Search results

The authors propose a family of tests for stationarity against a local unit root. It builds on the Karhunen–Loève (KL) expansions of the limiting CUSUM process under the null hypothesis and a local alternative. The variance ratio type statistic VRq is a ratio of quadratic forms of q weighted Gaussian sums such that the nuisance long-run variance cancels asymptotically without having to be estimated. Asymptotic critical values and local power functions can be calculated by standard numerical means, and power grows with q. However, Monte Carlo experiments show that q may not be too large in finite samples to obtain tests with correct size under the null. Balancing size and power results in a superior performance compared to the classic KPSS test.

This chapter proposes a nonparametric estimator of the risk neutral density (RND) based on cross-sectional European option prices. The authors recast the arbitrage-free equation for option pricing as a functional linear regression model where the regressor is a curve and the independent variable is a scalar corresponding to the option price. Then, the authors show that the RND can be viewed as the solution of an ill-posed integral equation. To estimate the RND, the authors use an iterative method called Landweber-Fridman (LF). Then, the authors establish the consistency and asymptotic normality of the estimated RND. These results can be used to construct a confidence interval around the curve. Finally, some Monte Carlo simulations and application to the S&P 500 options show that this method performs well compared to alternative methods.

Despite the difference in information sets, we are able to compare the asymptotic distribution of volatility estimators involving data sampled at different frequencies. To do so, we propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996, Econometrica, 64, 139–174). We focus on traditional historical volatility filters involving monthly, daily and intradaily observations. Theoretical results are complemented with Monte Carlo simulations in order to assess the validity of the asymptotics for sample sizes and filters encountered in empirical studies.