Calibration and Parameterization Methods for the Libor Market Model PDF Download
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Author: Christoph Hackl
Publisher: Springer Science & Business Media
ISBN: 3658046880
Category : Business & Economics
Languages : en
Pages : 69
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Book Description
The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and especially for implementation, computer science is necessary. The book provides the ne cessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the trade off of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown.
Author: Christoph Hackl
Publisher: Springer Science & Business Media
ISBN: 3658046880
Category : Business & Economics
Languages : en
Pages : 69
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Book Description
The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and especially for implementation, computer science is necessary. The book provides the ne cessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the trade off of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown.
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: 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:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This thesis presents a study of LIBOR market model calibration. In particular, the study builds on the prevailing calibration methodologies in an attempt to find a method that simultaneously recovers implied volatility and forward rate correlations structures from market prices of plain vanilla options. In order to ensure that complex derivative pricing and hedging requirements are jointly addressed, the study extends the performance analysis of calibration methods from a static level of goodness-of-fit with market prices test, to a dynamic level of approximation to next period's LIBOR (London Interbank Offer Rate) dynamics when tested on a series of market prices. Among the methodologies considered, the results show that for caplets, full calibration results in least pricing error when tested on an intra-day pricing prediction, and generates a stable evolution of day-to-day implied volatility. For swaptions, analytic approximation provides better estimate on an intra-day pricing but Monte Carlo simulation with parametrized correlations matrix provides a stable evolution of volatility and correlation (or covariance). This approach for swaptions calibration outperforms the other methods used despite the modifications made in volatility and initial thetas specifications. All together, the results suggest that the Monte Carlo method with parametrized correlations appear to be superior as it provides smooth evolution of covariance of forward rates that is desired in complex derivative pricing and hedging.
Author: John Schoenmakers
Publisher: CRC Press
ISBN: 1135436754
Category : Mathematics
Languages : en
Pages : 219
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Book Description
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.
Author: Natalia Bandera
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
We show a particular case of joint calibration of the Libor Market Model (LMM) to market-quoted implied cap and swaption volatilities using a linear-exponential parameterization. We also create a Monte Carlo vanilla swaption-pricing engine using the model in the first part of the paper. In the second part of the paper, an attempt will be made to incorporate the dynamics of the volatility skew for caplets though implementation of stochastic volatility SABR model.
Author: Dariusz Gatarek
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Book Description
Pricing of European or even exotic (but without early exercise feature) interest rate and swap options in LIBOR market model can be easily performed in so called quot;Monsieur Jourdain approachquot;. The general concept of quot;Monsieur Jourdain approachquot; is such, that all interest rate options without early exercise feature follow the Black-Merton-Scholes model. To this end we construct a set of quot;building blocksquot; consisting of volatilities of forward Libor rates and correlation parameters. A prescription for how to price a large class of instruments using forward Libor volatilities and the yield curve will be presented. Instantaneous volatilities are not used for model calibration and so the procedure is quite straightforward. In the paper we present three simple calibrations of the LIBOR market model useful in pricing.
Author: Irina Götsch
Publisher: GRIN Verlag
ISBN: 363848310X
Category : Business & Economics
Languages : en
Pages : 122
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Book Description
Diploma Thesis from the year 2006 in the subject Economics - Monetary theory and policy, grade: 2.0, University of Frankfurt (Main), language: English, abstract: The goal of this thesis is to examine the LMM theoretically and apply practically to derivatives pricing. The input data structuring and calibration to market and historical data, implementing and pricing issues will be specifically investigated. This work begins with the comparison of the LMM to alternative interest rate models in chapter 2. A review of basic theory of the valuation of derivatives, which will be used in the next chapters, is presented in chapter 3. Theoretical description of the LMM is presented in the next chapter. Chapter 5 investigates several methods of calibrating directly to market cap and swaption prices. The way of obtaining the initial Libor yield curve is also summarized. In chapter 6 and 7 modeling of forward Libor rates volatility and correlation is presented. Hedging issues are to find in chapter 8. Chapter 9 covers pricing with the LMM by Monte Carlo simulations. This chapter presents the results of imple-menting the cascade calibration and of valuation of derivatives to illustrate the performance of the LMM. Finally the last chapter summarises and concludes the thesis.
Author: Damiano Brigo
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
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.
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.
