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.

Author: Thomas Gerstner
Publisher: World Scientific
ISBN: 9814436429
Category : Business & Economics
Languages : en
Pages : 481

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Book Description
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.

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: Riccardo Rebonato
Publisher: Princeton University Press
ISBN: 0691089736
Category : Business & Economics
Languages : en
Pages : 485

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Book Description
In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer. Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness. Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.

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.