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Our model is an example of an affi ne stochastic volatility model. Affi ne stochastic volatility models date back at least to Heston (1993) in continuous time, and have been developed and discussed by Ghysels, Harvey, and Renault (1996), Meddahi and Renault (2004), and Darolles, Gourieroux, and Jasiak (2006) among others. Similar models have been applied in the long-run risk literature by Eraker (2008), Eraker and Shaliastovich (2008), and Hansen (2012), but much of this literature uses volatility specifications that are not guaranteed to remain positive.

Two precursors to our work are unpublished papers by Chen (2003) and Sohn (2010). Both papers explore the effects of stochastic volatility on asset prices in an ICAPM setting but make strong assumptions about the covariance structure of various news terms when deriving their pricing equations. Chen (2003) assumes constant covariances between shocks to the market return (and powers of those shocks) and news about future expected market return variance. Sohn (2010) makes two strong assumptions about asset returns and consumption growth, specifically that all assets have zero covariance with news about future consumption growth volatility and that the conditional contemporaneous correlation between the market return and consumption growth is constant through time. Duffee (2005) presents evidence against the latter assumption. It is in any case unattractive to make assumptions about consumption growth in an ICAPM that does not require accurate measurement of consumption.