dc.date.accessioned 
20221202T07:14:47Z 

dc.date.available 
20221202T07:14:47Z 

dc.date.issued 
20221202 

dc.identifier.uri 
http://hdl.handle.net/123456789/43699 

dc.title 
Heavytailed Distributions and Financial Risk Measures 
en 
ethesis.faculty 
Matemaattisluonnontieteellinen tiedekunta 
fi 
ethesis.faculty 
Faculty of Science 
en 
ethesis.faculty 
Matematisknaturvetenskapliga fakulteten 
sv 
ethesis.faculty.URI 
http://data.hulib.helsinki.fi/id/8d59209f66144edd97441ebdaf1d13ca 

ethesis.university.URI 
http://data.hulib.helsinki.fi/id/50ae46d87ba94821877cc994c78b0d97 

ethesis.university 
Helsingin yliopisto 
fi 
ethesis.university 
University of Helsinki 
en 
ethesis.university 
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 heavytailed distributions. Heavytailed distributions and the different classes of heavytailed distributions will be defined mathematically in this thesis but in more general terms, heavytailed 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. Heavytailed 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 heavytailed 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 lighttailed distribution and essentially it assigns less probability to the extreme events than a heavytailed 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 heavytailed 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. ValueatRisk (VaR) and the expected shortfall (ES) are two of the bestknown financial risk measures and the focus of this thesis. Both measures deal with the distribution and more specifically the tail of the loss distribution. ValueatRisk 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 heavytailed phenomena for a lighttailed 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 heavytails, it presents very interesting features and plays a key role in identifying heavytails. This thesis aims at answering the questions of what heavytailed 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 heavytailed 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 ValueatRisk 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 
Heavytailed distributions 

dct.subject 
risk measures 

dct.subject 
mean excess function 

dct.subject 
hazard rate 

dct.subject 
ValueatRisk 

dct.subject 
expected shortfall 

ethesis.isPublicationLicenseAccepted 
true 

ethesis.language.URI 
http://data.hulib.helsinki.fi/id/languages/eng 

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 graduavhandlingar 
sv 
ethesis.thesistype.URI 
http://data.hulib.helsinki.fi/id/thesistypes/mastersthesis 

dct.identifier.ethesis 
EthesisID:98c4d7ac9f4044fdae688aa42bd3df8f 

dct.identifier.urn 
URN:NBN:fi:hulib202212023920 

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.facultystudyline.URI 
http://data.hulib.helsinki.fi/id/SH50_MASTMSM 

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 
ethesis.mastersdegreeprogram.URI 
http://data.hulib.helsinki.fi/id/MH50_001 
