On identification of the threshold diffusion processes

Kutoyants, Yury A.

doi:10.1007/s10463-010-0318-1

Cited by 19 publications

(15 citation statements)

References 19 publications

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“…When the mean reversion speed always stays positive, the SET diffusion is known as an ergodic threshold OU (TOU) process. Kutoyants () renders parameter estimation scheme for several ergodic TOU processes.…”

Section: Introductionmentioning

confidence: 99%

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Option Pricing with Threshold Mean Reversion

Chi

Dong

Wong

2016

Journal of Futures Markets

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Mean reversion and regime switching are well‐known features of commodity prices. Recent empirical research additionally documents the time variation of the mean reversion rate and volatility. This paper considers the option pricing framework for an underlying commodity price with mean reversion rate and volatility change according to a self‐exciting regime switching model. We offer empirical evidence for the proposed model and derive analytic pricing formulas for the European and barrier options. Numerical examples demonstrate the application and the ability of the proposed model in capturing volatility smile and regime‐switching in the mean reversion rate, simultaneously. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:107–131, 2017

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Section: Introductionmentioning

confidence: 99%

“…When the mean reversion speed always stays positive, the SET diffusion is known as an ergodic threshold OU (TOU) process. Kutoyants (2012) renders parameter estimation scheme for several ergodic TOU processes. This paper develops a new option pricing framework where the underlying asset price is modeled by a generalized TOU process.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing with Threshold Mean Reversion

Chi

Dong

Wong

2016

Journal of Futures Markets

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“…Note that such windows were already used in a similar problem with threshold ergodic diffusion processes in Kutoyants (2011), where one can find the details of the proof of (6.2) (see Kutoyants (2004), p. 287 for a similar discussion).…”

Section: And the Pseudo Likelihood Ratio (Omitting The Multiplicativementioning

confidence: 99%

“…On the other hand, a relatively complete theory for the statistical inference for diffusion processes in continuous-time has emerged, see for example Kutoyants (2004Kutoyants ( , 2011. For more information relating to continuous-time threshold models, see Brockwell (1994), Chan and Tong (1987) and Stramer et al (1996) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Recent Developments of Threshold Estimation for Nonlinear Time Series

Hang

Kutoyants

2010

JJSS

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In this article, several important problems of threshold estimation in a Bayesian framework for nonlinear time series models are discussed. The paper starts with the issue of calculating the maximum likelihood and the Bayesian estimators for threshold autoregressive models. It turns out that the asymptotic efficiency of the Bayesian estimators in this type of singular estimation problems is superior than the maximum likelihood estimators. To illustrate the properties of these estimators and to explain the proposed method, the paper begins with the study of a linear threshold autoregressive model with i.i.d. Gaussian noise. The paper then extends the idea to other nonlinear and non-Gaussian models and illustrates the paradigm of limiting likelihood ratio, which is applicable to a much wider class of nonlinear models. The article also investigates the robustness issue and the possibility of restricting the observation window by narrow bands, which allows one to obtain asymptotically efficient estimators. Finally, the paper indicates how these results can be generalized from a TAR(1) model to a higher-order TAR(p) model with multiple thresholds. The paper concludes with a discussion of other related problems and illustrates the methodology by numerical simulations.

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“…The change‐point problem can be described by the following example:

d X_{t} = h (X_{t}) 1_{\{ϑ < X_{t}\}} d t + g (X_{t}) 1_{\{ϑ \geq X_{t}\}} d t + ε d W_{t}, X_{0} = x_{0}, 0 \leq t \leq T,

that is, we have a switching diffusion process with unknown threshold ϑ . Such models are called threshold diffusion processes like threshold autoregressive time series (Chan & Kutoyants, ), and statistical problems related to this model are singular (Kutoyants, ). If we have a cusp‐type singularity as

S (ϑ, x) = sgn (x - ϑ) {|x - ϑ|}^{κ} 1_{\{ϑ < x\}} + sgn (x - ϑ) {|x - ϑ|}^{κ} 1_{\{ϑ \geq x\}},

where

κ \in ((), 0, \frac{1}{2})

, then, for κ close to zero, we have cusp‐type switching similar to the change‐point case, but without jump.…”

Section: Introductionmentioning

confidence: 99%

On cusp location estimation for perturbed dynamical systems

Kutoyants

2019

Scandinavian J Statistics

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We consider the problem of parameter estimation in the case of observation of the trajectory of the diffusion process. We suppose that the drift coefficient has a singularity of cusp type and that the unknown parameter corresponds to the position of the point of the cusp. The asymptotic properties of the maximum likelihood estimator and Bayesian estimators are described in the asymptotic of small noise, that is, as the diffusion coefficient tends to zero. The consistency, limit distributions, and the convergence of moments of these estimators are established.

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On identification of the threshold diffusion processes

Cited by 19 publications

References 19 publications

Option Pricing with Threshold Mean Reversion

Option Pricing with Threshold Mean Reversion

Recent Developments of Threshold Estimation for Nonlinear Time Series

On cusp location estimation for perturbed dynamical systems

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