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Writers of index options earn high returns due to a significant and high volatility risk premium, but writers of options in single-stock markets earn lower returns. Using an incomplete information economy, the authors develop a structural model with multiple assets where agents have heterogeneous beliefs about the growth of firms' fundamentals and a business-cycle indicator and explain the different volatility risk premia of index and single-stock options. The wedge between the index and individual volatility risk premium can be explained by a correlation risk premium which emerges endogenously due to agents' optimal risk-sharing.
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