The αα-hypergeometric stochastic volatility model

• Propose a new homogeneous stochastic volatility model for equity derivatives.
• Clarify the conditions ensuring the stock is a martingale.
• Provide the expression for the Laplace transform for the integrated volatility.
• Give the Mellin transform for the stock that is useful to perform option pricing.
• Give short and long term asymptotic for variance swaps.

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 affine models, we define a new specification for the dynamics of the 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.