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Imputation of Missing Data with Application to Commodity Futures
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Imputation av saknad data med tillämpning på råvaruterminer (Swedish)
Abstract [en]

In recent years additional requirements have been imposed on financial institutions, including Central Counterparty clearing houses (CCPs), as an attempt to assess quantitative measures of their exposure to different types of risk. One of these requirements results in a need to perform stress tests to check the resilience in case of a stressed market/crisis. However, financial markets develop over time and this leads to a situation where some instruments traded today are not present at the chosen date because they were introduced after the considered historical event. Based on current routines, the main goal of this thesis is to provide a more sophisticated method to impute (fill in) historical missing data as a preparatory work in the context of stress testing. The models considered in this paper include two methods currently regarded as state-of-the-art techniques, based on maximum likelihood estimation (MLE) and multiple imputation (MI), together with a third alternative approach involving copulas. The different methods are applied on historical return data of commodity futures contracts from the Nordic energy market. By using conventional error metrics, and out-of-sample log-likelihood, the conclusion is that it is very hard (in general) to distinguish the performance of each method, or draw any conclusion about how good the models are in comparison to each other. Even if the Student’s t-distribution seems (in general) to be a more adequate assumption regarding the data compared to the normal distribution, all the models are showing quite poor performance. However, by analysing the conditional distributions more thoroughly, and evaluating how well each model performs by extracting certain quantile values, the performance of each method is increased significantly. By comparing the different models (when imputing more extreme quantile values) it can be concluded that all methods produce satisfying results, even if the g-copula and t-copula models seems to be more robust than the respective linear models.

Abstract [sv]

På senare år har ytterligare krav införts för finansiella institut (t.ex. Clearinghus) i ett försök att fastställa kvantitativa mått på deras exponering mot olika typer av risker. Ett av dessa krav innebär att utföra stresstester för att uppskatta motståndskraften under stressade marknader/kriser. Dock förändras finansiella marknader över tiden vilket leder till att vissa instrument som handlas idag inte fanns under den dåvarande perioden, eftersom de introducerades vid ett senare tillfälle. Baserat på nuvarande rutiner så är målet med detta arbete att tillhandahålla en mer sofistikerad metod för imputation (ifyllnad) av historisk data som ett förberedande arbete i utförandet av stresstester. I denna rapport implementeras två modeller som betraktas som de bäst presterande metoderna idag, baserade på maximum likelihood estimering (MLE) och multiple imputation (MI), samt en tredje alternativ metod som involverar copulas. Modellerna tillämpas på historisk data förterminskontrakt från den nordiska energimarkanden. Genom att använda väl etablerade mätmetoder för att skatta noggrannheten förrespektive modell, är det väldigt svårt (generellt) att särskilja prestandan för varje metod, eller att dra några slutsatser om hur bra varje modell är i jämförelse med varandra. även om Students t-fördelningen verkar (generellt) vara ett mer adekvat antagande rörande datan i jämförelse med normalfördelningen, så visar alla modeller ganska svag prestanda vid en första anblick. Däremot, genom att undersöka de betingade fördelningarna mer noggrant, för att se hur väl varje modell presterar genom att extrahera specifika kvantilvärden, kan varje metod förbättras markant. Genom att jämföra de olika modellerna (vid imputering av mer extrema kvantilvärden) kan slutsatsen dras att alla metoder producerar tillfredställande resultat, även om g-copula och t-copula modellerna verkar vara mer robusta än de motsvarande linjära modellerna.

Place, publisher, year, edition, pages
2016.
Series
TRITA-MAT-E, 2016:17
Keyword [en]
Missing Data, Bayesian Statistics, Expectation Conditional Maximization (ECM), Conditional Distribution, Robust Regression, MCMC, Copulas.
Keyword [sv]
Saknad Data, Bayesiansk Statistik, Expectation Conditional Maximization (ECM), Betingad Sannolikhet, Robust Regression, MCMC, Copulas.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-187459OAI: oai:DiVA.org:kth-187459DiVA: diva2:932785
External cooperation
NASDAQ
Subject / course
Mathematical Statistics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2016-06-02 Created: 2016-05-23 Last updated: 2016-06-06Bibliographically approved

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