Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

Select and execute the best trades—and reduce risk Rather than teaching options from a financial perspective, How to Price and Trade Options: Identify, Analyze, and Execute the Best Trade Probabilities goes back to the Nobel Prize-winning Black-Scholes model. Written by well-known options expert Al Sherbin, it looks at the basis for probability theory in option trading and explains how to put the odds in your favor when trading options. Inside, you'll discover how anyone can "operate their own casino" if they know how through proper option strategies. Plus, a supplemental website includes videos that walk you through various probability scenarios, pre-formatted spreadsheets, and code. All investors should have a portion of their portfolio set aside for option trades. Not only do options provide great opportunities for leveraged plays, they can also help you earn larger profits with a smaller amount of cash outlay. With the help of this book, traders, active investors, and self-directed investors of all stripes will learn how simple it can be to deploy probability-based trading strategies. Teaches both defined and undefined risk strategies Utilizes simple cost basis reduction strategies to enhance investment returns Draws on unique research studies Discusses volatility to include both historical (realized) and implied volatility: the interplay between the two is a key piece of information overlooked by option traders If you're a trader of any level and want to make the best trades possible, this book has you covered.

Statistics for the Trading Floor: Data Science for Investing is the best book on statistics for investing. Written for professionals by a professional trader and hedge fund manager, the book gives a thorough grounding in quantitative methods used by investing professionals.

A comprehensive guide that lets you play the options game with confidence Due to the uncontrollable elements associated with options, many traders find themselves without practical strategies for specific situations. The Option Trader's Guide to Probability, Volatility, and Timing offers traders a variety of strategies to trade options intelligently and confidently in any given situation. With detail and objectivity, this book sets forth risk assessment guidelines, explains risk curve analysis, discusses exit methods, and uncovers some of the biggest mistakes options traders make. The Option Trader's Guide provides readers with strategies for trading options as well as expert advice on when to implement those strategies.

This book is written for the experienced portfolio manager and professional options traders. It is a practical guide offering how to apply options math in a trading world that demands mathematical measurement. Every options trader deals with an array of calculations: beginners learn to identify risks and opportunities using a short list of strategies, while researchers and academics turn to advanced technical manuals. However, almost no books exist for the experienced portfolio managers and professional options traders who fall between these extremes. Michael C. Thomsett addresses this glaring gap with The Mathematics of Options, a practical guide with actionable tools for the practical application of options math in a world that demands quantification. It serves as a valuable reference for advanced methods of evaluating issues of pricing, payoff, probability, and risk. In his characteristic approachable style, Thomsett simplifies complex hot button issues—such as strategic payoffs, return calculations, and hedging options—that may be mentioned in introductory texts but are often underserved. The result is a comprehensive book that helps traders understand the mathematic concepts of options trading so that they can improve their skills and outcomes.

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.