The development of formal models of decision making under risk has been shaped largely by decisions between options with monetary outcomes, with the most prominent model being cumulative prospect theory (CPT). Whereas CPT is good at describing choices between monetary lotteries, it shows poorer performance in the context of decisions between options with nonmonetary and nonnumerical outcomes (e.g., medications with possible side effects). We suggest that this may be due to affective processes and context-dependent evaluation—which are not considered in CPT—playing a larger role in nonmonetary than in monetary choice. We propose three psychologically motivated modifications to CPT's modeling framework to capture these differences: (a) representing the subjective value of a nonmonetary outcome by an affect rating (rather than a monetary equivalent); (b) determining the subjective affective value of an outcome relative to the value of the worst outcome in the choice problem; (c) assuming that the probability weighting for an outcome depends on the amount of affect triggered. We submit model variants of CPT implementing the proposed modifications to a model comparison in three empirical data sets. For choices between options with negative nonmonetary outcomes (medications with possible side effects), these modifications substantially improve CPT's performance relative to that of the original version of CPT. The same does not hold for monetary choices. Overall, in addition to fleshing out key differences in the processing of monetary and nonmonetary risky options, our work demonstrates how affective processes can be formally integrated within classical theories of decisions under risk.