  We study the dependence of volatility on the stock price in the stochastic
volatility 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. The
behavior of this function depends on the initial stock price return
distribution density. In particular, we show that the graph of the conditional
expectation of variance is convex downwards near the mean value of the stock
price return. For the Gaussian distribution this effect is strong, but it
weakens and becomes negligible as the decay of distribution at infinity slows
down.
