Model Calibration for Financial Derivatives PDF Download

Author: Frederic Abergel
Publisher: Wiley
ISBN: 9781119952244
Category : Business & Economics
Languages : en
Pages : 384

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Book Description
Model calibration strategies and techniques for derivative products The calibration of derivatives has evolved significantly, covering new ground like implied volatility surface static and dynamics, first and higher-generation exotics calibration, local and stochastic volatility models, interest rates or multi-asset correlation modeling, default time modeling, credit derivatives, and more. This book introduces the fundamentals of model calibration by taking an intuitive approach to the Black, Scholes, and Merton and revisiting it in an incomplete markets setting, applying to a range of hedging strategies.

Author: Chia Chiang Tan
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814366540
Category : Business & Economics
Languages : en
Pages : 414

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Book Description
Written to bridge the gap between foundational quantitative finance and market practice, this book goes beyond the basics covered in most textbooks by presenting content concerning actual industry norms, thus resulting in a clearer picture of the field for the readers. These include, for instance, the practitioner's perspective of how local versus stochastic volume affects forward smile, or the implications of mean reversion on forward volume. Key considerations for modeling in rates, equities and foreign exchange are presented from the perspective of common themes across various assets, as well as their individual characteristics. The discussion on models emphasizes the key aspects that are relevant to the pricing of different types of financial derivatives, so that the reader can observe how an appropriate choice of models is essential in reflecting the risk profile and hedging considerations for different products. With the knowledge gleaned from this book, readers will attain a more comprehensive understanding of market practice in derivatives modeling.

Author: Janis Bauer
Publisher:
ISBN:
Category :
Languages : en
Pages : 33

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Book Description
Loss functions are widely used to calibrate option pricing models to cross-sectional derivatives quotes. However, these approaches come with the disadvantage that estimated model parameters often appear to lack stability over time. On small option markets, this sign of over-fitting is typically pronounced, in particular, when the number of traded options is small and bid-ask spreads are large. So far, there is only little academic literature addressing issues with over-fitting in the context of daily model calibration. In order to fill this gap, we implement a state-space system for the Heston and the PBS model that can be solved with Kalman filters. An empirical analysis using data from five different option markets suggests that Kalman filters are a promising alternative approach to prevent over-fitting, stabilize model parameters and Greeks, and improve the out-of-sample pricing performance on markets with low trading activity.

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: Anlong Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 16

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Book Description
A derivatives contract is a redundant security when there exists a self-financing strategy involving other traded securities that can replicate the payoff of this contract. The initial const of the replicating strategy equals the price of the contract if no arbitrage is allowed in the market. Due to the complexity of derivatives contracts or portfolios, mathematical pricing models are often used to help forming hedging strategies. Such models usually involves three stops: (1) calibrating model parameters to a set of calibrating instruments that are liquid in the market and contain the necessary market information to make the derivatives redundant securities; (2) calculating sensitivities of the derivatives portfolio with respect to model parameters; and (3) translating the parameter sensitivities into hedge ratios with respect to a given set of hedging instruments. This paper presents a methodology for analyzing these steps. Our analysis applies to models in general where exact calibration does not exist and the objective is to minimize calibration errors using numerical optimization techniques. We derive analytic solutions for model parameter sensitivities with respect to prices of calibrating instruments. This eliminates the need for time-consuming model re-calibrations required to calculate these sensitivities numerically. Since hedges are not unique we present two optimal hedges. One of them is additive in the sense that the sum of two optimal hedges of two portfolios is also an optimal hedge for the sum of the two portfolios. The other is self-recoverable which means the optimal hedge of a hedging instrument is the instrument itself. We also study the use of calibrating instruments as hedges by utilizing information such as model parameter sensitivities with respect to calibrating instruments obtained in the model calibration process. The methodology we developed for mapping the parameter sensitivities to their delta or vega equivalents helps not only the hedging but also the risk management of derivatives portfolios on a consistent basis.

Author: David Siska
Publisher:
ISBN:
Category :
Languages : en
Pages : 15

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Book Description
We consider the problem of risk model calibration that is faced by all decentralized derivative exchanges. Financial model calibration is hard for two reasons: firstly it relies on data inputs that can be unreliable, incorrect and in general needing manual cleaning. Secondly, even if perfectly correct data is available the problem typically involves non-convex minimization resulting in local minima that are moreover highly dependent on small perturbations to input. Thus even honest parties won't necessarily produce the same parameters. On a decentralized exchange multiple parties need to agree on the correct calibration. Moreover, malicious actors may benefit in providing calibration parameters that benefit their trading, in case they can convince others that their calibration is the right one. Effectively we have a problem of trying to achieve consensus in continuum.We propose a phenomenological model for the problem. We analyse this in the framework of stochastic differential games and we show that a Nash equilibrium exists. We present empirical results for simple situations that arise when the risk model is assumed to be a linear function of calibration parameters.

Author: Marek Musiela
Publisher: Springer Science & Business Media
ISBN: 3540266534
Category : Mathematics
Languages : en
Pages : 721

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Book Description
A new edition of a successful, well-established book that provides the reader with a text focused on practical rather than theoretical aspects of financial modelling Includes a new chapter devoted to volatility risk The theme of stochastic volatility reappears systematically and has been revised fundamentally, presenting a much more detailed analyses of interest-rate models

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: Michael Mastro, PhD
Publisher: John Wiley & Sons
ISBN: 1118501810
Category : Mathematics
Languages : en
Pages : 534

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Book Description
A road map for implementing quantitative financial models Financial Derivative and Energy Market Valuation brings the application of financial models to a higher level by helping readers capture the true behavior of energy markets and related financial derivatives. The book provides readers with a range of statistical and quantitative techniques and demonstrates how to implement the presented concepts and methods in Matlab®. Featuring an unparalleled level of detail, this unique work provides the underlying theory and various advanced topics without requiring a prior high-level understanding of mathematics or finance. In addition to a self-contained treatment of applied topics such as modern Fourier-based analysis and affine transforms, Financial Derivative and Energy Market Valuation also: • Provides the derivation, numerical implementation, and documentation of the corresponding Matlab for each topic • Extends seminal works developed over the last four decades to derive and utilize present-day financial models • Shows how to use applied methods such as fast Fourier transforms to generate statistical distributions for option pricing • Includes all Matlab code for readers wishing to replicate the figures found throughout the book Thorough, practical, and easy to use, Financial Derivative and Energy Market Valuation is a first-rate guide for readers who want to learn how to use advanced numerical methods to implement and apply state-of-the-art financial models. The book is also ideal for graduate-level courses in quantitative finance, mathematical finance, and financial engineering.

Author: Bin Li
Publisher: World Scientific
ISBN: 9814494240
Category : Business & Economics
Languages : en
Pages : 523

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Book Description
This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authors' own research and practice. It is written from the viewpoint of financial engineers or practitioners, and, as such, it puts more emphasis on the practical applications of financial mathematics in the real market than the mathematics itself with precise (and tedious) technical conditions. It attempts to combine economic insights with mathematics and modeling so as to help the reader to develop intuitions.Among the modeling and the numerical techniques presented are the practical applications of the martingale theories, such as martingale model factory and martingale resampling and interpolation. In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies from the perspective of a front office functionality and a revenue center (rather than merely a risk management functionality), which are relatively recent developments and are of increasing importance. It also discusses various trading structuring strategies and touches upon some popular credit/IR/FX hybrid products, such as PRDC, TARN, Snowballs, Snowbears, CCDS, and credit extinguishers.While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, foreign exchange, and commodity markets.