Climate change raises the issue of intergenerational equity. As climate change threatens irreversible and dangerous impacts, possibly leading to extinction, the most relevant trade-off may not be between present and future consumption, but between present consumption and the mere existence of future generations. To investigate this trade-off, we build an integrated assessment model that explicity accounts for the risk of extinction of future generations. We compare different climate policies, which change the probability of catastrophic outcomes yielding an early extinction, within the class of variable population utilitarian social welfare functions. We show that the risk of extinction is the main driver of the preferred policy over climate damages. We analyze the role of inequality aversion and population ethics. Usually a preference for large populations and a low inequality aversion favour the most ambitious climate policy, although there are cases where the effect of inequality aversion is reversed.