We propose a CEV-like local stochastic volatility model that that fixes one problem with the CEV model; namely, when the elasticity of variance is negative our local volatility function does not go to zero as the value of the underlying goes to infinity . Within our framework, we obtain an explicit expressions for both (i) the price of any European option and (ii) the  implied volatility smile  .
We introduce a class of local stochastic volatility models . Within our framework, we obtain an expression for both (i) the price of any European option and (ii) the induced implied volatility smile . To illustrate our method, we perform specific computations for a CEV-like model .
R
propose a CEV-like
introduce a class of
R
model that that fixes one problem with the CEV model; namely, when the elasticity of variance is negative our local volatility function does not go to zero as the value of the underlying goes to infinity
models
R
explicit expressions
expression
A
induced
A
. To illustrate our method, we perform specific computations for a CEV-like model