Algorithmic Approach To Delta Hedging

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.

This paper describes design and back-testing of an automated delta-hedging strategy applied to short-dated fx options (specifically - weekly and monthly at-the-money EURUSD straddles).The results indicate that systematic sale of options that are delta-hedged according to the suggested algorithm generates financial gain for the seller with an attractive Sharpe ratio exceeding 3.0 on after-cost basis (back-testing accounts for volatility bid-offer as well as spot market bid-offer).For weekly options Sharpe ratio significantly depends on the day of week on which the algorithm systematically sells options: delta-hedging of options sold on Thursdays results in highest Sharpe ratio; delta-hedging of options sold on Fridays results in second-best Sharpe ratio.The performance of the algorithmic strategy is not correlated with linear changes in spot price which is in line with Black-Scholes theory.The proposed algorithmic strategy has just a few parameters which serves as a natural protection against over-fitting bias. Further fine-tuning of the algorithm requires access to historical data over longer period and/or access to live trading environment.

Written for managers and professionals in business and industry, and using a minimum of mathematical language, The Management of Bond Investments and the Trading of Debt addresses three key issues: Bondholder’s options, risks and rewards in making investments in debt instruments; The dynamics of inflation, and how they affect both trading in the bond market, and investment decisions; and The democratization of lending, socialization of risk, and effect of the global economy on the bond market. Financial expert Dimitris Chorafas discusses these issues in straightforward language for managers and professionals in commercial banks, securities houses, financial services companies, merchandising firms, manufacturing companies, and consulting firms, placing the mathematical treatment of the issues in the appendices, available for study but not necessary for understanding the business issues addressed in the book. Focuses on new issues of central importance in bond and debt trading today Uses clear, straightforward language for managers and professionals in business and industry, with mathematical treatment provided in appendices Thorough treatment of operational risk new to books on this topic

We consider the delta-hedging strategy for a vanilla option under the discrete hedging and transaction costs, assuming that an option is delta-hedged using the Black-Scholes-Merton model with the log-normal volatility implied by the market price of the option. We analyze the expected profit-and-loss (P&L) of the delta-hedging strategy assuming the four possible dynamics of asset returns under the statistical measure: the log-normal diffusion, the jump-diffusion, the stochastic volatility and the stochastic volatility with jumps. For all of the four models, we derive analytic formulas for the expected P&L, expected transaction costs, and P&L volatility assuming hedging at fixed times. Using these formulas, we formulate the problem of finding the optimal hedging frequency to maximize the Sharpe ratio of the delta-hedging strategy. Also, we show that the Sharpe ratio of the delta-hedging strategy can be improved by incorporating the price and delta bands for the rebalancing of the delta-hedge and provide analytical approximations for computing the optimal bands in our optimization approach. As illustrations, we show that our method provides a very good approximation to the actual Sharpe ratio obtained by Monte Carlo simulations under the time-based re-hedging. In contrary to Monte Carlo simulations, our analytic approach provide a fast and an accurate way to estimate the risk-reward characteristic of the delta-hedging strategy for real time computations.

Whether you are a seasoned professional looking to explore new areas within the alternative investment arena or a new industry participant seeking to establish a solid understanding of alternative investments, Alternative Investments: An Allocator's Approach, Fourth Edition (CAIA Level II curriculum official text) is the best way to achieve these goals. In recent years, capital formation has shifted dramatically away from public markets as issuers pursue better financial and value alignment with ownership, less onerous and expensive regulatory requirements, market and information dislocation, and liberation from the short-term challenges that undergird the public capital markets. The careful and informed use of alternative investments in a diversified portfolio can reduce risk, lower volatility, and improve returns over the long-term, enhancing investors' ability to meet their investment outcomes. Alternative Investments: An Allocator's Approach (CAIA Level II curriculum official text) is a key resource that can be used to improve the sophistication of asset owners and those who work with them. This text comprises the curriculum, when combined with supplemental materials available at caia.org, for the CAIA Level II exam. "Over the course of my long career one tenet has held true, 'Continuing Education'. Since CalSTRS is a teachers' pension plan, it is no surprise that continuing education is a core attribute of our Investment Office culture. Overseeing one of the largest institutional pools of capital in the world requires a cohesive knowledge and understanding of both public and private market investments and strategies. We must understand how these opportunities might contribute to delivering on investment outcomes for our beneficiaries. Alternative Investments: An Allocator's Approach is the definitive core instruction manual for an institutional investor, and it puts you in the captain's chair of the asset owner." —Christopher J. Ailman, Chief Investment Officer, California State Teachers’ Retirement System "Given their diversified cash flow streams and returns, private markets continue to be a growing fixture of patient, long-term portfolios. As such, the need to have proficiency across these sophisticated strategies, asset classes, and instruments is critical for today's capital allocator. As a proud CAIA charterholder, I have seen the practical benefits in building a strong private markets foundation, allowing me to better assist my clients." —Jayne Bok, CAIA, CFA, Head of Investments, Asia, Willis Tower Watson

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.

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.

Algorithmic Trading and Quantitative Strategies provides an in-depth overview of this growing field with a unique mix of quantitative rigor and practitioner’s hands-on experience. The focus on empirical modeling and practical know-how makes this book a valuable resource for students and professionals. The book starts with the often overlooked context of why and how we trade via a detailed introduction to market structure and quantitative microstructure models. The authors then present the necessary quantitative toolbox including more advanced machine learning models needed to successfully operate in the field. They next discuss the subject of quantitative trading, alpha generation, active portfolio management and more recent topics like news and sentiment analytics. The last main topic of execution algorithms is covered in detail with emphasis on the state of the field and critical topics including the elusive concept of market impact. The book concludes with a discussion on the technology infrastructure necessary to implement algorithmic strategies in large-scale production settings. A git-hub repository includes data-sets and explanatory/exercise Jupyter notebooks. The exercises involve adding the correct code to solve the particular analysis/problem.

The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition. The Algorithmic Foundations of Differential Privacy starts out by motivating and discussing the meaning of differential privacy, and proceeds to explore the fundamental techniques for achieving differential privacy, and the application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some powerful computational results, there are still fundamental limitations. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power -- certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed. The monograph then turns from fundamentals to applications other than query-release, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams, is discussed. The Algorithmic Foundations of Differential Privacy is meant as a thorough introduction to the problems and techniques of differential privacy, and is an invaluable reference for anyone with an interest in the topic.

This book provides a hands-on, practical guide to understanding derivatives pricing. Aimed at the less quantitative practitioner, it provides a balanced account of options, Greeks and hedging techniques avoiding the complicated mathematics inherent to many texts, and with a focus on modelling, market practice and intuition.