Research Article
BibTex RIS Cite

EFFECT OF JUMP DIFUSION MODEL ON CONTINUOUS TIME PORTFOLIO SELECTION: BORSA İSTANBUL APPLICATION

Year 2015, Volume: 17 Issue: 2, 331 - 346, 30.06.2015

Özge Sezgin Alp

Abstract

In financial markets in stant price changes occurs therefore, the price changes may assumed to be continuous variables. This is why recent stock price modelling studies are using continuous time stochastic models. In this study, the Geometric Brownian Motion and Jump Diffusion models are evaluated to model BIST-100 index. In addition, Markowitz’s mean-variance portfolio selection problem‘s continuous time solutions are applied and Jump Diffusion model performance is evaluated. As a result, it is concluded that the Jump Diffusion model is more suitable for BIST-100 index because of the sudden ups and downs in the market.

Keywords

Portfolio Optimization Stochastic Geometric Brownian Motion Jump Diffusion

References

  • Ball A. ve W.N. Torous. 1983. “A Simplified Jump Processfor Common Stock Returns”, The Journal of Financial and Quantitative Analysis, 18.
  • Basak S. ve G. Chabakauri. 2010. “Dynamic Mean-Variance Asset Allocation”, Review Of Financial Studies, 23.
  • Beckers S. 1981. “A Note on Estimating The Parameters of The DiffusionJump Model Of Stock Returns”, The Journal of Financial and Quantitative Analysis, 16.
  • Costa O.L.M. ve M.V. Araujoa. 2008. “A Generalized Multi-Period Mean-Variance Portfolio Optimization with Markov Switching Parameters”, Automatica (Journal of IFAC), 44.
  • Costa O.L.M. ve R.B. Nabholz. 2007. “Multiperiod Mean-Variance Optimization with Intertemporal Restrictions”, Journal of Optimization Theory and Applications, 134.
  • Guo W. ve C. Xu. 2004. “Optimal Portfolio Selection When Stock Prices Follow and Jump Diffusion Process”, Mathematical Methods of Operations Research, 60.
  • Honor´e P. 1998. “Pitfalls in Estimating Jump Diffusion Models”, Technical Report. University of Aarhus.
  • Korn R. ve S. Trautmann. 1998. “Continuous-Time Portfolio Optimization Under Terminal Wealth Constraints”, ZOR - Mathematical Methods of Operational Research, 42.
  • Leippold M.,F. Trojani ve P. Vanini. 2004. “A Geometric Approach to Multiperiod Mean-Variance Optimization of Assets and Liabilities”, Journal of Economic Dynamic and Control, 28.
  • Li D. ve W.M. Ng. 2000. “Optimal Dynamic Portfolio Selection: Multi-Period Mean-Variance Formulation”, Mathematical Finance, 10.
  • Lindberg C. 2009. “Portfolio Optimization When Expected Stock Returns Are Determined by Exposureto Risk”, Bernoull, 15.
  • Markowitz H.M. 1952. “Portfolio Selection”, Journal of Finance, 7.
  • Sezgin-Alp Ö. ve R. Korn. 2011. “Continuous-Time Mean-Variance Portfolio Optimization in A Jump-Diffusion Market”, Decisions in Economics and Finance, 34 (1).
  • Schweizer M. 1994. “Approximating Random Variables By Stochastic Integrals”, Annals of Probability, 22.
  • Zhou X.Y. ve D. Li. 2000. “Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework”, Applied Mathematical Optimization, 42.

SIÇRAMALI DİFÜZYON MODELİNİN SÜREKLİ ZAMAN PORTFÖY SEÇİMİNE ETKİSİ: BORSA İSTANBUL ÜZERİNE BİR UYGULAMA

Year 2015, Volume: 17 Issue: 2, 331 - 346, 30.06.2015

Özge Sezgin Alp

Abstract

Finansal piyasalar anlık değişimlerin değişimlere bağlı olarak fiyat değişimlerinin yaşandığı piyasalardır. Bu nedenle son yıllarda yapılan çalışmalar, hisse senedi fiyatlarının modellenmesinde sürekli zamanlı stokastik modeller üzerine yoğunlaşmaktadır. Bu çalışmada, Sıçramalı Difüzyon ve Geometrik Brownian Hareketi Difüzyon modellerinin BIST-100 endeksi için kullanılabilirliği değerlendirilmiştir. Buna ek olarak, Markowitz’in ortalama-varyansportföy seçim yönteminin sürekli zaman geliştirilmiş çözümleri Türkiye portföy örneği üzerinde uygulanmış ve sıçramalı modelinin portföy performansına etkisi incelenmiştir. Çalışmanın sonunda elde edilen bulgular, piyasada oluşan ani iniş ve çıkışlar nedeni ile Sıçramalı Difüzyon modelinin BIST-100 endeksi için daha uygun olacağını ortaya koymuştur.

