Continuous Time Finance Model Of Time-variant Testing

In mathematical finance, there has been a large number of literature on the estimation of the continuous-time models, however, there is relatively little effort on specification analysis for continuous-times models. Model misspecificaton generally leads to misleading conclusions in inference and hypothesis testing, more, misspecified model can yield large errors in pricing, hedging, and risk management. It is necessary to develop reliable specification tests for continuous-times models.In this paper, we first reviewed the fruit of continuous-time models estimation in theory and applications, and then discussed the nonparametric specification test problem in continuous-time models as follows:In chapter 2 we introduced the nonparametric specification test for continuous-time models using the transition density, which need to compute the model generalized residuals, then compute the boundary-modified kernel joint density estimator, and finally compute the test statistic Q(j).In chapter 3, on the theoretical basis of chapter 2, we chose geometric Brown motion as the null hypothesis, CKLS model and CIR model as the alternative hypothesis. Through analyzing the test statistic, we concluded that the method in this paper can obtain the good result. Furthermore, we discussed the time-dependent features of segmented geometric Brown motion.In chapter 4, we tested our method by analyzing Shanghai A Share Index and concluded that Shanghai A Share Index is the time-dependent segmented geometric Brown motion. We analyzed a sustainable growth stock, and concluded it can be described by the geometric Brown motion.