This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specificity is that the volatility process is assumed not only to be stochastic, but also to have long memory features and properties.

We study the problem of estimating some unknown regression or autoregression function in a B-mixing dependent framework (for the design or the errors). For this end, we consider some collection of models which are finite dimensional spaces. A penalized least-squares estimator (PLSE) is built on...