375 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
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
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
LIBOR Fallback and Quantitative Finance
No full textWith the expected discontinuation of the LIBOR publication, a robust fallback for related financial instruments is paramount. In recent months, several consultations have taken place on the subject. The results of the first ISDA consultation have been published in November 2018 and a new one just finished at the time of writing. This note describes issues associated to the proposed approaches and potential alternative approaches in the framework and the context of quantitative finance. It evidences a clear lack of details and lack of measurability of the proposed approaches which would not be achievable in practice. It also describes the potential of asymmetrical information between market participants coming from the adjustment spread computation. In the opinion of this author, a fundamental revision of the fallback’s foundations is required
SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives
No full text© 2014 Elsevier. This manuscript version is made available under the CCBY-
NC-ND 4.0 license https://creativecommons.org/licenses/by-ncnd/
4.0/. This version of the article has been accepted for publication in
Applied Mathematics and Computation (ISSN 1873-5649). The Version of
Record is available online at 10.1016/j.amc.2014.05.017.[Abstract]: In order to overcome the drawbacks of assuming deterministic volatility coefficients in the standard LIBOR market models to capture volatility smiles and skews in real markets, several extensions of LIBOR models to incorporate stochastic volatilities have been proposed. The efficient calibration to market data of these more complex models becomes a relevant target in practice. The main objective of the present work is to efficiently calibrate some recent SABR/LIBOR market models to real market prices of caplets and swaptions. For the calibration we propose a parallelized version of the simulated annealing algorithm for multi-GPUs. The numerical results clearly illustrate the advantages of using the proposed multi-GPUs tools when applied to real market data and popular SABR/LIBOR models.Partially financed by MICINN (MTM2010-21135-C02-01) and by Xunta de Galicia (Grant CN2011/004 cofunded with FEDER funds). Third author has
also been funded by a FPU Spanish grant. The authors are very grateful to Nicolás Gómez Sellés and María Rodríguez Nogueiras for their collaboration in the
development of this work
Electron Beam Micromachining of Nonmetalic Materials
No full textThe thesis deals with electron beam micromachining of nonmetallic materials like glass, ceramics and plastics. A brief description of the device on which the experiments were carried out is included; the author has participated on its development. Main topic is experimental study of influence of main electron beam parameters on results of machining. Examined parameters include accelerating voltage, beam current, focusing and speed of machining. Influence of beam deflection is analyzed. Method of sequential machining by repeated passes of the electron beam is presented. Main examined materials are quartz glass, alumina and selected plastics. The usefulness of the technology is shown by several practical applications
Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model
No full text©2017 This version of the article has been accepted for publication, after
peer review and is subject to Springer Nature’s AM terms of use, but is not
the Version of Record and does not reflect post-acceptance improvements,
or any corrections. The Version of Record is available online at:
https://doi.org/10.1007/978-3-319-61282-9_27[Abstract]: SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with SABR/LIBOR market models (SABR/LMMs) is mainly carried out with Monte Carlo simulation. However, this approach could involve excessively long computational times. In the present chapter we propose an alternative pricing based on partial differential equations (PDEs). Thus, we pose the PDE formulation associated to the SABR/LMM proposed by Hagan and Lesniewski (LIBOR market model with SABR style stochastic volatility. Working paper, available at http://lesniewski.us/papers/working/SABRLMM.pdf (2008)). As this PDE is high dimensional in space, traditional full grid methods (like standard finite differences or finite elements) are not able to price derivatives over more than one or two underlying interest rates and their corresponding stochastic volatilities. In order to overcome this curse of dimensionality, a sparse grid combination technique is proposed. So as to assess on the performance of the method a comparison with Monte Carlo is presented.Partially financed by Spanish Grant MTM2013-47800-C2-1-P and by Xunta
de Galicia (Grant CN2014/044). First author has also been founded by a FPU Spanish GrantXunta de Galicia; CN2014/04
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