against loss caused by extreme events. Traditional insurance risk models employ statistical analyses that are inaccurate and are becoming increasingly flawed as climate change renders weather more erratic and extreme. Data-driven parametric insurance could provide necessary protection to supplement traditional insurance. We use a technique referred to as the deep sigma point process, which is one of the Bayesian neural network approaches, for the data analysis portion of parametric insurance using residential internet connectivity dropout in US as a case study. We show that our model has significantly improved accuracy compared to traditional statistical models. We further demonstrate that each state in US has a unique weather factor that primarily influences dropout rates and that by combining multiple weather factors we can build highly accurate risk models for parametric insurance. We expect that our method can be applied to many types of risk to build parametric insurance options, particularly as climate change makes risk modeling more challenging.