https://hdl.handle.net/10419/130 2026-10-25T15:55:16Z 2026-10-25T15:55:16Z Linton, Oliver Maasoumi, Esfandiar Whang, Yoon-Jae https://hdl.handle.net/10419/22246 2023-11-10T02:09:36Z 2003-01-01T00:00:00Z

Title: Consistent Testing for Stochastic Dominance under General Sampling Schemes Authors: Linton, Oliver; Maasoumi, Esfandiar; Whang, Yoon-Jae Abstract: We propose a procedure for estimating the critical values of the extended Kolmogorov- Smirnov tests of First and Second Order Stochastic Dominance in the general K-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is subsampling; we show that the resulting tests are consistent and powerful against some N|1/2 local alternatives even when computed with a data-based subsample size. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We show that our test is asymptotically similar on the entire boundary of the null hypothesis, and is unbiased. In comparison, any method based on resampling or simulating from the least favorable distribution does not have these properties and consequently will have less power against some alternatives.

2003-01-01T00:00:00Z Gapeev, Pavel V. Reiß, M. https://hdl.handle.net/10419/22261 2023-11-12T02:08:24Z 2003-01-01T00:00:00Z

Title: A Note on Optimal Stopping in Models with Delay Authors: Gapeev, Pavel V.; Reiß, M. Abstract: We consider an optimal stopping problem in a certain model described by a stochastic delay differential equation. We reduce the initial problem to a free-boundary problem of parabolic type and prove the corresponding verification assertion. We also give an example of such an optimal stopping problem related to mathematical finance.

2003-01-01T00:00:00Z Cai, Zongwu https://hdl.handle.net/10419/22222 2023-11-15T02:09:50Z 2003-01-01T00:00:00Z

Title: Trending Time-Varying Coefficient Models With Serially Correlated Errors Authors: Cai, Zongwu Abstract: In this paper we study time-varying coefficient models with time trend function and serially correlated errors to characterize nonlinear, nonstationary and trending phenomenon in time series. Compared with the Nadaraya-Watson method, the local linear approach is developed to estimate the time trend and coefficient functions. The consistency of the proposed estimators is obtained without any specification of the error distribution and the asymptotic normality of the proposed estimators is established under the alpha-mixing conditions. The explicit expressions of the asymptotic bias and variance are given for both estimators. The asymptotic bias is just in a regular nonparametric form but the asymptotic variance is shared by parametric estimators. Also, the asymptotic behaviors at both interior and boundary points are studied for both estimators and it shows that two estimators share the exact same asymptotic properties at the interior points but not at the boundaries. Moreover, proposed are a new bandwidth selector based on the nonparametric version of the Akaike information criterion, a consistent estimator of the asymptotic variance, and a simple nonparametric version of bootstrap (i.e. wild bootstrap) test for testing the misspecification and stationarity. Finally, we conduct some Monte Carlo experiments to examine the finite sample performances of the proposed modeling procedures and test.

2003-01-01T00:00:00Z Fengler, Matthias R. Wang, Qihua https://hdl.handle.net/10419/22240 2023-11-15T02:08:55Z 2003-01-01T00:00:00Z

Title: Fitting the Smile Revisited: A Least Squares Kernel Estimator for the Implied Volatility Surface Authors: Fengler, Matthias R.; Wang, Qihua Abstract: Nonparametric methods for estimating the implied volatility surface or the implied volatility smile are very popular, since they do not impose a specific functional form on the estimate. Traditionally, these methods are two-step estimators. The first step requires to extract implied volatility data from observed option prices, in the second step the actual fitting algorithm is applied. These two-step estimators may be seriously biased when option prices are observed with measurement errors. Moreover, after the nonlinear transformation of the option prices the error distribution will be complicated and less tractable. In this study, we propose a one-step estimator for the implied volatility surface based on a least squares kernel smoother of the Black-Scholes formula. Consistency and the asymptotic distribution of the estimate are provided. We demonstrate the estimator using German DAX index option data to recover the smile and the implied volatility surface.

2003-01-01T00:00:00Z