On a continuous-time stock price model with two mean reverting regimes

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.

Original languageEnglish
Title of host publicationStudies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies
EditorsJ. Lita da Silva, F. Caeiro, I. Natário, C. Braumann
Place of PublicationBerlin, Heidelberg
PublisherSpringer International Publishing Switzerland
Pages297-305
Number of pages9
ISBN (Electronic)978-3-642-34904-1
ISBN (Print)978-3-642-34903-4
DOIs
Publication statusPublished - 1 Jan 2013

Publication series

NameStudies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies
PublisherSpringer International Publishing
ISSN (Print)2194-7767
ISSN (Electronic)2194-7775

Fingerprint

Stock Prices
Continuous Time
Regime Switching
Consistent Estimator
Diffusion Coefficient
Stochastic Processes
Classify
Model
Observation

Keywords

  • Consistent estimator
  • Single threshold
  • Stochastic differential equation
  • Stock prex
  • Uhlenbeck process

Cite this

Mota, P. P. (2013). On a continuous-time stock price model with two mean reverting regimes. In J. Lita da Silva, F. Caeiro, I. Natário, & C. Braumann (Eds.), Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies (pp. 297-305). (Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies). Berlin, Heidelberg: Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-642-34904-1_31
Mota, Pedro P. / On a continuous-time stock price model with two mean reverting regimes. Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies. editor / J. Lita da Silva ; F. Caeiro ; I. Natário ; C. Braumann. Berlin, Heidelberg : Springer International Publishing Switzerland, 2013. pp. 297-305 (Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies).
@inbook{86e5ab41bc3548ad8186327ba17c232a,
title = "On a continuous-time stock price model with two mean reverting regimes",
abstract = "Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.",
keywords = "Consistent estimator, Single threshold, Stochastic differential equation, Stock prex, Uhlenbeck process",
author = "Mota, {Pedro P.}",
note = "This work was partially supported by the Funda{\cc}{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through PEst-OE/MAT/UI0297/2011 (CMA).",
year = "2013",
month = "1",
day = "1",
doi = "10.1007/978-3-642-34904-1_31",
language = "English",
isbn = "978-3-642-34903-4",
series = "Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies",
publisher = "Springer International Publishing Switzerland",
pages = "297--305",
editor = "{Lita da Silva}, J. and F. Caeiro and I. Nat{\'a}rio and C. Braumann",
booktitle = "Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies",

}

Mota, PP 2013, On a continuous-time stock price model with two mean reverting regimes. in J Lita da Silva, F Caeiro, I Natário & C Braumann (eds), Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies. Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies, Springer International Publishing Switzerland, Berlin, Heidelberg, pp. 297-305. https://doi.org/10.1007/978-3-642-34904-1_31

On a continuous-time stock price model with two mean reverting regimes. / Mota, Pedro P.

Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies. ed. / J. Lita da Silva; F. Caeiro; I. Natário; C. Braumann. Berlin, Heidelberg : Springer International Publishing Switzerland, 2013. p. 297-305 (Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - On a continuous-time stock price model with two mean reverting regimes

AU - Mota, Pedro P.

N1 - This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through PEst-OE/MAT/UI0297/2011 (CMA).

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.

AB - Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.

KW - Consistent estimator

KW - Single threshold

KW - Stochastic differential equation

KW - Stock prex

KW - Uhlenbeck process

UR - http://www.scopus.com/inward/record.url?scp=85060281972&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-34904-1_31

DO - 10.1007/978-3-642-34904-1_31

M3 - Chapter

SN - 978-3-642-34903-4

T3 - Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies

SP - 297

EP - 305

BT - Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies

A2 - Lita da Silva, J.

A2 - Caeiro, F.

A2 - Natário, I.

A2 - Braumann, C.

PB - Springer International Publishing Switzerland

CY - Berlin, Heidelberg

ER -

Mota PP. On a continuous-time stock price model with two mean reverting regimes. In Lita da Silva J, Caeiro F, Natário I, Braumann C, editors, Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies. Berlin, Heidelberg: Springer International Publishing Switzerland. 2013. p. 297-305. (Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies). https://doi.org/10.1007/978-3-642-34904-1_31