Browsing by Author "Varis, Karri"
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- Computational methods for finite thickness photonic crystals
Doctoral dissertation (article-based)(2005-12-02) Varis, KarriWe develop a computational algorithm for finite thickness photonic crystals and apply it to photonic crystal slabs and artificial opals. The algorithm is not limited to solving only photonic crystals but can be applied to any electromagnetic problem, which is periodic in a plane and has a finite thickness in the perpendicular direction. An application in cylindrical coordinates is also presented. The method is based on the diagonalized form of Maxwell's equations, in which one spatial direction is distinguished and isolated. We show that this formulation is especially suitable for problems, which are periodic along two and non-periodic along the third axis. The fields are expanded in a combination of several bases, planewaves in the transversal plane, finite differences and eigenvectors in the perpendicular direction. The method is applied to both eigenmode and excitation problems. Furthermore, we develop an efficient scheme for computing the reflection of arbitrarily shaped and polarised beams from the surface of a periodic media. A great emphasis is laid on accuracy and efficiency. The resulting equations are solved using iterative techniques together with problem adapted, operator level preconditioners. Finally, we compare the computations to measurement results obtained from artificial opals. - Default-implied asset correlations for Finnish small and medium-sized enterprises
Perustieteiden korkeakoulu | Master's thesis(2021-03-17) Ryhänen Rodellas, MarcosDefault-implied asset correlation plays a critical role in determining regulatory capital and in measuring credit risk. Modelling correlations between default events is one of the biggest challenges in credit risk modelling. The Basel committee aims to strengthen the capital market by specifying the asset correlations for bank exposures. The dependence between borrowers in credit risk models is estimated using asset correlations. The accuracy of these models therefore depends on the precision of the estimated asset correlations. Asset correlation set by authorities can be overly conservative for Finnish small and medium-sized enterprises (SMEs). High asset correlations can lead to overly large credit risk estimates. In this work we estimate asset correlations between different Finnish SME industry sectors. The joint default probabilities between borrowers are estimated from historical default data. The asset correlations between borrowers are calculated numerically from the joint default probabilities. The effect of asset correlations on credit risk is simulated using one-factor and multi-factor models. Our results suggest that larger companies have higher asset correlations. Our results also suggest that supervisory estimates of asset correlations are overly conservative for Finnish SMEs. Well-defined industry groups with high mutual asset correlations were not found, but there exists higher asset correlations between some industry sectors. However, our grouping of industry sectors may understate asset correlations. Our simulations show that credit risk is higher for portfolios with higher asset correlations. The implication to Finnish banks would be to use a more precise analysis of asset correlations in their risk management. - Aktiivisen fotonikiderakenteen suunnittelu ja valmistus
Helsinki University of Technology | Master's thesis(2000) Kainu, Kalle - Valokanavan valmistaminen indiumfosfidille
Helsinki University of Technology | Master's thesis(2000) Säynätjoki, Antti - Non-maturity deposit valuation and hedging
Helsinki University of Technology | Master's thesis(2008) Eronen, Tanja Susanne ElisabethUsually non-maturity deposits form a considerable part of banks' assets and funding and thus hedging the interest rate risk of them is important. However, the available research addressing non-maturity deposit valuation is very limited. In this Thesis, we compare models for estimating the deposit rate and stock evolution and suggest suitable hedging possibilities for non-maturity deposits. Non-maturity deposits have no stated maturity and they can be withdrawn at any time. However, they often remain with the financial institution for extended periods of time. The previous studies show that the deposit rate follows usually a short market rate, but with stickiness and asymmetric mean reversion. The stock of the non- maturity deposits tend to be highest when the interest rates are low because then the opportunity cost is low. The value of the non-maturity deposit is computed with the Jarrow-Van Deventer -model and the interest rate risk is analysed with the duration and average life of the non-maturity deposits. We compare the different hedging methods by simulating the cash flows with the Vasicek model and the error correction model for the deposit rate. The error correction model estimates better the deposit rate of interest than ordinary dynamic models. When the error correction model is modified, it can explain also the asymmetric adjustment of the rate. The deposit stock has a strong time trend and it also depends on the market rate. The non-maturity deposits have a very long duration of over 20 years and an average life over 5 years. From the hedging methods, deposit swap was found to be the most efficient one when considering variances. However, the plain vanilla swap seems to be almost as efficient, but a more simple and liquid way to hedge the non-maturity deposits. - Optinen kytkin
Helsinki University of Technology | Master's thesis(1999) Varis, KarriTyön tavoitteena on tutustua erilaisiin III-V-puolijohteista valmistettaviin optisiin kytkimiin ja tutkia lähemmin digitaalisen optisen kytkimen toimintaa ja valmistamista. Digitaalisen optisen kytkimen toiminta perustuu adiabaattiseen muodon kehittymiseen ja sen hyvänä puolena on lähes digitaalinen vaste kytkentäjännitteeseen ja verrattain suuret toleranssit valmistuksen epätarkkuuksille. Kytkimen toiminnan kannalta on olennaista, että siinä käytetään yksimuotoisia aaltojohteita, joiden taitekerrointa voidaan muuttaa dynaamisesti. Työn pääpaino on sopivan harjannevalokanavan tutkimisessa käyttäen apuna tietokonemallitusta. Työn osana kirjoitettiin tietokoneohjelmat, joilla optisten rakenteiden muotokentät voidaan laskea kaksi- ja kolmiulotteisille valokanaville. Tavoitteena on löytää sellainen harjannevalokanava, joka toimii yksimuotoisesti pienistä valmistuksen ja toiminta-aallonpituuden epätarkkuuksista huolimatta. Työssä on perehdytty myös taitekertoimen muuttamisen erilaisiin menetelmiin. Vaihtoehtoina olivat elektro-optinen efekti sekä varauksenkuljettajatiheyden muuttamiseen perustuvat menetelmät. Kytkimen ohjauksessa päätettiin käyttää taitekertoimen muuttamista suoralla virran injektiolla, koska siten saavutetaan kaikista suurin efekti, joka on lisäksi isotrooppinen. Taitekertoimen muutosta valituissa materiaaleissa, InP:ssä ja GaInAsP:ssa, tutkittiin työn osana kirjoitetulla tietokoneohjelmalla. Aaltojohteen sähköisiä ominaisuuksia tutkittiin, jotta voitaisiin selvittää toiminnan kannalta optimaaliset seostukset. Seostuksien valinnalla pyritään aikaansaamaan sellainen pin-liitos, jossa injektoitava virta aikaansaa mahdollisimman suuren spatiaalisen varauksenkuljettajatiheyden. Toinen seostuksien valintaan vaikuttava tekijä on liitoksen sähkönvastus, koska liiallinen tehonkulutus ja lämpeneminen saattaa tuhota komponentin. Viimeisessä kappaleessa on tehty alustavat mallitukset itse digitaaliselle kytkimelle. Tarkemmat mallitukset on tarkoitus tehdä kun ensimmäiset aaltojohteet on valmistettu ja mitattu.