Improving partial mutual information-based input variable selection by consideration of boundary issues associated with bandwidth estimation

Abstract not availableXuyuan Li, Aaron C. Zecchin, Holger R. Maie

A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics

A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.Smile, local volatility, generalized additive model, backfitting, functional principal component analysis

Option data and modeling BSM implied volatility

This contribution to the Handbook of Computational Finance, Springer-Verlag, gives an overview on modeling implied volatility data. After introducing the concept of Black-Scholes-Merton implied volatility (IV), the empirical stylized facts of IV data are reviewed. We then discuss recent results on IV surface dynamics and the computational aspects of IV. The main focus is on various parametric, semi- and nonparametric modeling strategies for IV data, including ones which respect no-arbitrage bounds.Implied volatility

Optimal adaptive estimation on R or R+ of the derivatives of a density

In this paper, we consider the problem of estimating the d-order derivative of a density f, relying on a sample of n i.i.d. observations with density f supported on R or R+. We propose projection estimators defined in the orthonormal Hermite or Laguerre bases and study their integrated L2-risk. For the density f belonging to regularity spaces and for a projection space chosen with adequate dimension, we obtain rates of convergence for our estimators, which are proved to be optimal in the minimax sense. The optimal choice of the projection space depends on unknown parameters, so a general data-driven procedure is proposed to reach the bias-variance compromise automatically. We discuss the assumptions and the estimator is compared to the one obtained by simply differentiating the density estimator. Simulations are finally performed and illustrate the good performances of the procedure and provide numerical comparison of projection and kernel estimators