On Volatility Swaps for Stock Market Forecast: Application Example CAC 40 French Index

This paper focuses on the pricing of variance and volatility swaps under Heston model (1993). To this end, we apply this model to the empirical financial data: CAC 40 French Index. More precisely, we make an application example for stock market forecast: CAC 40 French Index to price swap on the volatility using GARCH(1,1) model

On Stochastic Orders and their Applications: Policy Limits and Deductibles

The paper deals with several types of stochastic order affecting random variables and linear combinations of random variables. We study the problem of finding maximal expected utility for some functionals on insurance portfolios involving some additional (independent) randomization. Applications in policy limits and deductible are obtained, and some relationships with other actuarial main topics (comparison of copulas, individual and collective risk models, reinsurance contracts, etc.) are studied too

Relative error prediction: Strong uniform consistency for censoring time series model

International audienceThis article considers an adaptive method based on the relative error criteria to estimate the regression operator by a kernel smoothing. It is assumed that the variable of interest is subject to random right censoring and that the observations are from a stationary α-mixing process. The uniform almost sure consistency over a compact set with rate where we highlighted the covariance term is established. The simulation study indicates that the proposed approach has better performance in the presence of high level censoring and outliers in data to an existing classical method based on the least squares. An experiment prediction shows the quality of the relative error predicto

Nonparametric relative error estimation of the regression function for censored data

Let $(T_i)_{i }$ be a sequence of independent identically distributed (i.i.d.) random variables (r.v.) of interest distributed as $T$ and $(X_i)_{ i }$ be a corresponding vector of covariates taking values on $\mathbb{R}^d$. In censorship models the r.v. $T$ is subject to random censoring by another r.v. $C$. In this paper we built a new kernel estimator based on the so-called synthetic data of the mean squared relative error for the regression function. We establish the uniform almost sure convergence with rate over a compact set and its asymptotic normality. The asymptotic variance is explicitly given and as product we give a confidence bands. A simulation study has been conducted to comfort our theoretical result