BRUSSELS—Regulators around the globe are researching potential risks to financial stability from a failure to contain climate change or a sudden collapse in the value of fossil-fuel assets.

Institutions such as the Bank of England, the Financial Stability Board and the European Systemic Risk Board are examining how banks, insurers and pension funds would cope if policies designed to reduce carbon-dioxide emissions led to a sharp drop in the share price of oil, gas and coal companies.

They are looking at new rules to disclose exposures to both stocks and bonds in such companies, conducting stress tests based on different climate scenarios or even requiring additional capital buffers.

The regulators’ concerns rest on scientific assessments that much of the world’s known fossil-fuel reserves would have to stay underground if governments want to limit global warming to 2 degrees Celsius above preindustrial levels. If they aim to contain average temperature increases to 1.5 degrees, as set out in an international climate deal sealed in Paris in December, the so-called carbon budget would shrink even more.

That has triggered fears that a poorly managed switch to less-polluting energy sources, such as solar or wind power, could cause selloffs of fossil-fuel companies and broader economic problems caused by energy shortages.