We examine the asset pricing properties of an endowment economy featuring stochastic volatility and an agent who fears his model is misspecified. Due to the nonlinearities inherent in our stochastic volatility model, we are forced to expand the toolkit of the robust control literature. We propose novel algorithms to characterize and simulate the robust agent’s worst case model. Using US consumption data, we estimate the parameters of the endowment process and find evidence of stochastic volatility. Introducing stochastic volatility helps the model generate a more plausible unconditional market price of risk and increases the measured welfare costs of business cycles by about 15%. These asset pricing and welfare results are the result of an agent valuing consumption streams as if a worst case model has generated the data. In our stochastic volatility set up, the robust agent’s worst case consumption growth process contains both disasters and a long run risk component.
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