We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Itô process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the...

We propose a new methodology based on Fourier analysis to estimate the fourth power of the volatility function (spot quarticity) and, as a byproduct, the integrated function. We prove the consistency of the proposed estimator of the integrated quarticity. Further, we analyse its efficiency in...

We consider the option pricing model proposed by Mancino and Ogawa, where the implementation of dynamic hedging strategies has a feedback impact on the price process of the underlying asset. We present numerical results showing that the smile and skewness patterns of implied volatility can...

In this paper we consider the optimal impulse control of a system which evolves randomly in accordance with a homogeneous diffusion process in ℜ<Superscript>1</Superscript>. Whenever the system is controlled a cost is incurred which has a fixed component and a component which increases with the magnitude of the control...</superscript>

We analyze the effects of market microstructure noise on the Fourier estimator of multivariate volatilities. We prove that the estimator is consistent in the case of asynchronous data and asymptotically unbiased in the presence of various types of microstructure noise. This result is obtained...