We analyse questions of arbitrage in financial markets in which asset prices change in time as stationary stochastic processes. The main focus of the paper is on a model where the price vectors are independent and identically distributed. In the framework of this model, we find conditions that...

In this paper we construct arbitrage-free market models of stochastic volatility type for one stock, one bank account and a finite family of European call options with various strikes and maturities. We first introduce local implied volatilities and price level as market observables which...

This paper develops a new estimation procedure for characteristic-based factor models of security returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time-varying weights, and a set of univariate non-parametric functions...

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using the law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile...

The evaluation of the likelihood function of the stochastic conditional duration model requires to compute an integral that has the dimension of the sample size. We apply the efficient importance sampling method for computing this integral. We compare EIS-based ML estimation with QML estimation...