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Modelling of yield curves
Šmejkal, Jan ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In practice, yield curves, i.e. plots of relation between yields and times to maturity for a group of comparable securities, are an important tool for assets and liabilities pricing as well as for financial decision making. The theoretical risk-free yield curve represents the term structure of interest rates that are used e.g. in insurance industry for pricing the liabilities, for which reserves are created, or also as a benchmark for pricing other assets in the market. When constructing the yield curve, it is not possible to observe yields of a group of assets for all maturities. That is why we use various mathematical methods which enable us to construct the yield curve also for unobserved maturities. In this thesis, some of these methods are introduced. The Svensson's method is one of the most important and frequently used ones. We use this method to derive the coupon curve from Czech government bonds aiming to construct the risk-free zero coupon yield curve. Later on, we use different weights for particular bonds trying to improve pricing of all the bonds based on the derived curve. Then, we also look for the curve that minimizes the mean squared error of estimated (compared to observed) prices. Because problems with liquidity can appear especially for long maturities, we apply all of the procedures to a...
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Updating the Ultimate Forward Rate over Time: a Possible Approach
Žigraiová, Diana ; Jakubík, Petr
This study proposes a potential methodological approach to be used by regulators when updating the Ultimate Forward Rate (UFR) for the evaluation of insurers’ liabilities beyond the last liquid point observable in the market. Our approach is based on the optimisation of two contradictory aspects – stability and accuracy implied by economic fundamentals. We use U.S. Treasury term structure data over the period 1985-2015 to calibrate an algorithm that dynamically revises the UFR based on the distance between the value implied by the long-term growth of economic fundamentals in a given year and the regulatory value of the UFR valid in the prior year. We employ both the Nelson-Siegel and Svensson models to extrapolate yields over maturities of 21-30 years employing the selected value of the UFR and compare them with the observed yields using the mean square error statistic. Furthermore, we optimise the parameters of the proposed UFR formula by minimising the defined loss function capturing both mentioned factors.
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Modelling of yield curves
Šmejkal, Jan ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In practice, yield curves, i.e. plots of relation between yields and times to maturity for a group of comparable securities, are an important tool for assets and liabilities pricing as well as for financial decision making. The theoretical risk-free yield curve represents the term structure of interest rates that are used e.g. in insurance industry for pricing the liabilities, for which reserves are created, or also as a benchmark for pricing other assets in the market. When constructing the yield curve, it is not possible to observe yields of a group of assets for all maturities. That is why we use various mathematical methods which enable us to construct the yield curve also for unobserved maturities. In this thesis, some of these methods are introduced. The Svensson's method is one of the most important and frequently used ones. We use this method to derive the coupon curve from Czech government bonds aiming to construct the risk-free zero coupon yield curve. Later on, we use different weights for particular bonds trying to improve pricing of all the bonds based on the derived curve. Then, we also look for the curve that minimizes the mean squared error of estimated (compared to observed) prices. Because problems with liquidity can appear especially for long maturities, we apply all of the procedures to a...
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Analysis of methods for constructing yield curves
Matějka, Martin ; Janeček, Martin (advisor) ; Sitař, Milan (referee)
The thesis is focused on finding the most appropriate method for constructing the yield curve which will meet the criteria of Solvency II and also the selected evaluation criteria. An overview of advantages of each method is obtained by comparing these methods. Yield curves are constructed using the Czech interest rate swap data from 2007 to 2013. The selection of the evaluated methods respects their public availability and their practical application in life insurance or central banks. This thesis is divided into two parts. The first part describes the theoretical background which is necessary to understand the examined issues. In the second part the analysis of selected methods was carried out with detailed evaluation.
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