Asymptotic Chaos Expansions in Finance

Asymptotic Chaos Expansions in Finance
Author: David Nicolay
Publisher: Springer
Total Pages: 503
Release: 2014-11-25
Genre: Mathematics
ISBN: 1447165063

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.

Proceedings of the International Workshop on Finance 2011. Doshisha University, Kyoto, Japan. 3-4 August 2011

Proceedings of the International Workshop on Finance 2011. Doshisha University, Kyoto, Japan. 3-4 August 2011
Author: Akihiko Takahashi
Publisher: World Scientific
Total Pages: 231
Release: 2012-05-21
Genre: Business & Economics
ISBN: 981440733X

This book is the Proceedings of the International Workshop on Finance 2011, held in Kyoto in the summer of 2011 with the aim of exchanging new ideas in financial engineering among researchers from various countries from both academia and industry. The workshop was held as a successor to the Daiwa International Workshop (2004OCo2008), and the KIER-TMU International Workshop (2009OCo2010). This workshop was organized by the Center for Advanced Research in Finance (CARF), Graduate School of Economics, the University of Tokyo, and Graduate School of Social Sciences, Tokyo Metropolitan University OCo and co-organized by Life Risk Research Center, Doshisha University. The workshop serves as a bridge between academic researchers and practitioners. This book contains about fifteen papers, all refereed, representing the presentations at the workshop. The papers address state-of-the-art techniques in financial engineering."

Recent Advances In Financial Engineering 2011 - Proceedings Of The International Workshop On Finance 2011

Recent Advances In Financial Engineering 2011 - Proceedings Of The International Workshop On Finance 2011
Author: Akihiko Takahashi
Publisher: World Scientific
Total Pages: 231
Release: 2012-05-21
Genre: Mathematics
ISBN: 9814407348

This book is the Proceedings of the International Workshop on Finance 2011, held in Kyoto in the summer of 2011 with the aim of exchanging new ideas in financial engineering among researchers from various countries from both academia and industry. The workshop was held as a successor to the Daiwa International Workshop (2004-2008), and the KIER-TMU International Workshop (2009-2010). This workshop was organized by the Center for Advanced Research in Finance (CARF), Graduate School of Economics, the University of Tokyo, and Graduate School of Social Sciences, Tokyo Metropolitan University — and co-organized by Life Risk Research Center, Doshisha University.The workshop serves as a bridge between academic researchers and practitioners. This book contains about fifteen papers, all refereed, representing the presentations at the workshop. The papers address state-of-the-art techniques in financial engineering.

Interest Rate Rules, Endogenous Cycles, and Chaotic Dynamics in Open Economies

Interest Rate Rules, Endogenous Cycles, and Chaotic Dynamics in Open Economies
Author: Mr.Marco Airaudo
Publisher: International Monetary Fund
Total Pages: 68
Release: 2012-05-01
Genre: Business & Economics
ISBN: 1475546416

We present an extensive analysis of the consequences for global equilibrium determinacy in flexible-price open economies of implementing active interest rate rules, i.e., monetary rules where the nominal interest rate responds more than proportionally to inflation. We show that conditions under which these rules generate aggregate instability by inducing liquidity traps, endogenous cycles, and chaotic dynamics depend on specific characteristics of open economies. In particular, rules that respond to expected future inflation are more prone to induce endogenous cyclical and chaotic dynamics the more open the economy to trade.

Interest Rate Modelling

Interest Rate Modelling
Author: Jessica James
Publisher: John Wiley & Sons
Total Pages: 680
Release: 2000-06-08
Genre: Business & Economics
ISBN:

