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Author: Anlong Li Publisher: ISBN: Category : Languages : en Pages : 16
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: Anlong Li Publisher: ISBN: Category : Languages : en Pages : 16
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: Frederic Abergel Publisher: Wiley ISBN: 9781119952244 Category : Business & Economics Languages : en Pages : 384
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: Massimo Morini Publisher: John Wiley & Sons ISBN: 0470977612 Category : Business & Economics Languages : en Pages : 452
Book Description
A guide to the validation and risk management of quantitative models used for pricing and hedging Whereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature--the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.
Author: Riccardo Rebonato Publisher: Wiley ISBN: 047074488X Category : Business & Economics Languages : en Pages : 296
Book Description
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
Author: George J Kaye Publisher: World Scientific Publishing Company ISBN: 1908979585 Category : Business & Economics Languages : en Pages : 438
Book Description
Along with the extraordinary growth in the derivatives market over the last decade, the impact of model choice, and model parameter usage, has become a major source of valuation uncertainty. This book concentrates on equity derivatives and charts, step by step, how key assumptions on the dynamics of stocks impact on the value of exotics. The presentation is technical, but maintains a strong focus on intuition and practical application./a
Author: Rajna Gibson Publisher: Risk Publications ISBN: Category : Business & Economics Languages : en Pages : 378
Book Description
A comprehensive compilation on the concept of model risk and the potential pitfalls associated with modelling financial risks, this book provides an assessment of various models, examining the weaknesses and provides methods to mitigate potential model failures and deficiencies. It also covers the testing of models, what should be tested and what the parameters should be, with core contributions selected and introduced by Professor Rajna Gibson.
Author: Yves Hilpisch Publisher: John Wiley & Sons ISBN: 1119038006 Category : Business & Economics Languages : en Pages : 390
Book Description
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: Kathrin Glau Publisher: Springer ISBN: 3319334468 Category : Mathematics Languages : en Pages : 446
Book Description
This book presents 20 peer-reviewed chapters on current aspects of derivatives markets and derivative pricing. The contributions, written by leading researchers in the field as well as experienced authors from the financial industry, present the state of the art in: • Modeling counterparty credit risk: credit valuation adjustment, debit valuation adjustment, funding valuation adjustment, and wrong way risk. • Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling. • Recent developments concerning contingent convertible bonds, the measuring of basis spreads, and the modeling of implied correlations. The recent financial crisis has cast tremendous doubts on the classical view on derivative pricing. Now, counterparty credit risk and liquidity issues are integral aspects of a prudent valuation procedure and the reference interest rates are represented by a multitude of curves according to their different periods and maturities. A panel discussion included in the book (featuring Damiano Brigo, Christian Fries, John Hull, and Daniel Sommer) on the foundations of modeling and pricing in the presence of counterparty credit risk provides intriguing insights on the debate.
Author: Thorsten Rheinlander Publisher: World Scientific ISBN: 9814338796 Category : Business & Economics Languages : en Pages : 244
Book Description
Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field.
Author: Anlong Li
Author: Anlong Li
Author: Frederic Abergel
Author: Oliver Brockhaus
Author: Massimo Morini
Author: Riccardo Rebonato
Author: George J Kaye
Author: Rajna Gibson
Author: Yves Hilpisch
Author: Kathrin Glau
Author: Thorsten Rheinlander