Download or read book A Jump diffusion Libor Model and Its Robust Calibration written by Denis Belomestny and published by . This book was released on 2006 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ein Jump Diffusion Libor Modell und Dessen Kalibrierung Auf Caplets written by Alexander Heidebrecht and published by . This book was released on 2014 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Libor Modelling and Pricing of Derivative Products written by John Schoenmakers and published by CRC Press. This book was released on 2005-03-29 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of Riskbook.com's Best of 2005 - Top Ten Finance Books The Libor market model remains one of the most popular and advanced tools for modelling interest rates and interest rate derivatives, but finding a useful procedure for calibrating the model has been a perennial problem. Also the respective pricing of exotic derivative products such as Bermudan callable structures is considered highly non-trivial. In recent studies, author John Schoenmakers and his colleagues developed a fast and robust implied method for calibrating the Libor model and a new generic procedure for the pricing of callable derivative instruments in this model. Within a compact, self-contained review of the requisite mathematical theory on interest rate modelling, Robust Libor Modelling and Pricing of Derivative Products introduces the author's new approaches and their impact on Libor modelling and derivative pricing. Discussions include economically sensible parametrisations of the Libor market model, stability issues connected to direct least-squares calibration methods, European and Bermudan style exotics pricing, and lognormal approximations suitable for the Libor market model. A look at the available literature on Libor modelling shows that the issues surrounding instabilty of calibration and its consequences have not been well documented, and an effective general approach for treating Bermudan callable Libor products has been missing. This book fills these gaps and with clear illustrations, examples, and explanations, offers new methods that surmount some of the Libor model's thornier obstacles.
Download or read book Hidden Markov Models in Finance written by Rogemar S. Mamon and published by Springer. This book was released on 2014-05-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the groundbreaking research of Harry Markowitz into the application of operations research to the optimization of investment portfolios, finance has been one of the most important areas of application of operations research. The use of hidden Markov models (HMMs) has become one of the hottest areas of research for such applications to finance. This handbook offers systemic applications of different methodologies that have been used for decision making solutions to the financial problems of global markets. As the follow-up to the authors’ Hidden Markov Models in Finance (2007), this offers the latest research developments and applications of HMMs to finance and other related fields. Amongst the fields of quantitative finance and actuarial science that will be covered are: interest rate theory, fixed-income instruments, currency market, annuity and insurance policies with option-embedded features, investment strategies, commodity markets, energy, high-frequency trading, credit risk, numerical algorithms, financial econometrics and operational risk. Hidden Markov Models in Finance: Further Developments and Applications, Volume II presents recent applications and case studies in finance and showcases the formulation of emerging potential applications of new research over the book’s 11 chapters. This will benefit not only researchers in financial modeling, but also others in fields such as engineering, the physical sciences and social sciences. Ultimately the handbook should prove to be a valuable resource to dynamic researchers interested in taking full advantage of the power and versatility of HMMs in accurately and efficiently capturing many of the processes in the financial market.
Download or read book L vy Matters IV written by Denis Belomestny and published by Springer. This book was released on 2014-12-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the estimation of discretely observed Lévy processes, when the observation scheme is regular, from an up-to-date viewpoint.
Download or read book Advanced Modelling in Mathematical Finance written by Jan Kallsen and published by Springer. This book was released on 2016-12-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.
Download or read book Recent Developments in Computational Finance written by Thomas Gerstner and published by World Scientific. This book was released on 2013 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.
Download or read book A Moment Matching Market Implied Calibration Method for Jump diffusion Models written by Cédric Cavents and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The SABR LIBOR Market Model written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress
Download or read book Calibrating Drift of Short Rate Models with Jump Diffusion written by Shankar Subramaniam and published by . This book was released on 2013 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: The drift or the mean-reversion level of short-rate models under jump-diffusion is derived to fit the initial term-structure of zero-coupon bond. In particular, the drift is obtained for Hull-White and Cox-Ingersoll-Ross short-rate models. The purpose of obtaining the drift is for the Monte-Carlo simulations for pricing exotic equity options under stochastic interest rates and exotic interest rate derivatives. The theoretical expressions for the drift are verified by Monte-Carlo simulations of the short-rate and bond paths, and show that the expectation of the discounted entities reproduce the initial zero-coupon bond term-structure. For the Cox-Ingersoll-Ross model the drift is obtained by a numerical computation of a second-order ordinary differential equation using a perturbation method. The correctness of this method is verified by the Monte-Carlo results. Further, the bond partial differential equation (PDE) for the Cox-Ingersoll-Ross jump-diffusion short-rate model is also solved numerically and the results reproduce the initial zero-coupon bond term-structure. This bond PDE computation verifies the self-consistency of the drift computation, and also validates the numerical boundary conditions used in the finite-difference computations of this final-value problem. Similar results are presented from the finite-difference computation of the Hull-White PDE also.
Download or read book Smart Expansion and Fast Calibration for Jump Diffusion written by Eric Benhamou and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.
Download or read book Applications of Fourier Transform to Smile Modeling written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.
Download or read book An Empirically Efficient Analytical Cascade Calibration of the Libor Market Model Based Only on Directly Quoted Swaptions Data written by Damiano Brigo and published by . This book was released on 2006 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work focuses on the swaptions automatic cascade calibration algorithm (CCA) for the LIBOR Market Model (LMM) first appeared in Brigo and Mercurio (2001). This method induces a direct analytical correspondence between market swaption volatilities and LMM parameters, and allows for a perfect recovery of market quoted swaption volatilities if a common industry swaptions approximation is used.We present explicitly an extension of the CCA to calibrate the entire swaption matrix rather than its upper triangular part. Then, while previous tests on earlier data showed the appearance of numerical problems, we present here different calibration cases leading to acceptable results. We analyze the characteristics of the configurations used and concentrate on the effects of different exogenous instantaneous historical or parametric correlation matrices. We also investigate the influence of manipulations in input swaptions data for missing quotes, and devise a new algorithm maintaining all the positive characteristics of the CCA while relying only on directly quoted market data. Empirical results on a larger range of market situations and instantaneous covariance assumptions show this algorithm to be more robust and efficient than the previous version. Calibrated parameters are in general regular and financially satisfactory, as confirmed by the analysis of various diagnostics implied structures.Finally we Monte Carlo investigate the reliability of the underlying LMM swaption analytical approximation in the new context, and present some possibilities to include information coming from the semi-annual tenor cap market.
Download or read book Jump Diffusion Calibration Using Differential Evolution written by David Ardia and published by . This book was released on 2017 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation of a jump-diffusion model via Differential Evolution is presented. Finding the maximum likelihood estimator for such processes is a tedious task due to the multimodality of the likelihood function. The performance of the Differential Evolution algorithm is compared with standard optimization techniques.
Download or read book Advances in Risk Management written by G. Gregoriou and published by Springer. This book was released on 2006-11-17 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book brings together an edited series of papers about risk management and the latest developments in the field. Covering topics such as Stochastic Volatility, Risk Dynamics and Portfolio Diversification, this book is vital for optimal portfolio allocation for private and institutional investors, and is an indispensable tool.
Download or read book Modeling Derivatives in C written by Justin London and published by John Wiley & Sons. This book was released on 2005-01-21 with total page 922 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.
Download or read book New and Robust Drift Approximations for the Libor Market Model written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
