441 research outputs found
Monte Carlo Greeks in the lognormal Libor market model
No full textGreeks are sensitivities of option prices with respect to certain parameters. The calculation of Greeks is needed for hedge strategies and to manage or measure risk. As the underlying models get more complicated, the calculation of these Greeks can become far more difficult than the pricing of options. In this thesis we consider the Greeks of both European- and Bermudan-style Libor rate contracts. To model forward Libor rates we use the lognormal forward Libor market model. Because of the dimensionality of the model, only Monte Carlo methods are capable to estimate these Greeks. Therefore various Monte Carlo methods to estimate the Greeks will be considered and adjusted to our model settings. The methods are tested and compared, and if possible, improved. We improve the likelihood ratio method for the Greeks of Bermudan-style options by the use of a predictor-corrector scheme. Another succesful method which can be used for Greek calculations is given by the pathwise sensitivity method.Numerical analysisApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Modelling the Libor transition: Implementing and extending the generalized forward market model
No full textInterbank-offered-rates play a critical role in the hedging processes of banks, hedge funds or institutional investors. However, the financial stability board recommended to replace these rates by alternative risk-free-rates at the end of 2021. The new rates will be backward-looking rates and therefore, the payoff definitions of interest rate derivatives will change and the currently used Libor Market model to price exotic interest rate derivatives is no longer feasible. This thesis examines a new type of model, the forward market model, which is able to generate both the new backward-looking rates as the current forward-looking rates under the same stochastic process. Besides, contrary to the Libor Market Model, the dynamics under the risk-neutral measure can obtained. Consequently, the new forward market model should always be chosen over the Libor market model. Two issues regarding the forward market model are also considered in this thesis. First of all, the forward market model cannot deal with negative interest rate, this is solved by implementing a shifted version of the log-normal model. Second, a log-normal model is unable to reproduce the implied volatility smile which is present in the market. We solve this issue by combining the forward market model together with the SABR model. Under a few assumptions we derive the shifted SABR forward market model which hasn't been derived in the literature. The model is validated by pricing a new type of caplet that will be present in the post-Libor world, where the payoff won't be known until the payment date. We find that the implementation of this new shifted SABR-FMM can accurately price zero-coupon bonds and caplets in the market. Therefore, we conclude that this new type of model is a possible solution to price exotic interest rate derivatives in the post-Libor world.Applied Mathematic
On the pricing of Bermudan swaptions in the multi-curve LIBOR Market Model
No full textThe aim of this research is to extend the classical LMM to a multi-curve framework and to analyze the impact of this extended model on the most liquid exotic interest rate derivatives. A possible parametrization for the instantaneous volatility and correlation structure is presented and the (log-)normal dynamics of the OIS rates under different measures are obtained. The forward LIBOR rates are modeled at a constant additive spread over the OIS curve. An analytical closed-form approximation of the European swaption volatility in the multi-curve framework is derived and its accuracy is verified by comparing the Monte Carlo prices of a set of European swaptions with the corresponding prices obtained using the approximation. It is demonstrated that the approximation reaches the highest accuracy for swaptions characterized by short underlying tenors and strikes close to the swap rate. The multi-curve LIBOR Market Model is calibrated to the swaption market applying this approximation. Using the calibrated model distinct Bermudan swaptions are priced by means of Monte Carlo. These prices are compared to the corresponding prices obtained using the one-factor Hull-White model and the impact of the model selection is analyzed.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied MathematicsApplied Probabilit
Ab initio calculations of BN molecule and small fused hydrocarbons with single-reference and Brillouin-Wigner multireference coupled clusters methods
No full textDepartment of Physical and Macromolecular ChemistryKatedra fyzikální a makromol. chemiePřírodovědecká fakultaFaculty of Scienc
L^2-theoretical study of the relation between the LIBOR market model and the HJM model
No full textIn previous works, the author introduced metric spaces of term structure models to study the relation between the LIBOR market model and the HJM model. However that framework is not comprehensive, nor does it admit an extendable structure. This paper introduces a new metric space to better develop the perspective argument. A metric space is naturally constructed on the set of bond price processes such that the space allows many types of term structure models. This metric presents a general view on the relation between the LIBOR market model and the HJM model. Consequently, the LIBOR market model is placed at the boundary of the HJM model set.MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点
L^2-theoretical study of the relation between the LIBOR market model and the HJM model
No full textMI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」In previous works, the author introduced metric spaces of term structure models to study the relation between the LIBOR market model and the HJM model. However that framework is not comprehensive, nor does it admit an extendable structure. This paper introduces a new metric space to better develop the perspective argument. A metric space is naturally constructed on the set of bond price processes such that the space allows many types of term structure models. This metric presents a general view on the relation between the LIBOR market model and the HJM model. Consequently, the LIBOR market model is placed at the boundary of the HJM model set
Modelling of Ultracold Gases in Multidimensional Optical Lattices
No full textTitle: Modelling of Ultracold Gases in Multidimensional Optical Lattices Author: Miroslav Urbanek Department: Department of Chemical Physics and Optics Supervisor: doc. Ing. Pavel Soldán, Dr. Abstract: Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model. Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model. The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices. The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems. Keywords: Bose-Hubbard model, multidimensional system, optical lattice, tensor networ
O potrzebie socjologii snów słów kilka
No full textThe article by Grzegorz Libor treating about the need of creating the sociology of
dreams, a new branch in sociology, constitutes an intellectual provocation. The author, in his considerations, moves from an individual dimension of the notion of a dream to the social one, and explains how the dream is interpreted in the Biblical tradition, psychology, psychoanalysis, cognitivism, as well as popular culture. The researcher also outlines the methodology of studies in the sociology of dreams thanks to the proposal of realizing traditional questionnaires and conducting Internet analysis. For example social portals where people share their dream experiences
Short-lived Delocalization and Absorption by Light
No full textCoherent exciton delocalization improves the light harvesting function of photosyn- thetic antennae by creating conditions for very fast excitation transfer in space. This thesis focuses on two different effects creating coherence - short-lived excitation by light and weak coupling between pigments that is present in the system on longer timescales. The evolution and relaxation of simple systems - the dimer and trimer - are calculated. The core of this thesis are newly developed numerical methods for distinguishing and quantifying the effect of the two types of coherence throughout evolution, which are applied to the aforementioned systems.
Quantum computing approach to non-relativistic and relativistic molecular energy calculations
No full textQuantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. In fact, they have a potential to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling only. This is in contrast to con- ventional computers where FCI scales exponentially. We provide a detailed description of the quantum version of the FCI method and the results of numerical simulations of the ground and excited state energy calculations of the methylene molecule. We further generalize this method to the relativistic four component regime and show how to efficiently solve the eigenproblem of the Dirac-Coulomb(-Breit) Hamiltonian on a quantum computer. We demonstrate the func- tionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.
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