The term structure of interest rates, also known as yield curve, is defined as the relationship between the yield to maturity on a zero coupon bond and the bond's maturity. Zero yield curves play an essential role in the valuation of all financial products. Yield curves can be derived from government bonds or LIBOR/swap instruments. The LIBOR/swap term structure offers several advantages over government curves, and is a robust tool for pricing and hedging financial products. Correlations among governments and other fixed income products have declined, making the swap term structure a more efficient hedging and pricing vehicle. ; https://ia801406.us.archive.org/33/items/ir-curve-introduction-1_202105/IrCurveIntroduction-1.pdf
Treasury curve or treasury benchmark curve is the term structures of treasury bill/bond prices vs maturities. The two major types of marketable securities issued by government are treasury bills and treasury bonds. ; https://ia801507.us.archive.org/7/items/fi-treasury-curve-11/FiTreasuryCurve-11.pdf
The creative industries have become the government's attention for contributing to economic accretion. But due to the lack of artistic creativity and appeal, the evolution of the creative industries' craft section is not optimal. So that it was needed a variation of relief items to increase attractiveness. In general, an industrial object's design is still limited to the space geometry objects or a Bezier curve of degree two. Therefore, Bezier curves of degree are selected and modified it into a quartic Bezier forms and then applied to the design of industrial objects (glassware). The purpose of this research is to determine the formula of the quartic Bezier form of cubic Bezier modifications and to determine the rotary surface shape of quartic Bezier from cubic Bezier modifications. Then, from some form of the revolving surface of modified cubic Bezier, the glassware designs are generated. The results of this research are, first, the formula of the quartic Bezier result of Bezier cubic modifications. Second, the form of the revolving surface of modified cubic Bezier which is influenced by five control points P0, NP31, NP32, NP33, P3, and parameter lambda. For further research, it is expected to develop a modification of cubic Bezier into Bezier of degree-n
The creative industries have become the government's attention for contributing to economic accretion. But due to the lack of artistic creativity and appeal, the evolution of the creative industries' craft section is not optimal. So that it was needed a variation of relief items to increase attractiveness. In general, an industrial object's design is still limited to the space geometry objects or a Bezier curve of degree two. Therefore, Bezier curves of degree are selected and modified it into a quartic Bezier forms and then applied to the design of industrial objects (glassware). The purpose of this research is to determine the formula of the quartic Bezier form of cubic Bezier modifications and to determine the rotary surface shape of quartic Bezier from cubic Bezier modifications. Then, from some form of the revolving surface of modified cubic Bezier, the glassware designs are generated. The results of this research are, first, the formula of the quartic Bezier result of Bezier cubic modifications. Second, the form of the revolving surface of modified cubic Bezier which is influenced by five control points P_0,NP_31,NP_32,NP_33,P_3 and parameter selection λ_31,λ_32,λ_33. For further research, it is expected to develop a modification of cubic Bezier into Bezier of degree-n
The European Central Bank (ECB), as part of its forward-looking strategy, needs high-quality financial market statistical indicators as a means to facilitate evidence-based and sound decision-making. Such indicators include timely market intelligence and information to gauge investors' expectations and reaction functions with regard to policy decisions. The main use of yield curve estimations from an ECB monetary policy perspective is to obtain a proper empirical representation of the term structure of interest rates for the euro area which can be interpreted in terms of market expectations of monetary policy, economic activity and inflation expectations over short-, medium- and long-term horizons. Yield curves therefore play a pivotal role in the monitoring of the term structure of interest rates in the euro area. In this context, the purpose of this paper is twofold: firstly, to pave the way for a conceptual framework with recommendations for selecting a high-quality government bond sample for yield curve estimations, where changes mainly reflect changes in the yields-to-maturity rather than in other attributes of the underlying debt securities and models; and secondly, to supplement the comprehensive - mainly theoretical - literature with the more empirical side of term structure estimations by applying statistical tests to select and produce representative yield curves for policymakers and market-makers.
