New tools for volatility models

In the first part of this work, we propose a new estimation method of the spot volatility, based on a semi-nonparametric model, which employs the information content of a complete panel of European options, daily quoted in the market, under no arbitrage assumptions. The technique we propose is based on the idea of model-free implied volatility and exploits the observed VIX term structure to make inference on the unobserved spot volatility. We show that this new estimation method can be applied to a very general class of stochastic volatility models, such as one-factor or two-factor models. Moreover, the presence of jumps both in return and volatility processes does not affect our spot volatility estimates. In the second part of the study, we propose a simple and flexible extension of the Heston (1993) model and its multifactor affine versions: the addition of a deterministic volatility factor meant to automatically fit the term structure of model-free implied volatilities. When calibrated on daily panels of FX EURUSD options for 5 strikes (ATM, 25Δ and 10Δ) and 10 maturities (from one week to two years) in the period 2005-2012, we can obtain a pricing error (in terms of RMSE on implied volatility) of 0,167%, and never above 1,72%. The proposed class of models is then a suitable stochastic volatility candidate for fast and arbitrage-free interpolation of the volatility surface.