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Heavy-tailed Distributions and Financial Risk Measures

Show simple item record 2022-12-02T07:14:47Z 2022-12-02T07:14:47Z 2022-12-02
dc.title Heavy-tailed Distributions and Financial Risk Measures en
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty.URI Helsingin yliopisto fi University of Helsinki en Helsingfors universitet sv
dct.creator Schauman, Julia
dct.issued 2022 xx
dct.abstract In this thesis, we explore financial risk measures in the context of heavy-tailed distributions. Heavy-tailed distributions and the different classes of heavy-tailed distributions will be defined mathematically in this thesis but in more general terms, heavy-tailed distributions are distributions that have a tail or tails that are heavier than the exponential distribution. In other words, distributions which have tails that go to zero more slowly than the exponential distribution. Heavy-tailed distributions are much more common than we tend to think and can be observed in everyday situations. Most extreme events, such as large natural phenomena like large floods, are good examples of heavy-tailed phenomena. Nevertheless, we often expect that most phenomena surrounding us are normally distributed. This probably arises from the beauty and effortlessness of the central limit theorem which explains why we can find the normal distribution all around us within natural phenomena. The normal distribution is a light-tailed distribution and essentially it assigns less probability to the extreme events than a heavy-tailed distribution. When we don’t understand heavy tails, we underestimate the probability of extreme events such as large earthquakes, catastrophic financial losses or major insurance claims. Understanding heavy-tailed distributions also plays a key role when measuring financial risks. In finance, risk measuring is important for all market participants and using correct assumptions on the distribution of the phenomena in question ensures good results and appropriate risk management. Value-at-Risk (VaR) and the expected shortfall (ES) are two of the best-known financial risk measures and the focus of this thesis. Both measures deal with the distribution and more specifically the tail of the loss distribution. Value-at-Risk aims at measuring the risk of a loss whereas ES describes the size of a loss exceeding the VaR. Since both risk measures are focused on the tail of the distribution, mistaking a heavy-tailed phenomena for a light-tailed one can lead to drastically wrong conclusions. The mean excess function is an important mathematical concept closely tied to VaR and ES as the expected shortfall is mathematically a mean excess function. When examining the mean excess function in the context of heavy-tails, it presents very interesting features and plays a key role in identifying heavy-tails. This thesis aims at answering the questions of what heavy-tailed distributions are and why are they are so important, especially in the context of risk management and financial risk measures. Chapter 2 of this thesis provides some key definitions for the reader. In Chapter 3, the different classes of heavy-tailed distributions are defined and described. In Chapter 4, the mean excess function and the closely related hazard rate function are presented. In Chapter 5, risk measures are discussed on a general level and Value-at-Risk and expected shortfall are presented. Moreover, the presence of heavy tails in the context of risk measures is explored. Finally, in Chapter 6, simulations on the topics presented in previous chapters are shown to shed a more practical light on the presentation of the previous chapters. en
dct.subject Heavy-tailed distributions
dct.subject risk measures
dct.subject mean excess function
dct.subject hazard rate
dct.subject Value-at-Risk
dct.subject expected shortfall
ethesis.isPublicationLicenseAccepted true
ethesis.language englanti fi
ethesis.language English en
ethesis.language engelska sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
ethesis.thesistype pro gradu-avhandlingar sv
dct.identifier.ethesis E-thesisID:98c4d7ac-9f40-44fd-ae68-8aa42bd3df8f
dct.identifier.urn URN:NBN:fi:hulib-202212023920
dct.alternative Paksuhäntäiset jakaumat ja riskimitat fi
ethesis.facultystudyline Matematiikka ja soveltava matematiikka fi
ethesis.facultystudyline Mathematics and applied mathematics en
ethesis.facultystudyline Matematik och tillämpande matematik sv
ethesis.mastersdegreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi
ethesis.mastersdegreeprogram Master 's Programme in Mathematics and Statistics en
ethesis.mastersdegreeprogram Magisterprogrammet i matematik och statistik sv

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