Before revision:  By exhibiting a Karhunen-Lo\`{e}ve expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the stock price density and implied volatility in these models in the limit of large or small strikes .
After revision:  By exhibiting a Karhunen-Lo\`{e}ve expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the stock price density and implied volatility in these models .