The $\alpha$-Hypergeometric Stochastic Volatility Model

TL;DR

This paper introduces the $oldsymbol{ ext{ extalpha}}$-Hypergeometric Stochastic Volatility Model, a new framework for equity derivatives that addresses limitations of existing models like Heston, providing tools for pricing options and derivatives.

Contribution

It proposes a novel stochastic volatility model with improved properties over affine models, including explicit pricing methods and implementation guidelines.

Findings

Model overcomes known issues of Heston and affine models.

Provides explicit formulas for vanilla and volatility derivatives.

Clarifies martingale conditions and implementation procedures.

Abstract

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the dynamics of the stock and its volatility. Within this framework we develop all the key elements to perform the pricing of vanilla European options as well as of volatility derivatives. We clarify the conditions under which the stock price is a martingale and illustrate how the model can be implemented.