The Exact Smile of some Local Volatility Models

Abstract

We introduce a new class of local volatility models. Within this framework, we obtain expressions for both (i) the price of any European option and (ii) the induced implied volatility smile. As an illustration of our framework, we perform specific pricing and implied volatility computations for a CEV-like example. Numerical examples are provided.

14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1207.1630