Keywords

Portföy Optimizayon Stokastik Geometrik Brownian Hareketi Sıçramalı Difüzyon

References

  • Ball A. ve W.N. Torous. 1983. “A Simplified Jump Processfor Common Stock Returns”, The Journal of Financial and Quantitative Analysis, 18.
  • Basak S. ve G. Chabakauri. 2010. “Dynamic Mean-Variance Asset Allocation”, Review Of Financial Studies, 23.
  • Beckers S. 1981. “A Note on Estimating The Parameters of The DiffusionJump Model Of Stock Returns”, The Journal of Financial and Quantitative Analysis, 16.
  • Costa O.L.M. ve M.V. Araujoa. 2008. “A Generalized Multi-Period Mean-Variance Portfolio Optimization with Markov Switching Parameters”, Automatica (Journal of IFAC), 44.
  • Costa O.L.M. ve R.B. Nabholz. 2007. “Multiperiod Mean-Variance Optimization with Intertemporal Restrictions”, Journal of Optimization Theory and Applications, 134.
  • Guo W. ve C. Xu. 2004. “Optimal Portfolio Selection When Stock Prices Follow and Jump Diffusion Process”, Mathematical Methods of Operations Research, 60.
  • Honor´e P. 1998. “Pitfalls in Estimating Jump Diffusion Models”, Technical Report. University of Aarhus.
  • Korn R. ve S. Trautmann. 1998. “Continuous-Time Portfolio Optimization Under Terminal Wealth Constraints”, ZOR - Mathematical Methods of Operational Research, 42.
  • Leippold M.,F. Trojani ve P. Vanini. 2004. “A Geometric Approach to Multiperiod Mean-Variance Optimization of Assets and Liabilities”, Journal of Economic Dynamic and Control, 28.
  • Li D. ve W.M. Ng. 2000. “Optimal Dynamic Portfolio Selection: Multi-Period Mean-Variance Formulation”, Mathematical Finance, 10.
  • Lindberg C. 2009. “Portfolio Optimization When Expected Stock Returns Are Determined by Exposureto Risk”, Bernoull, 15.
  • Markowitz H.M. 1952. “Portfolio Selection”, Journal of Finance, 7.
  • Sezgin-Alp Ö. ve R. Korn. 2011. “Continuous-Time Mean-Variance Portfolio Optimization in A Jump-Diffusion Market”, Decisions in Economics and Finance, 34 (1).
  • Schweizer M. 1994. “Approximating Random Variables By Stochastic Integrals”, Annals of Probability, 22.
  • Zhou X.Y. ve D. Li. 2000. “Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework”, Applied Mathematical Optimization, 42.
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Business Administration
Journal Section MAIN SECTION
Authors

Özge Sezgin Alp This is me

Publication Date June 30, 2015
Submission Date January 26, 2015
Published in Issue Year 2015 Volume: 17 Issue: 2

Cite

APA Alp, Ö. S. (2015). SIÇRAMALI DİFÜZYON MODELİNİN SÜREKLİ ZAMAN PORTFÖY SEÇİMİNE ETKİSİ: BORSA İSTANBUL ÜZERİNE BİR UYGULAMA. Muhasebe Bilim Dünyası Dergisi, 17(2), 331-346.
 Download Cover Image

Authorship
MBDD follows the guidelines in COPE Authorship Guideline to ensure fair recognition of contributions to a research paper (https://publicationethics.org/guidance/discussion-document/authorship ). Authorship carries both credit and responsibility, and it is essential that all listed authors have made significant contributions to the research.

For multi-author studies, the Contributions of Authors must be declared after the conclusion and before the bibliography of the paper. The authors' initials and last names should be used to indicate which author contributed to which part of the manuscript. Details can be found by clicking the “Article Submission Checklist” button. The authors can acknowledge contributions that do not merit authorship.


The author(s) should disclose the use of generative Artificial Intelligence (AI) and AI-assisted tools in design and implementation of the research. Such use need to be disclosed within the methodology section of the manuscript. Use of AI does not preclude the manuscript from publication, rather provides a transparent picture of the research.