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A test for a parametric form of the volatility in second-order diffusion models. (English) Zbl 1417.62302

Summary: Second-order diffusion models have been found to be promising in analyzing financial market data. Based on nonparametric fitting, J. Nicolau [Stat. Probab. Lett. 78, No. 16, 2700–2704 (2008; Zbl 1155.62078)] suggested that the quadratic function may be an appropriate specification of the volatility when a second-order diffusion model is used to analyze some European and American financial market data sets, which motivates us to develop a formal statistical test for this finding. To achieve the task, a generalized likelihood ratio test is proposed in this paper and a residual-based bootstrap is suggested to compute the \(p\) value of the test. The analysis of many real-world financial market data sets demonstrates that the quadratic specification of the volatility function is in general reasonable.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62M02 Markov processes: hypothesis testing
62F03 Parametric hypothesis testing
91G30 Interest rates, asset pricing, etc. (stochastic models)

Citations:

Zbl 1155.62078
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References:

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