Durch die zunehmende Digitalisierung, und insbesondere dem sogenannten "Internet of Things", ist der Bedarf an zuverlässigen kryptografischen Verfahren nicht nur für Behörden, sondern auch für Privatpersonen wichtig geworden. In den letzten Jahrzehnten wurde eine Vielzahl an unterschiedlichsten Lösungen präsentiert. Diese Arbeit befasst sich mit elliptischen Kurven und kryptographischen Verfahren, deren Sicherheit auf dem "Elliptic Curve Discrete Logarithm Problem" beruht. Zunächst wird ein grober Überblick über die erforderlichen algebraischen Konzepte, den projektiven Raum und grundlegende Begriffe und Konzepte aus der Kryptographie gegeben. Im Folgenden werden elliptische Kurven als projektive ebene Kurven eingeführt, welche durch ein nichtsinguläres Weierstraß-Polynom definiert sind. Eigenschaften der Schnittpunkte von (elliptischen) Kurven und projektiven Geraden werden herausgearbeitet und ein Spezialfall des Satzes von Bézout wird bewiesen. Dadurch kann im Anschluss gezeigt werden, dass durch wiederholtes Schneiden von Geraden mit einer elliptischen Kurve ein Gruppengesetz für die Menge der Schnittpunkte aufgestellt werden kann. Es werden explizite Formeln für die "Punktaddition" hergeleitet. Danach werden kryptographische Verfahren vorgestellt, die eben diese Gruppe nutzen. Abschließend wird ein Ausblick in die Zukunft der "Elliptic Curve Cryptography" gegeben. ; The increasing digitization, and in particular the Internet of Things, has made the need for reliable cryptographic processes important not only for government use but also for private individuals. Over the last decades, many different solutions have been proposed. This thesis deals with elliptic curves and cryptographic schemes whose security rely on the "Elliptic Curve Discrete Logarithm Problem". First, a rough overview of the required algebraic concepts, projective space, and basic terms and concepts from cryptography is given. In the following, elliptic curves are introduced as projective plane curves defined by a non-singular Weierstraß polynomial. The properties of the intersection of (elliptic) curves and projective lines are worked out, and a special case of Bézout's theorem is proved. By repeatedly intersecting lines with an elliptic curve, a group law can be established on the set of intersection points. Explicit formulas for performing "point addition" are derived. Subsequently, cryptographic schemes making use of the elliptic curve group are presented. Finally, an outlook into the future of "Elliptic Curve Cryptography" is given. ; Arbeit an der Bibliothek noch nicht eingelangt - Daten nicht geprüft ; Abweichender Titel laut Übersetzung des Verfassers/der Verfasserin ; Karl-Franzens-Universität Graz, Diplomarbeit, 2021 ; (VLID)6525764
Traditional derivatives pricing theory is based on the assumption that trading desks can lend and borrow at some risk-free rate. Since the credit crunch in 2007, there has been a divergence between government rates, bank funding rates, repo rats, LIBOR rates and overnight rates. To mitigate counterparty credit risks, derivatives have been increasingly collateralized in the interbank market since. We therefore present a consistent pricing framework taking into account different funding assets and collateral schemes as well as risky assets for which a repo market may exist. The current multiple-curve reality in the interest rates market is analyzed in detail for uncollateralized and perfectly collateralized derivatives. Different multiple-curve models from recent papers are recalled, extended and embedded into a consistent framework. Valuation formulas for swaps, forward rate agreements, caps, swaptions and futures are derived in different multiple-curve LIBOR market models. We discuss various dynamics of the forward rates associated with the discounting curve as well as various dynamics of the forward spread between a one-period swap curve and the discounting curve. The considered models could be used for pricing products where a deterministic basis spread is too simplistic, despite the fact that the market does not readily quote volatilities and correlations of OIS rates.
Elliptic Curve Cryptography (ECC) is a branch of public-key cryptography based on the arithmetic of elliptic curves. In the short life of ECC, most standards have proposed curves defined over prime finite fields using the short Weierstrass form. However, some researchers have started to propose as a more secure alternative the use of Edwards and Montgomery elliptic curves, which could have an impact in current ECC deployments. This chapter presents the different types of elliptic curves used in Cryptography together with the best-known procedure for generating secure elliptic curves, Brainpool. The contribution is completed with the examination of the latest proposals regarding secure elliptic curves analyzed by the SafeCurves initiative. ; Acknowledgements: This work has been partly supported by Ministerio de Economía y Competitividad (Spain) under the project TIN2014-55325-C2-1-R (ProCriCiS), and by Comunidad de Madrid (Spain) under the project S2013/ICE-3095-CM (CIBERDINE), cofinanced with the European Union FEDER funds.
We set out and solve a static neoclassical model with a labor/leisure choice for agents and a government sector producing a Samuelsonian public good. Numerical solutions vary considerably with the elasticity of substitution for commodities in an agent's utility function. We focus on solutions with an income tax rate set by the government (second best solutions). Government revenue varies with the rate of income tax (expressed in a Laffer Curve) and we observe that such curves generally peak "internally" only for case of "high" elasticity values in the utility function of a representative agent. Inelastic substitution possibilities involve the peaking of the Laffer Curve at a corner with the rate of income tax tending to unity. We report on welfare analysis for small changes in the rate of income tax and on first best outcomes (agents charged Samuelson "prices" for the public good).
