The Exact Smile of some Local Volatility Models

TL;DR

This paper introduces a new class of local volatility models that allow exact computation of European option prices and implied volatility smiles, demonstrated through a CEV-like example with numerical results.

Contribution

The paper presents a novel class of local volatility models enabling exact pricing and implied volatility calculations, expanding analytical tools in option pricing.

Findings

Exact formulas for European option prices

Explicit implied volatility smile expressions

Numerical illustrations for a CEV-like model

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.