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We study the dependence of volatility on the stock price in the stochasticvolatility framework on the example of the Heston model. To be more specific,we consider the conditional expectation of variance (square of volatility)under fixed stock price return as a function of the return and time. Thebehavior of this function depends on the initial stock price returndistribution density. In particular, we show that the graph of the conditionalexpectation of variance is convex downwards near the mean value of the stockprice return. For the Gaussian distribution this effect is strong, but itweakens and becomes negligible as the decay of distribution at infinity slowsdown.

A certain estimate of volatility through return for stochastic volatility models