A Multi-Factor Cross-Currency LIBOR Market Model PDF Download
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Author: Wolfgang Benner
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We develop a rigorous two-currency pricing framework that can be constructed under either a domestic or a foreign currency numeraire. While plain vanilla interest rate derivative prices are recovered by design, exotic cross-currency interest rate products can be priced by determining no-arbitrage drifts for both the domestic and the foreign LIBORs under a uniform probability measure and by specifying the dynamics of the domestic and foreign currency leg of the exotic product. In a single-currency world, no-arbitrage drifts can always be found by specifying the evolution of the terminal LIBOR as a function of bond price volatilities, first, and solving for the drifts of all remaining LIBORs by backward induction. After introducing a second currency, we show that traditional backward induction for the second currency must fail due to interdependence between the respective bond price volatilities and LIBOR dynamics. In order to resolve any such interdependence, we propose calibrating the volatility function of the spot exchange rate to the terminal maturity spectrum of FX options and specifying a functional form for all dates prior to the terminal one. By choosing a multi-factor model setup, rather than relying on terminal decorrelation within a single-factor model, we allow for model calibration to an exogenous market correlation mix. Extending the model, we outline modifications to account for volatility skews by introducing displaced-diffusion to the LIBOR and FX rate dynamics.
Author: Wolfgang Benner
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We develop a rigorous two-currency pricing framework that can be constructed under either a domestic or a foreign currency numeraire. While plain vanilla interest rate derivative prices are recovered by design, exotic cross-currency interest rate products can be priced by determining no-arbitrage drifts for both the domestic and the foreign LIBORs under a uniform probability measure and by specifying the dynamics of the domestic and foreign currency leg of the exotic product. In a single-currency world, no-arbitrage drifts can always be found by specifying the evolution of the terminal LIBOR as a function of bond price volatilities, first, and solving for the drifts of all remaining LIBORs by backward induction. After introducing a second currency, we show that traditional backward induction for the second currency must fail due to interdependence between the respective bond price volatilities and LIBOR dynamics. In order to resolve any such interdependence, we propose calibrating the volatility function of the spot exchange rate to the terminal maturity spectrum of FX options and specifying a functional form for all dates prior to the terminal one. By choosing a multi-factor model setup, rather than relying on terminal decorrelation within a single-factor model, we allow for model calibration to an exogenous market correlation mix. Extending the model, we outline modifications to account for volatility skews by introducing displaced-diffusion to the LIBOR and FX rate dynamics.
Author: Ahsan Amin
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
We review multi-factor cross-currency LIBOR market models. We present a new method for the calibration of cross-currency market models to FX markets. We study the case of Power Reverse Dual Currency derivatives. We also present a new version of Least Square monte carlo method which makes handling of complex Bermudan callable structured derivatives much simpler.
Author: Mogens Johansen
Publisher:
ISBN:
Category :
Languages : da
Pages : 69
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Book Description
Author: Dariusz Gatarek
Publisher: John Wiley & Sons
ISBN: 0470060417
Category : Business & Economics
Languages : en
Pages : 290
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Book Description
The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.
Author: Damiano Brigo
Publisher: Springer Science & Business Media
ISBN: 354034604X
Category : Mathematics
Languages : en
Pages : 1016
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Book Description
The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
![Cross-curreny [i.e. Currency] LIBOR Market Model with Stochastic Volatilities PDF](https://books.google.com/books/content/images/frontcover/ctflZwEACAAJ?fife=w80-h100)
Author: Kai Ma
Publisher:
ISBN:
Category : Foreign exchange futures
Languages : en
Pages : 53
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Book Description
Author:
Publisher:
ISBN:
Category : Futures
Languages : en
Pages : 788
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Book Description
Author: Morten Bjerregaard Pedersen
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
The Libor Market Models arise from the general multi-factor Heath-Jarrow-Morton interest rate model. The Libor Market Models assume that, say, 3 months simple rates are log-normal. With pricing formulae for caps/floors and swaptions this makes the model easy to calibrate for a specific choice of volatility function. We describe how to calibrate the model using a non-parametric volatility function. We apply a smoothness criteria to the quality of fit used in calibration as erratic volatilities otherwise result from the calibration. We perform numerical studies using real market data from several markets to check the robustness of the implementation towards changes in model/calibration parameters. The implementation is indeed very robust and market quotes are matched within bid-offer spread.
Author: Andreas Binder
Publisher: John Wiley & Sons
ISBN: 111997349X
Category : Business & Economics
Languages : en
Pages : 341
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Book Description
A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.
Author: M. A. H. Dempster
Publisher: CRC Press
ISBN: 1482299674
Category : Computers
Languages : en
Pages : 637
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Book Description
High-Performance Computing (HPC) delivers higher computational performance to solve problems in science, engineering and finance. There are various HPC resources available for different needs, ranging from cloud computing– that can be used without much expertise and expense – to more tailored hardware, such as Field-Programmable Gate Arrays (FPGAs) or D-Wave’s quantum computer systems. High-Performance Computing in Finance is the first book that provides a state-of-the-art introduction to HPC for finance, capturing both academically and practically relevant problems.
