LUCA CAPRIOTTI, Credit Suisse Group
Email: luca.capriotti@credit-suisse.com

We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables solve the well-known problem of the divergence of the variance of Delta for short maturities and small volatilities. With numerical examples within a Gaussian Copula framework, we show how simple Control Variates and Importance Sampling strategies provide computational savings up to several orders of magnitude.

MANFRED GILLI, University of Geneva, Swiss Finance Institute
Email: Manfred.Gilli@metri.unige.ch
ENRICO SCHUMANN, University of Geneva
Email: enricoschumann@yahoo.de

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not 'well-behaved' in other ways (e.g., discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.

SAMI MESTIRI, affiliation not provided to SSRN
Email: mestiri_sami2007@yahoo.fr
ABDEJELIL FARHAT, affiliation not provided to SSRN

The mixed linear models are frequently used in the studies of research in medicine and social science. In this article, we presented the method of robust maximum likelihood for estimating the parameters of these models. Since this method is sensitive to outliers observations, we concentrated on the approach of the case-deletion diagnostic suggested by Cooks (1977). The influence diagnostics on the parameters of the mixed linear model estimated by the robust method is proposed. The goal of this paper is to make a comparison of the efficiency of the diagnostics which is based on a non robust procedure of estimate and those which is based on a robust procedure of estimate. Finally, we illustrate the use of our new statistics of influence by examining a linear mixed model adjusted with the data of the Cholesterol level.