Download or read book Model Calibration for Financial Derivatives written by Frederic Abergel and published by Wiley. This book was released on 2015-05-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Financial Derivatives Modeling written by Christian Ekstrand and published by Springer Science & Business Media. This book was released on 2011-08-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to the modeling of financial derivatives, covering all major asset classes (equities, commodities, interest rates and foreign exchange) and stretching from Black and Scholes' lognormal modeling to current-day research on skew and smile models. The intended reader has a solid mathematical background and is a graduate/final-year undergraduate student specializing in Mathematical Finance, or works at a financial institution such as an investment bank or a hedge fund.
Download or read book Derivatives Analytics with Python written by Yves Hilpisch and published by John Wiley & Sons. This book was released on 2015-08-03 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercharge options analytics and hedging using the power of Python Derivatives Analytics with Python shows you how to implement market-consistent valuation and hedging approaches using advanced financial models, efficient numerical techniques, and the powerful capabilities of the Python programming language. This unique guide offers detailed explanations of all theory, methods, and processes, giving you the background and tools necessary to value stock index options from a sound foundation. You'll find and use self-contained Python scripts and modules and learn how to apply Python to advanced data and derivatives analytics as you benefit from the 5,000+ lines of code that are provided to help you reproduce the results and graphics presented. Coverage includes market data analysis, risk-neutral valuation, Monte Carlo simulation, model calibration, valuation, and dynamic hedging, with models that exhibit stochastic volatility, jump components, stochastic short rates, and more. The companion website features all code and IPython Notebooks for immediate execution and automation. Python is gaining ground in the derivatives analytics space, allowing institutions to quickly and efficiently deliver portfolio, trading, and risk management results. This book is the finance professional's guide to exploiting Python's capabilities for efficient and performing derivatives analytics. Reproduce major stylized facts of equity and options markets yourself Apply Fourier transform techniques and advanced Monte Carlo pricing Calibrate advanced option pricing models to market data Integrate advanced models and numeric methods to dynamically hedge options Recent developments in the Python ecosystem enable analysts to implement analytics tasks as performing as with C or C++, but using only about one-tenth of the code or even less. Derivatives Analytics with Python — Data Analysis, Models, Simulation, Calibration and Hedging shows you what you need to know to supercharge your derivatives and risk analytics efforts.
Download or read book Incentives for Model Calibration on Decentralized Derivatives Exchanges written by David Siska and published by . This book was released on 2020 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Market Practice In Financial Modelling written by Chia Chiang Tan and published by World Scientific Publishing Company. This book was released on 2012-07-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 volatility affects forward smile, or the implications of mean reversion on forward volatility.Key considerations for modelling 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 modelling.
Download or read book Model Calibration in Thinly Traded Derivatives Markets written by Janis Bauer and published by . This book was released on 2017 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Interest Rate Derivatives written by Ingo Beyna and published by Springer Science & Business Media. This book was released on 2013-02-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.
Download or read book Modelling Financial Derivatives with MATHEMATICA written by William T. Shaw and published by Cambridge University Press. This book was released on 1998-12-10 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD plus book for financial modelling, requires Mathematica 3 or 2.2; runs on most platforms.
Download or read book Model Calibration Risk Measurement and the Hedging of Derivatives written by Anlong Li and published by . This book was released on 2006 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Financial Derivatives in Theory and Practice written by Philip Hunt and published by John Wiley and Sons. This book was released on 2004-07-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term Financial Derivative is a very broad term which has come to mean any financial transaction whose value depends on the underlying value of the asset concerned. Sophisticated statistical modelling of derivatives enables practitioners in the banking industry to reduce financial risk and ultimately increase profits made from these transactions. The book originally published in March 2000 to widespread acclaim. This revised edition has been updated with minor corrections and new references, and now includes a chapter of exercises and solutions, enabling use as a course text. Comprehensive introduction to the theory and practice of financial derivatives. Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest. Divided into two self-contained parts ? the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice. Written by well respected academics with experience in the banking industry. A valuable text for practitioners in research departments of all banking and finance sectors. Academic researchers and graduate students working in mathematical finance.
Download or read book Model Calibration for Financial Derivatives written by Frederic Abergel and published by John Wiley & Sons. This book was released on 2020-04-21 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 224 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
Download or read book Quantitative Analysis Derivatives Modeling and Trading Strategies written by Yi Tang and published by World Scientific. This book was released on 2007 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 authorsOCO own research and practice. 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, and foreign exchange markets. This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view 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 develop intuitions. In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies, 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, credit extinguishers."
Download or read book Derivatives Pricing and Model Calibration Using Continuous Time Markov Chain Approximation Model written by Chia Lo and published by . This book was released on 2014 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a non-equidistant Q rate matrix setting formula such that a well-defined continuous time Markov chain can lead to excellent approximations to jump-diffusions with affine or non-affine functional specifications. This approach also accommodates state-dependent jump intensity and jump distribution, a fexibility that is very hard to achieve with traditional numerical methods. Our approach not only satisfies Kushner (1990) local consistency conditions but also resolves the approximation errors induced by Piccioni (1987) scheme. European stock option pricing examples based on jump-diffusions illustrate the ease of implementation of our model. The proposed algorithm for pricing American options highlights the speed and accuracy. Finally the empirical analysis using daily VIX data shows that the maximum likelihood estimates of the underlying jump-diffusions can be efficiently computed by the model proposed in this article.
Download or read book Derivatives Analytics with Python written by Yves Hilpisch and published by John Wiley & Sons. This book was released on 2015-06-15 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercharge options analytics and hedging using the power of Python Derivatives Analytics with Python shows you how to implement market-consistent valuation and hedging approaches using advanced financial models, efficient numerical techniques, and the powerful capabilities of the Python programming language. This unique guide offers detailed explanations of all theory, methods, and processes, giving you the background and tools necessary to value stock index options from a sound foundation. You'll find and use self-contained Python scripts and modules and learn how to apply Python to advanced data and derivatives analytics as you benefit from the 5,000+ lines of code that are provided to help you reproduce the results and graphics presented. Coverage includes market data analysis, risk-neutral valuation, Monte Carlo simulation, model calibration, valuation, and dynamic hedging, with models that exhibit stochastic volatility, jump components, stochastic short rates, and more. The companion website features all code and IPython Notebooks for immediate execution and automation. Python is gaining ground in the derivatives analytics space, allowing institutions to quickly and efficiently deliver portfolio, trading, and risk management results. This book is the finance professional's guide to exploiting Python's capabilities for efficient and performing derivatives analytics. Reproduce major stylized facts of equity and options markets yourself Apply Fourier transform techniques and advanced Monte Carlo pricing Calibrate advanced option pricing models to market data Integrate advanced models and numeric methods to dynamically hedge options Recent developments in the Python ecosystem enable analysts to implement analytics tasks as performing as with C or C++, but using only about one-tenth of the code or even less. Derivatives Analytics with Python — Data Analysis, Models, Simulation, Calibration and Hedging shows you what you need to know to supercharge your derivatives and risk analytics efforts.
Download or read book Financial Modeling written by Stephane Crepey and published by Springer Science & Business Media. This book was released on 2013-06-13 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance
