Introduction to Option Pricing Theory


Book Description

Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.




Market Expectations and Option Prices


Book Description

This book is a slightly revised version of my doctoral dissertation which has been accepted by the Department of Economics and Business Administration of the Justus-Liebig-Universitat Giessen in July 2002. I am indebted to my advisor Prof. Dr. Volbert Alexander for encouraging and supporting my research. I am also grateful to the second member of the doctoral committee, Prof. Dr. Horst Rinne. Special thanks go to Dr. Ralf Ahrens for providing part of the data and to my colleague Carsten Lang, who spent much time reading the complete first draft. Wetzlar, January 2003 Martin Mandler Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I Theoretical Foundations 2 Arbitrage Pricing and Risk-Neutral Probabilities........ .. 7 2.1 Arbitrage Pricing in the Black/Scholes-Merton Model... . . .. . 7 2.2 The Equivalent Martingale Measure and Risk-Neutral Valuation ............................................... 11 2.3 Extracting Risk-Neutral Probabilities from Option Prices. . . .. 13 2.4 Summary............................................... 15 Appendix 2A: The Valuation Function in the Black/Scholes-Merton Model .................................................. 16 Appendix 2B: Some Further Details on the Replication Strategy ... 21 3 Survey of the Related Literature .......................... 23 3.1 The Information Content of Forward and Futures Prices. . . .. . 24 3.2 The Information Content of Implied Volatilities ............. 25 3.2.1 Implied Volatilities and the Risk-Neutral Probability Density .......................................... 27 3.2.2 The Term Structure of Implied Volatilities. . . . . . . .. . . 29 . 3.2.3 The Forecasting Information in Implied Volatilities. . .. 30 3.2.4 Implied Correlations as Forecasts of Future Correlations 43 VIII Contents 3.3 The Skewness Premium ..... . . . . . . . . . . . . . . . . . . .. . . 45 . . . . . . .




Handbook of the Economics of Finance


Book Description

Volume 1B covers the economics of financial markets: the saving and investment decisions; the valuation of equities, derivatives, and fixed income securities; and market microstructure.




Options


Book Description




Understanding Options


Book Description

It's not hard to understand why options trading continues to growin popularity, especially among sophisticated investors with largestock portfolios. Options are a cheaper and therefore, inherentlyless risky way of speculating on the price movements of stocks orother under-lying goods, yet, due to their volatility, they providemore price action per dollar than do stocks. And, when traded inconjunction with stock portfolios, options can significantlyenhance an investor's ability to manipulate the risk and returncharacteristics of their entire investment. Yet, despite these andother advantages of options, many investors shy away from thishighly lucrative type of speculation because of the seemingimpenetrability of many of its underlying concepts and technicalprinciples. Now in a book that demystifies options for financial professionals,Professor Robert W. Kolb, one of the nation's leading authoritieson the subject, provides readers with a solid grounding in theprinciples and practices of options trading. An excellent resourcefor investors who need to quickly get up to speed in options,Understanding Options offers a balanced presentation that buildsswiftly from the most basic concepts and terms to advanced tradingstrategies and techniques. Written in plain English and filled withreal-life examples and case studies, it schools readers in: * All essential terms, concepts, principles, and practices * Popular trading techniques and their payoffs * Option strategies * Option hedging * Formal trading models, including the Binomial and Merton models * Options on stock indexes, foreign currency, and futures * Option pricing in both the American and European markets * The options approach to corporate securities * And much more Concise yet comprehensive, authoritative yet highly accessible,Understanding Options gives you everything you need to feel rightat home in the lucrative world of options. Comprehensive, practical, authoritative--the fastest, mostaccessible route to the lucrative world of options From the basics of what an option is to advanced techniques forprofiting from options in a variety of markets, UnderstandingOptions covers all the bases. Written by a leading internationalauthority on options trading, this practical, hands-on guide offersdetailed, step-by-step coverage of option trading techniques andtheir payoffs, option strategies, European and American optionpricing, option hedging, and much more. It also explores options onstock indexes, foreign currency, and futures, and takes a closelook at the options approach to corporate securities. A concise, yet comprehensive, introduction to options for financialprofessionals * Gets you quickly up and running with all the essential knowledgeyou need to break into the options markets * Featuring a balanced presentation that moves swiftly from basicterms and concepts to advanced trading models * Packed with easy-to-follow examples and case studies that lucidlyillustrate all points covered




The Oxford Handbook of Quantitative Asset Management


Book Description

This book explores the current state of the art in quantitative investment management across seven key areas. Chapters by academics and practitioners working in leading investment management organizations bring together major theoretical and practical aspects of the field.




Handbook of Economic Forecasting


Book Description

The highly prized ability to make financial plans with some certainty about the future comes from the core fields of economics. In recent years the availability of more data, analytical tools of greater precision, and ex post studies of business decisions have increased demand for information about economic forecasting. Volumes 2A and 2B, which follows Nobel laureate Clive Granger's Volume 1 (2006), concentrate on two major subjects. Volume 2A covers innovations in methodologies, specifically macroforecasting and forecasting financial variables. Volume 2B investigates commercial applications, with sections on forecasters' objectives and methodologies. Experts provide surveys of a large range of literature scattered across applied and theoretical statistics journals as well as econometrics and empirical economics journals. The Handbook of Economic Forecasting Volumes 2A and 2B provide a unique compilation of chapters giving a coherent overview of forecasting theory and applications in one place and with up-to-date accounts of all major conceptual issues. - Focuses on innovation in economic forecasting via industry applications - Presents coherent summaries of subjects in economic forecasting that stretch from methodologies to applications - Makes details about economic forecasting accessible to scholars in fields outside economics




Advanced Asset Pricing Theory


Book Description

This book provides a broad introduction of modern asset pricing theory with equal treatments for both discrete-time and continuous-time modeling. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework.The analyses and coverage are up to date, comprehensive and in-depth. Topics include microeconomic foundation of asset pricing theory, the no-arbitrage principle and fundamental theorem, risk measurement and risk management, sequential portfolio choice, equity premium decomposition, option pricing, bond pricing and term structure of interest rates. The merits and limitations are expounded with respect to allocation and information market efficiency, along with the classical expectations hypothesis concerning the information content of yield curve and bond prices. Efforts are also made towards the resolution of several well-documented puzzles in empirical finance, which include the equity premium puzzle, the risk free rate puzzle, and the money-ness bias phenomenon of Black-Scholes option pricing model.The theory is self-contained and unified in presentation. The inclusion of proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory makes an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The explanations are detailed enough to capture the interest of those curious readers, and complete enough to provide necessary background material needed to explore further the subject and research literature.