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

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

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

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

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