Financial fluctuations were generally neglected in classical ecnomics and their basic statistical properties have only recently been elucidated in the emerging field of econophysics, a new science that analyzes data using methods developed by statistical physics, such as chaos, fractals, and phase transitions. This volume is the proceedings of a workshop at which leading international researchers in this discipline discussed their most recent results and examined the validity of the empirical laws of econophysics. Topics include stock market prices and foreign exchange rates, income distribution, market anomalies, and risk management. The papers herein relate econophysics to other models, present new models, and illustrate the mechanisms by which financial fluctuations occur using actual financial data. Containing the most recent econophysics results, this volume will serve as an indispensable reference for economic theorists and practitioners alike.
In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School
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
This book constitutes the refereed proceedings of the 4th IFIP TC 12 International Conference on Artificial Intelligence, IFIP AI 2015, Held as Part of WCC 2015, in Daejeon, South Korea, in October 2015. The 13 full papers presented were carefully reviewed and selected from 36 submissions. The papers are organized in topical sections on artificial intelligence techniques in biomedicine, artificial intelligence for knowledge management, computational intelligence and algorithms, and intelligent decision support systems.
Featuring papers from the Third International Conference on Computational Finance and its Applications, the text includes papers that encompass a wide range of topics such as modern financial services technologies, derivatives pricing, portfolio management and asset allocation, and intelligent trading agents.
A framework for financial market modeling, the benchmark approach extends beyond standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. This book presents the necessary mathematical tools, followed by a thorough introduction to financial modeling under the benchmark approach, explaining various quantitative methods for the fair pricing and hedging of derivatives.
This book demonstrates the power of neural networks in learning complex behavior from the underlying financial time series data. The results presented also show how neural networks can successfully be applied to volatility modeling, option pricing, and value-at-risk modeling. These features mean that they can be applied to market-risk problems to overcome classic problems associated with statistical models.
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
This book provides a hands-on guide to how financial models are actually implemented and used in practice, on a daily basis, for pricing and risk-management purposes. It shows how to put these models into use in production while minimizing the cost of implementation and maximizing robustness and control. Addressing some of the most important and cutting-edge issues, it describes how to build the necessary models in order to risk manage all the costs involved in options fabrication within the world of equity derivatives and hybrids. This is achieved by extending classical models and improving them in order to account for complex features. The book is primarily aimed at market practitioners (traders, risk managers, risk control, top managers), as well as Masters students in Quantitative/Mathematical Finance. It will also be useful for instructors hoping to enrich their courses with practical examples. The prerequisites are basic stochastic calculus and a general knowledge of financial markets and financial derivatives.
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.
