A Model Free Approach To Delta Hedging

We utilize the existence of trends for financial time series (Fliess M., Join C.: A Mathematical Proof of the Existence of Trends in Financial Time Series, http://ssrn.com/abstract=1459662) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.

Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.

Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.

Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.

The book conclusively solves problems associated with the control and estimation of nonlinear and chaotic dynamics in financial systems when these are described in the form of nonlinear ordinary differential equations. It then addresses problems associated with the control and estimation of financial systems governed by partial differential equations (e.g. the Black–Scholes partial differential equation (PDE) and its variants). Lastly it an offers optimal solution to the problem of statistical validation of computational models and tools used to support financial engineers in decision making. The application of state-space models in financial engineering means that the heuristics and empirical methods currently in use in decision-making procedures for finance can be eliminated. It also allows methods of fault-free performance and optimality in the management of assets and capitals and methods assuring stability in the functioning of financial systems to be established. Covering the following key areas of financial engineering: (i) control and stabilization of financial systems dynamics, (ii) state estimation and forecasting, and (iii) statistical validation of decision-making tools, the book can be used for teaching undergraduate or postgraduate courses in financial engineering. It is also a useful resource for the engineering and computer science community

Businesses consistently work on new projects, products, and workflows to remain competitive and successful in the modern business environment. To remain zealous, businesses must employ the most effective methods and tools in human resources, project management, and overall business plan execution as competitors work to succeed as well. Advanced Methodologies and Technologies in Business Operations and Management provides emerging research on business tools such as employee engagement, payout policies, and financial investing to promote operational success. While highlighting the challenges facing modern organizations, readers will learn how corporate social responsibility and utilizing artificial intelligence improve a company’s culture and management. This book is an ideal resource for executives and managers, researchers, accountants, and financial investors seeking current research on business operations and management.

I present substantially extended back-testing results of the algorithmic approach to delta-hedging described in my earlier paper. Along with previously researched EURUSD straddles I research USDJPY and GBPUSD straddles as well as call and put spread option combinations. Back-tested period is extended from 5 to 7 years.The results re-confirm previously discovered phenomenon (weekly options sold at the end of the week are ”richer” than the options sold on Monday-Wednesday) and raise new interesting questions: ”cheap” GBPUSD options, substantial skew for USDJPY spread options that realizes at micro level, etc. The results also imply there is the same level of average ”break-even” volatility for all researched FX markets (weekly at-the-money volatility is around 8.8-9.0%), i.e. idiosyncratic element of volatility markets could be overestimated.

Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models

The series of recent financial crises have thrown open the world of quantitative finance and financial modeling. This book brings together proven and new methodologies from finance, physics and engineering, along with years of industry and academic experience to provide a cookbook of models for dealing with the challenges of today's markets.

Gain a deep, intuitive and technical understanding of practical options theory The main challenges in successful options trading are conceptual, not mathematical. Volatility: Practical Options Theory provides financial professionals, academics, students and others with an intuitive as well as technical understanding of both the basic and advanced ideas in options theory to a level that facilitates practical options trading. The approach taken in this book will prove particularly valuable to options traders and other practitioners tasked with making pricing and risk management decisions in an environment where time constraints mean that simplicity and intuition are of greater value than mathematical formalism. The most important areas of options theory, namely implied volatility, delta hedging, time value and the so-called options greeks are explored based on intuitive economic arguments alone before turning to formal models such as the seminal Black-Scholes-Merton model. The reader will understand how the model free approach and mathematical models are related to each other, their underlying theoretical assumptions and their implications to level that facilitates practical implementation. There are several excellent mathematical descriptions of options theory, but few focus on a translational approach to convert the theory into practice. This book emphasizes the translational aspect, while first building an intuitive, technical understanding that allows market makers, portfolio managers, investment managers, risk managers, and other traders to work more effectively within—and beyond—the bounds of everyday practice. Gain a deeper understanding of the assumptions underlying options theory Translate theoretical ideas into practice Develop a more accurate intuition for better time-constrained decision making This book allows its readers to gain more than a superficial understanding of the mechanisms at work in options markets. Volatility gives its readers the edge by providing a true bedrock foundation upon which practical knowledge becomes stronger.