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Avrasya Ekonometri �statistik ve Ampirik Ekonomi DergisiYl:2017 Say: 8 Alan: statistik-Saysal Yntemler-Ekonometri

Kutluk Kaan SMER
Monte Carlo Metodu ve Smerin Yeni Zplama ve Daralma Srecinin BIST(Borsa stanbul) Getirileri Uygulamas
 
Bu alma Wiener Sreci, Genelletirilmi Wiener Sreci, Ortalamaya Dnme Sreci, Ortalamaya Dnme Srama Difzyon Sreci ile Monte Carlo tahminleri yaparak bunlar karlatrmak amacyla balamakla beraber sonrasnda altn piyasasnda negatif ve pozitif haber oklarnn da bu Monte Carlo tahmine nasl eklenebilecei dncesiyle genilemitir. Klasik Ortalamaya Dnme Srama Difzyon Srecinin 3 standart sapmalk oklarn tespiti gelitirilerek 1.96 ve 3 standart sapmalk oklara ait gelitirilmi bir model kullanlm buna ek olarak pozitif ve negatif haber oklar da sisteme farkl ekilde eklenmitir. Smerin gelitirdii bu yeni Ortalamaya Dnme Srama Difzyon Sreci standart normal dalmdan ekilen 1 ve Poisson dalmndan ekilen 5 tesadfi deikenle Altn Getirisine ait Monte Carlo tahmini yapmaktadr. Ek olarak, gerek geleneksel ortalama getiri ve standart sapmalar (volatilite) gerekse iyi ve kt haber etkisindeki 1.96 ve 3 standart sapmann zerindeki volatiliteleri outlier kabul ederek elde edilen yeni ortalama getiri ve yeni standart sapmalar (volatilite) ile olan Monte Carlo tahminlerini mukayese etmektedir.

Anahtar Kelimeler: Monte Carlo simulation; quasi-random sequences; Faure sequences; numerical finance, Jump Diffusion Processes


Monte Carlo Methods and Smers New Jump Diffusion Processes and their Application in Gold Price
 
This study aimed to execute Monte Carlo simulation method with Wiener Process, Generalized Wiener Process, Mean Reversion Process and Mean Reversion Jump Diffusion Process and to compare them and then expended with the idea of how to include negative and positive news shocks in the gold market to the Monte Carlo simulation. By enhancing the determination of the 3 standard deviation shocks within the process of Classic Mean Jump Diffusion Process, an enchanted model for the 1,96 and 3 standard deviation shocks were being used and additionally positive and negative shocks were added to the system in a different way. This new Mean Reversion Jump Diffusion Process that have been developed by Smer, executes Monte Carlo simulation regarding the gold market return with five random variables that are chosen from Poisson distribution and one random variable chosen from the normal distribution. Additionally, by accepting volatilities as outlies over the 1,96 and 3 standard deviations with the effect of the new and good news and the standard deviations on the traditional approximate return and the standard deviations (volatility) and the obtained new approximate return and the new standard deviation (volatility) and compares them with the Monte Carlo simulations

Keywords: Monte Carlo simulation; quasi-random sequences; Faure sequences; numerical finance, Jump Diffusion Processes


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