This paper attempts to model the widely studied relationship between a country's economic growth and its level of democracy, with an emphasis on possible non-linearities. We adopt the concept of "political capital" as a measure of democracy, which is extremely uncommon in the literature and brings considerable advantages both in terms of dynamic considerations and plausibility. While the literature is not consensual on this matter, we obtain significant and robust results that indicate that the impact of democratization on economic growth varies according to the stage of democratic development each country is in.
Cryptography is one of the most important applications and widely used in our life especially in the information security that needed by many government institutions, banks, communications and others to keep data over internet and other transportations that it is ensure safety of transfers between the sender and the recipient. The most important system in cryptography is public key cryptography and the mostly used is the elliptic curves cryptosystem, because of it is very efficient and secure and difficult to solve the discrete logarithm problem and find the secret key. In this study a new method is introduced using the Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC) for data based on quadratic Bézier curve techniques. The purpose of this proposal is to increase the security of this cryptosystem. We will apply this proposed method to all measurements of National Institute of Standards and Technology (NIST) tests and running time and compared it with the original method.
13 páginas, 2 tablas ; Elliptic Curve Cryptography (ECC) is a branch of public-key cryptography based on the arithmetic of elliptic curves. In the short life of ECC, most standards have proposed curves defined over prime finite fields satisfying the curve equation in the short Weierstrass form. However, some researchers have started to propose as a securer alternative the use of Edwards and Montgomery elliptic curves, which could have an impact in current ECC deployments. This contribution evaluates the performance of the three types of elliptic curves using some of the examples provided by the initiative SafeCurves and a Java implementation developed by the authors, which allows us to offer some conclusions about this topic. ; This work has been partially supported by Ministerio de Econom´ıa, Industria y Competitividad (MINECO), Agencia Estatal de Investigaci´on (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R, and by Comunidad de Madrid (Spain) under project CIBERDINE, reference S2013/ICE-3095-CM, also co-financed by European Union FEDER funds.
13 páginas, 2 tablas ; Elliptic Curve Cryptography (ECC) is a branch of public-key cryptography based on the arithmetic of elliptic curves. In the short life of ECC, most standards have proposed curves defined over prime finite fields satisfying the curve equation in the short Weierstrass form. However, some researchers have started to propose as a securer alternative the use of Edwards and Montgomery elliptic curves, which could have an impact in current ECC deployments. This contribution evaluates the performance of the three types of elliptic curves using some of the examples provided by the initiative SafeCurves and a Java implementation developed by the authors, which allows us to offer some conclusions about this topic. ; This work has been partially supported by Ministerio de Econom´ıa, Industria y Competitividad (MINECO), Agencia Estatal de Investigaci´on (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R, and by Comunidad de Madrid (Spain) under project CIBERDINE, reference S2013/ICE-3095-CM, also co-financed by European Union FEDER funds.
The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor Miller in 1985. Being a relatively new field, there is still a lot of ongoing research on the subject, but elliptic curve cryptography, or ECC for short, has already been implemented in real-life applications. Its strength was proved in 2003 when the U.S. National Security Agency adopted ECC for protecting information classified as mission-critical by the U.S. government. The security of public-key cryptographic systems that can be considered secure, efficient, and commercially viable is directly tied to the relative hardness of their underlying mathematical problems. In the case of ECC, this mathematical problem is to solve the discrete logarithm problem over elliptic curves, or ECDLP for short. Because the best-known way to solve ECDLP is fully exponential, we can use substantially smaller key sizes to obtain equivalent strengths compared to other systems. Hence, ECC provides the most security per bit of any public-key scheme known. In this thesis we have focused on presenting the known attacks on the ECDLP. We started by introducing some basic facts from the theory of elliptic curves. In the rest of the thesis we have described, analyzed and presented running time estimates of attacks on the ECDLP. This included a presentation of attacks which are specially designed to exploit weaknesses in the structure of some classes of elliptic curves. We have also presented attacks which can be used to solve the ECDLP over general elliptic curves. This included Pollard's rho and lambda algorithms, where the former was used for solving the ECDLP challenges set by the Certicom company.
The dynamic properties of the The New Keynesian Phillips curve (NPC) is analysed within the framework of a small system of linear di.erence equations.We evaluate the empirical results of existing studies which uses 'Euroland' and US data. The debate has been centered around the goodness-of-fit, but this is a weak criterion since the NPC-fit is typically well approximated by purely statistical models (e.g., a random walk). Several other parametric tests are then considered, and the importance of modelling a system that includes the forcing variables as well as the rate of inflation is emphasized. We also highlight the role of existing studies in providing new information relative to that which underlies the typical NPC. This encompassing approach is applied to open economy versions of the NPC for UK and Norway.
