Model Calibration For Financial Derivatives
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| Author | : Frederic Abergel |
| Publisher | : Wiley |
| Total Pages | : 384 |
| Release | : 2015-05-04 |
| Genre | : Business & Economics |
| ISBN | : 9781119952244 |
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 | : Yves Hilpisch |
| Publisher | : John Wiley & Sons |
| Total Pages | : 390 |
| Release | : 2015-08-03 |
| Genre | : Business & Economics |
| ISBN | : 1119037999 |
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.
| Author | : Christian Ekstrand |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2011-08-26 |
| Genre | : Business & Economics |
| ISBN | : 3642221556 |
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.
| Author | : Janis Bauer |
| Publisher | : |
| Total Pages | : 33 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
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 | : Ingo Beyna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 220 |
| Release | : 2013-02-20 |
| Genre | : Mathematics |
| ISBN | : 3642349250 |
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.
| Author | : Chia Chiang Tan |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 439 |
| Release | : 2012-07-11 |
| Genre | : Business & Economics |
| ISBN | : 9814434582 |
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.
| Author | : William T. Shaw |
| Publisher | : Cambridge University Press |
| Total Pages | : 570 |
| Release | : 1998-12-10 |
| Genre | : Business & Economics |
| ISBN | : 9780521592338 |
CD plus book for financial modelling, requires Mathematica 3 or 2.2; runs on most platforms.
| Author | : David Siska |
| Publisher | : |
| Total Pages | : 15 |
| Release | : 2020 |
| Genre | : |
| ISBN | : |
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 | : Philip Hunt |
| Publisher | : John Wiley and Sons |
| Total Pages | : 476 |
| Release | : 2004-07-02 |
| Genre | : Mathematics |
| ISBN | : 9780470863589 |
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.
| Author | : Riccardo Rebonato |
| Publisher | : John Wiley & Sons |
| Total Pages | : 308 |
| Release | : 2011-03-01 |
| Genre | : Business & Economics |
| ISBN | : 1119995639 |
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
