Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available. Through the problem of option pricing, the author introduces powerful tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. He mainly focuses on the calibration and dynamics of implied volatility, which is commonly called smile. The book covers the Black–Scholes, local volatility, and stochastic volatility models, along with the Kolmogorov, Schrödinger, and Bellman–Hamilton–Jacobi equations. Providing both theoretical and numerical results throughout, this book offers new ways of solving financial problems using techniques found in physics and mathematics.
Choose statistically significant stock selection models using SAS® Portfolio and Investment Analysis with SAS®: Financial Modeling Techniques for Optimization is an introduction to using SAS to choose statistically significant stock selection models, create mean-variance efficient portfolios, and aggressively invest to maximize the geometric mean. Based on the pioneering portfolio selection techniques of Harry Markowitz and others, this book shows that maximizing the geometric mean maximizes the utility of final wealth. The authors draw on decades of experience as teachers and practitioners of financial modeling to bridge the gap between theory and application. Using real-world data, the book illustrates the concept of risk-return analysis and explains why intelligent investors prefer stocks over bonds. The authors first explain how to build expected return models based on expected earnings data, valuation ratios, and past stock price performance using PROC ROBUSTREG. They then show how to construct and manage portfolios by combining the expected return and risk models. Finally, readers learn how to perform hypothesis testing using Bayesian methods to add confidence when data mining from large financial databases.
Computational finance deals with the mathematics of computer programs that realize financial models or systems. This book outlines the epistemic risks associated with the current valuations of different financial instruments and discusses the corresponding risk management strategies. It covers most of the research and practical areas in computational finance. Starting from traditional fundamental analysis and using algebraic and geometric tools, it is guided by the logic of science to explore information from financial data without prejudice. In fact, this book has the unique feature that it is structured around the simple requirement of objective science: the geometric structure of the data = the information contained in the data.
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
The authors reconsider the problem of parametrically specifying distribution suitable for asset-return models. They describe alternative distributions, showing how they can be estimated and applied to stock-index and exchange-rate data. The implications for options pricing are also investigated.
Taking a data-driven approach, A Course on Statistics for Finance presents statistical methods for financial investment analysis. The author introduces regression analysis, time series analysis, and multivariate analysis step by step using models and methods from finance. The book begins with a review of basic statistics, including descriptive statistics, kinds of variables, and types of data sets. It then discusses regression analysis in general terms and in terms of financial investment models, such as the capital asset pricing model and the Fama/French model. It also describes mean-variance portfolio analysis and concludes with a focus on time series analysis. Providing the connection between elementary statistics courses and quantitative finance courses, this text helps both existing and future quants improve their data analysis skills and better understand the modeling process.
A Geometric Approach to Hedging and Risk Management
Author: Alvin Kuruc
Publisher: Pearson Education
Category: Business & Economics
This work on mathematical finance offers practical guidance on how to underpin efficient risk management systems. The emphasis is on techniques for dealing with large numbers of correlated risk factors.
This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.
This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.
A variety of quantitative concepts and models essential to understanding financial markets are introduced and explained in this broad overview of financial analytical tools. Coverage ranges from matrices and elementary calculus to stochastic processes, with applications to a wide range of financial topics. Practitioners, researchers, and advanced students of finance will find these tools invaluable.
Illustrates how R may be used successfully to solve problems in quantitative finance Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering—walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed—along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN. Covers optimization methodologies in probabilistic calculus for financial engineering Answers the question: What does a "Random Walk" Financial Theory look like? Covers the GBM Model and the Random Walk Model Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R is an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.
Weather derivatives provide a tool for weather risk management, and the markets for these exotic financial products are gradually emerging in size and importance. This unique monograph presents a unified approach to the modeling and analysis of such weather derivatives, including financial contracts on temperature, wind and rain. Based on a deep statistical analysis of weather factors, sophisticated stochastic processes are introduced modeling the time and space dynamics. Applying ideas from the modern theory of mathematical finance, weather derivatives are priced, and questions of hedging analyzed. The treatise contains an in-depth analysis of typical weather contracts traded at the Chicago Mercantile Exchange (CME), including so-called CDD and HDD futures. The statistical analysis of weather variables are based on a large data set from Lithuania. The monograph includes the research done by the authors over the last decade on weather markets. Their work has gained considerable attention, and has been applied in many contexts.