On a test for a parametric form of volatility in continuous time financial models

Dette, Holger; Wilkau, Carsten von Lieres und

doi:10.1007/s007800200087

Cited by 28 publications

(27 citation statements)

References 17 publications

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“…Gerety and Mulherin (1994)]. Note that the test suggested in the present paper reduces to the test proposed by Dette and von Lieres und Wilkau (2003) in the case where the volatility function does not depend on x. These authors observed larger p-values for the hypothesis (3.4).…”

Section: A Data Examplementioning

confidence: 49%

“…A test for the hypotheses of the form (2.6) has recently been proposed by Dette and von Lieres und Wilkau (2003) under the additional assumption that the functions σ, σ 1 , . .…”

Section: Basic Asumptions and Main Resultsmentioning

confidence: 99%

“…In the case, where the variance function depends only on the time parameter t, Dette and von Lieres und Wilkau (2003) pointed out that the approximation by the normal distribution (as proposed in Remark 2.5) is not very accurate. For this reason these authors proposed a resampling method, and the results of Section 2 show that this method can easily be adapted to the more general situation considered in this paper.…”

Section: Finite Sample Properties and A Data Examplementioning

confidence: 99%

“…However, many of the common models in mathematical finance contain a volatility function, which also depends on the values of X t , and cannot be checked by this method. It is the purpose of the present note to give a more refined asymptotic analysis of a generalization of the test statistic proposed by Dette and von Lieres und Wilkau (2003) in the diffusion model (1.1), where the volatility also depends on the variable x. It is shown in Section 2 that in this case the analysis of the asymptotic properties of the estimates for the integrated volatility is substantially more difficult.…”

Section: Introductionmentioning

confidence: 97%

“…Therefore many authors propose to test the goodness-of-fit of the postulated model [see Ait-Sahalia (1996), Kleinow (2002) among many others]. In a recent paper Dette and von Lieres und Wilkau (2003) suggest a test for the parametric form of the volatility function, which is based on estimates of the integrated volatility function 1 0 σ 2n (t, X t )dt (n ∈ N). Under the assumption that the volatility function in the diffusion model (1.1) does not depend on the variable x, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing

Dette

Podolskij

Vetter

2006

Scandinavian J Statistics

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Properties of a specification test for the parametric form of the variance function in diffusionThe test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable x it is known that the corresponding statistics have an asymptotic normal distribution. However, most models of mathematical finance use a volatility function which depends on the state x. In this paper we prove that in the general case, where σ depends also on x the estimates of integrals of the volatility converge stably in law to random variables with a non-standard limit distribution. The limit distribution depends on the diffusion process X t itself and we use this result to develop a bootstrap test for the parametric form of the volatility function, which is consistent in the general diffusion model.

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Section: A Data Examplementioning

confidence: 49%

“…A test for the hypotheses of the form (2.6) has recently been proposed by Dette and von Lieres und Wilkau (2003) under the additional assumption that the functions σ, σ 1 , . .…”

Section: Basic Asumptions and Main Resultsmentioning

confidence: 99%

Section: Finite Sample Properties and A Data Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing

Dette

Podolskij

Vetter

2006

Scandinavian J Statistics

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Heteroscedasticity test of high‐frequency data with jumps and market microstructure noise

Liu

Zhi

Zhang

2022

Appl Stoch Models Bus & Ind

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In this paper, we are interested in testing whether the volatility process is constant or not during a given time span by using high‐frequency data with the presence of jumps and market microstructure noise. Based on estimators of integrated volatility and spot volatility, we propose a nonparametric procedure to depict the discrepancy between local variation and global variation. We show that our proposed test statistic converges to a standard normal distribution if the volatility is constant, and diverges to infinity otherwise. Simulation studies verify the theoretical results and show a good finite sample performance of the test procedure. We also apply our test procedure to some real high‐frequency financial datasets. We observe that in almost half of the days tested, the assumption of constant volatility within a day is violated. And this is due to that the stock prices in the periods near the opening and closing are highly volatile and account for a relatively large proportion of intraday variation.

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Kolmogorov–Smirnov‐type testing for the partial homogeneity of Markov processes—with application to credit risk

Weißbach

Dette

2007

Appl Stoch Models Bus & Ind

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Provided in Cooperation with November 2005 AbstractIn banking the default behavior of the counterpart is of interest not only for the pricing of transactions under credit risk but also for the assessment of portfolio credit risk. We develop a test against the hypothesis that default intensities are constant over time within a homogeneous group of counterparts under investigation, e.g. a rating class. The Kolmogorov-Smirnov-type test builds on the asymptotic normality of counting processes in event history analysis. Right-censoring accommodates for Markov process with more than one no-absorbing state. A simulation study and an example of rating migrations support the usefulness of the test.

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On a test for a parametric form of volatility in continuous time financial models

Cited by 28 publications

References 17 publications

Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing

Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing

Heteroscedasticity test of high‐frequency data with jumps and market microstructure noise

Kolmogorov–Smirnov‐type testing for the partial homogeneity of Markov processes—with application to credit risk

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