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.

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.

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.

Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.