Identifikacija bimodalnih distribucija u financijskim vremenskim nizovima

master's thesis

• Title (english): Identification of bimodal distributions in financial time series
• Author: Goran Dubček
• Mentor: Zvonko Kostanjčar (mentor)
• Committee member: Zvonko Kostanjčar (predsjednik povjerenstva)
• Committee member: Dražen Jurišić (član povjerenstva)
• Committee member: Marko Subašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2016-07-15, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu obrađena su teme vjerojatnosnih razdioba i pojave bimodalnosti kod prinosa indeksa S&P 500. Predikcija volatilnosti predstavlja jedan od ključnih problema u portfolio managementu i investicijskim strategijama. U sklopu rada razvijen je model za predikciju volatilnosti s kojim se ujedno pokušala identificirati i predvidjeti bimodalnost. Prava bimodalnost nije nađena, međutim identificirani su uvjeti pod kojima se vjerojatnost prinosa većih od apsolutno 2% značajno povećava. Ti rezultati su uspoređeni sa rezultatima koje daje model ako mu se ulazni dio, koji određuje režim rada, zamijeni sa GARCH(1,1) modelom. Zatim je ispitano daje li model vrijednu informaciju u usporedbi sa volatilnošću koju implicira tržište kroz cijene opcija, a koja je izračunata preko Black-Scholesove formule. Statistička svojstva modela odgovaraju stvojstvima stvarnih prinosa, te model isključivo na osnovu povijesnih cijena vrlo dobro predviđa periode povišene volatilnosti.

Abstract (english)

In this work the topics of probability density functions and emergence of bimodal distributions of returns were elaborated based on the historical data of the S&P 500 index. Volatility prediction is one of the key problems in portfolio management and investment strategies. A volatility prediction model was developed and used for bimodality identification and prediction. True bimodality wasn’t detected, but the market conditions that significantly raise the probability of absolute returns greater than 2% were identified. These results have been compared to those that the model returns when the input that determines the volatility regime is replaced by GARCH(1,1) model. The output was tested in comparison to the implied volatility the market prices into the options prices, calculated via the Black-Scholes formula. The statistical properties of the model correspond to the properties of the real returns and the model is successful in predicting periods with raised volatility using solely the historical prices.

• Keywords: Bimodalnost; financijski vreneski nizovi; S&P 500; implicirana volatilnost; opcije; Black-Scholesov model; GARCH
• Keywords (english): Bimodality; financial time series; S&P 500; implied volatility; options; Black-Scholes model; GARCH
• Language: croatian
• URN:NBN: urn:nbn:hr:168:613644
• Study programme: Title: Information and Communication Technology; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije (magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-19 13:38:47