Modeling the term structure of zero-coupon bonds

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dc.contributor Helsingin yliopisto, Matemaattis-luonnontieteellinen tiedekunta fi
dc.contributor University of Helsinki, Faculty of Science en
dc.contributor Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten sv Duevski, Teodor 2019
dc.identifier.uri URN:NBN:fi:hulib-201905242129
dc.description.abstract In this thesis we model the term structure of zero-coupon bonds. Firstly, in the static setting by norm optimization Hilbert space techniques and starting from a set of benchmark fixed income instruments, we obtain a closed from expression for a smooth discount curve. Moving on to the dynamic setting, we describe the stochastic modeling of the fixed income market. Finally, we introduce the Heath-Jarrow-Morton (HJM) methodology. We derive the evolution of zero-coupon bond prices implied by the HJM methodology and prove the HJM drift condition for non arbitrage pricing in the fixed income market under a dynamic setting. Knowing the current discount curve is crucial for pricing and hedging fixed income securities as it is a basic input to the HJM valuation methodology. Starting from the non arbitrage prices of a set of benchmark fixed income instruments, we find a smooth discount curve which perfectly reproduces the current market quotes by minimizing a suitably defined norm related to the flatness of the forward curve. The regularity of the discount curve estimated makes it suitable for use as an input in the HJM methodlogy. This thesis includes a self-contained introduction to the mathematical modeling of the most commonly traded fixed income securities. In addition, we present the mathematical background necessary for modeling the fixed income market in a dynamic setting. Some familiarity with analysis, basic probability theory and functional analysis is assumed. en
dc.language.iso eng
dc.publisher Helsingin yliopisto fi
dc.publisher University of Helsinki en
dc.publisher Helsingfors universitet sv
dc.title Modeling the term structure of zero-coupon bonds en
dc.type.ontasot pro gradu -tutkielmat fi
dc.type.ontasot master's thesis en
dc.type.ontasot pro gradu-avhandlingar sv
dc.subject.discipline none und
dct.identifier.urn URN:NBN:fi:hulib-201905242129
dc.subject.specialization Matematiikka fi
dc.subject.specialization Mathematics en
dc.subject.specialization Matematik sv
dc.subject.degreeprogram Teoreettisten ja laskennallisten menetelmien maisteriohjelma fi
dc.subject.degreeprogram Master's Programme in Theoretical and Computational Methods en
dc.subject.degreeprogram Magisterprogrammet i teoretiska och beräkningsmetoder sv

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