Back Cover ( this section should include endorsements also) As interest rate markets continue to innovate and expand it is becoming increasingly important to remain up-to-date with the latest practical and theoretical developments. This book covers the latest developments in full, with descriptions and implementation techniques for all the major classes of interest rate models - both those actively used in practice as well as theoretical models still 'waiting in the wings'. Interest rate models, implementation methods and estimation issues are discussed at length by the authors as are important new developments such as kernel estimation techniques, economic based models, implied pricing methods and models on manifolds. Providing balanced coverage of both the practical use of models and the theory that underlies them, Interest Rate Modelling adopts an implementation orientation throughout making it an ideal resource for both practitioners and researchers. Back Flap Jessica James Jessica James is Head of Research for Bank One's Strategic Risk Management group, based in the UK. Jessica started life as a physicist at Manchester University and completed her D Phil in Theoretical Atomic and Nuclear Physics at Christ Church, Oxford, under Professor Sandars. After a year as a college lecturer at Trinity, Oxford, she began work at the First National Bank of Chicago, now Bank One, where she still works. She is well known as a speaker on the conference circuit, lecturing on a variety of topics such as VaR, capital allocation, credit derivatives and interest rate modelling, and has published articles on various aspects of financial modelling. Nick Webber Nick Webber is a lecturer in Finance at Warwick Business School. Prior to his academic career, Nick had extensive experience in the industrial and commercial world in operational research and computing. After obtaining a PhD in Theoretical Physics from Imperial College he began research into financial options. His main area of research centres on interest rate modelling and computational finance. He has taught practitioner and academic courses for many years, chiefly on options and interest rates. Front Flap Interest Rate Modelling provides a comprehensive resource on all the main aspects of valuing and hedging interest rate products. A series of introductory chapters reviews the theoretical background, pointing out the problems in using naïve valuation and implementation techniques. There follows a full analysis of interest rate models including major categories, such as Affine, HJM and Market models, and in addition, lesser well known types that include Consol, Random field and Jump-augmented Models. Implementation methods are discussed in depth including the latest developments in the use of finite difference, Lattice and Monte Carlo methods and their particular application to the valuation of interest rate derivatives. Containing previously unpublished material, Interest Rate Modelling is a key reference work both for practitioners developing and implementing models for real and for academics teaching and researching in the field.

An Elementary Introduction to Stochastic Interest Rate Modeling

An Elementary Introduction to Stochastic Interest Rate Modeling
Author: Nicolas Privault
Publisher: World Scientific
Total Pages: 243
Release: 2012
Genre: Business & Economics
ISBN: 9814390860

Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students. This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.

The Logistic Map and the Route to Chaos

The Logistic Map and the Route to Chaos
Author: Marcel Ausloos
Publisher: Springer Science & Business Media
Total Pages: 442
Release: 2006-02-10
Genre: Language Arts & Disciplines
ISBN: 9783540283669

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Interest Rate Modeling

Interest Rate Modeling
Author: Lixin Wu
Publisher: CRC Press
Total Pages: 494
Release: 2019-03-04
Genre: Mathematics
ISBN: 1351227416

Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Features Presents a complete cycle of model construction and applications, showing readers how to build and use models Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments Contains exercise sets and a number of examples, with many based on real market data Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.

Making Sense of Chaos

Making Sense of Chaos
Author: J. Doyne Farmer
Publisher: Yale University Press
Total Pages: 427
Release: 2024-08-06
Genre: Business & Economics
ISBN: 0300280335

From a pioneer in the field of complexity science and chaos theory, a plan for solving the world’s most pressing problems “Farmer convincingly argues that by using big data and today’s more powerful computers, we can build more realistic models and simulations of the global economy. . . . Farmer’s vision will undoubtedly be significant in how economics evolves.”—Tej Parikh, Financial Times, “Best New Books on Economics” “Both a manifesto for a revolution in economics and a memoir of an unusual career.”—Ed Ballard, Wall Street Journal We live in an age of increasing complexity—an era of accelerating technology and global interconnection that holds more promise, and more peril, than any other time in human history. The fossil fuels that have powered global wealth creation now threaten to destroy the world they helped build. Automation and digitization promise prosperity for some, unemployment for others. Financial crises fuel growing inequality, polarization, and the retreat of democracy. At heart, all these problems are rooted in the economy, yet the guidance provided by economic models has often failed. Many books have been written about J. Doyne Farmer and his work, but this is the first in his own words. It presents a manifesto for how to do economics better. In this tale of science and ideas, Farmer fuses his profound knowledge and expertise with stories from his life to explain how we can bring a scientific revolution to bear on the economic conundrums facing society. Using big data and ever more powerful computers, we are now able for the first time to apply complex systems science to economic activity, building realistic models of the global economy. The resulting simulations and the emergent behavior we observe form the cornerstone of the science of complexity economics, allowing us to test ideas and make significantly better economic predictions—to better address the hard problems facing the world.