The Black–Scholes Model

The Black–Scholes Model

The Black–Scholes option pricing model is the first and by far the best-known continuous-time mathematical model used in mathematical finance. Here, it provides a sufficiently complex, yet tractable, testbed for exploring the basic methodology of option pricing. The discussion of extended markets, the careful attention paid to the requirements for admissible trading strategies, the development of pricing formulae for many widely traded instruments and the additional complications offered by multi-stock models will appeal to a wide class of instructors. Students, practitioners and researchers alike will benefit from the book's rigorous, but unfussy, approach to technical issues. It highlights potential pitfalls, gives clear motivation for results and techniques and includes carefully chosen examples and exercises, all of which make it suitable for self-study.

Black Scholes and Beyond: Option Pricing Models

Black Scholes and Beyond: Option Pricing Models

This text explains the basics of modern option pricing using minimal mathematics. The Black-Scholes equation is discussed as well as other methods that have built upon the success of Black-Scholes, including Cox-Ross-Rubinstein binomial trees, the Derman-Kani theory on implied volatility trees and Mark Rubenstein's implied binomial trees. Other topics covered include, pricing and hedging options, volatility smiles and how to price options in the presence of a smile, pricing barrier options and current theoretical developments from Wall Street.

How to Calculate Options Prices and Their Greeks

Exploring the Black Scholes Model from Delta to Vega + WS

How to Calculate Options Prices and Their Greeks

Too often option payoffs are merely based on a two-dimensional approach consisting of a P&L versus underlying at expiry as is evident in most existing literature. This is misleading as the Greeks can make or break a strategy during its lifetime. In How to Calculate the Value of Options Prices and their Greeks, emphasis is placed on a deep and thorough understanding of the Greeks (first, second and third order), informing the reader how the pay-off of an option (strategy) will be influenced by time, underlying, strike and volatility. The book fully explains the distribution of the Greeks along a range of strikes (the whole range wherein an option has optionality), assisting the reader to understand how the Greeks are changing in relation to different strikes, but also in relation to time, volatility and underlying. Further it will discuss many trading strategies such as spreads, straddle, strangle, butterflies, kurtosis, vega, and convexity to name but a few. The author discusses how hedging strategies on the gamma can make or break a P&L. The text begins by guiding the reader through the more basic options, such as the put-call parity towards the concepts of probability distribution and volatility. The book then covers the main Greeks (delta, gamma vega and theta) followed by an in-depth discussion of several trading strategies including a four dimensional approach of P&L versus strike, underlying, volatility and time to maturity.

The Black-Scholes-Merton Model as an Idealization of Discrete-time Economies

The Black-Scholes-Merton Model as an Idealization of Discrete-time Economies

This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

Probability Theory in Finance

A Mathematical Guide to the Black-Scholes Formula

Probability Theory in Finance

The use of the Black-Scholes model and formula is pervasive in financialmarkets. There are very few undergraduate textbooks available on thesubject and, until now, almost none written by mathematicians. Basedon a course given by the author, the goal of this book is to introduceadvanced undergraduates and beginning graduate students studying themathematics of finance to the Black-Scholes formula. The author uses afirst-principles approach, developing only the minimum backgroundnecessary to justify mathematical concepts and placing mathematicaldevelopments in context.

Methods and Applications of Statistics in Business, Finance, and Management Science

Methods and Applications of Statistics in Business, Finance, and Management Science

Inspired by the Encyclopedia of Statistical Sciences, Second Edition (ESS2e), this volume presents a concise, well-rounded focus on the statistical concepts and applications that are essential for understanding gathered data in the study of business, finance, and management science. The book successfully upholds the goals of ESS2e by combining both previously-published and newly developed contributions written by over 100 leading academics, researchers, and practitioner in a comprehensive, approachable format. The result is a succinct reference that unveils modern, cutting-edge approaches to acquiring and analyzing data across diverse subject areas within these three disciplines, including risk management, mathematical finance, economics, supply chain management, derivative pricing, and resource allocation. In addition, techniques related to survey methodology, computational statistics, and operations research are discussed, where applicable. Topics of coverage include: Logistics Decision analysis Optimization Simulation Forecasting Mathematical modeling Data mining

A Course in Financial Calculus

A Course in Financial Calculus

A text for first courses in financial calculus; lots of examples and exercises, first published in 2002.

The Oxford Guide to Financial Modeling

Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions

The Oxford Guide to Financial Modeling

The essential premise of this book is that theory and practice are equally important in describing financial modeling. In it the authors try to strike a balance in their discussions between theories that provide foundations for financial models and the institutional details that provide the context for applications of the models. The book presents the financial models of stock and bond options, exotic options, investment grade and high-yield bonds, convertible bonds, mortgage-backed securities, liabilities of financial institutions--the business model and the corporate model. It also describes the applications of the models to corporate finance. Furthermore, it relates the models to financial statements, risk management for an enterprise, and asset/liability management with illiquid instruments. The financial models are progressively presented from option pricing in the securities markets to firm valuation in corporate finance, following a format to emphasize the three aspects of a model: the set of assumptions, the model specification, and the model applications. Generally, financial modeling books segment the world of finance as "investments," "financial institutions," "corporate finance," and "securities analysis," and in so doing they rarely emphasize the relationships between the subjects. This unique book successfully ties the thought processes and applications of the financial models together and describes them as one process that provides business solutions. Created as a companion website to the book readers can visit www.thomasho.com to gain deeper understanding of the book's financial models. Interested readers can build and test the models described in the book using Excel, and they can submit their models to the site. Readers can also use the site's forum to discuss the models and can browse server based models to gain insights into the applications of the models. For those using the book in meetings or class settings the site provides Power Point descriptions of the chapters. Students can use available question banks on the chapters for studying.

Risk Management, Speculation, and Derivative Securities

Risk Management, Speculation, and Derivative Securities

Presenting an integrated explanation of speculative trading and risk management from the practitioner's point of view, "Risk Management, Speculation, and Derivative Securities" is a standard text on financial risk management that departs from the perspective of an agent whose main concerns are pricing and hedging derivatives.