Format:
Online-Ressource (XVI, 287p. 49 illus, digital)
Edition:
2nd ed. 2012
ISBN:
9781461435822
Series Statement:
Undergraduate Texts in Mathematics
Content:
Preface -- Notation Key and Greek Alphabet -- 0 Introduction -- Part 1 Options and Arbitrage -- 1 Background on Options -- 2 An Aperitif on Arbitrage -- Part 2 Discrete-Time Pricing Models -- 3 Discrete Probability -- 4 Stochastic Processes, Filtrations and Martingales -- 5 Discrete-Time Pricing Models -- 6 The Binomial Model -- 7 Pricing Nonattainable Alternatives in an Incomplete Market -- 8 Optimal Stopping and American Options -- Part 3 the Black-Scholes Option Pricing Formula -- 9 Continuous Probability -- 10 The Black-Scholes Option Pricing Formula -- Appendix A: Convexity and the Separation Theorem -- Appendix B: Closed, Convex Cones -- Selected Solutions -- References -- Index.
Content:
The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.
Note:
Description based upon print version of record
,
Introduction to the Mathematics of Finance; Preface; The Second Edition; Organization of the Book; A Word on Definitions; Thanks Be To ...; Contents; Notation Key and Greek Alphabet; Greek Alphabet; Introduction; Motivation; The Derivative Pricing Problem; Assumptions; Risk-free Asset; Arbitrage; Miscellaneous Mathematical Facts; The Fundamental Counting Principle; Permutations; Combinations; Miscellanea; Part 1-Options and Arbitrage; Chapter 1 Background on Options; Stock Options; Exchanges; Option Terminology; Expiration Dates; Strike Prices; Option Symbols
,
The Role of the Options Clearing CorporationOpen Interest; Underlyings; The Purpose of Options; Leverage; Profit and Payoff Curves; Long Call; Short Call; Long Put; Short Put; Covered Calls; Profit Curves for Option Portfolios; The Time Value of an Option; The Delta of an Option; Selling Short; Exercises; Chapter 2 An Aperitif on Arbitrage; Forward Contracts; Forward Prices and Delivery Prices; Spot Prices; The Pricing of Forward Contracts; Futures Contracts; Daily Settlement; The Put-Call Option Parity Formula; The European Case; The American Case; Comparing Option Prices; Exercises
,
Part 2-Discrete-Time Pricing ModelsChapter 3 Discrete Probability; Partitions; Refinements; Algebras; Partitions and Algebras; Overview of Probability; Probability Spaces; Probability Mass Functions; The Theorem on Total Probability; Independence; The Binomial Distribution; Conditional Probability; Random Variables; Indicator Random Variables; The Partition of a Random Variable; The Probability Distribution of a Random Variable; Measurability of a Random Variable with Respect to a Partition; Independence of Random Variables; Positive Random Variables; Random Vectors; Expectation
,
Expected Value of a Function of a Random VariableExpectation and Independence; Variance and Standard Deviation; Standardizing a Random Variable; Expected Value of a Bernoulli Random Variable; Expected Value of a Binomial Random Variable; Conditional Expectation; Conditional Expectation with Respect to an Event; Conditional Expectation with Respect to a Partition; Exercises; Chapter 4 Stochastic Processes, Filtrations and Martingales; State Trees; Information Structures; Information Structures, Probabilities and Path Numbers; Probability Measures and Edge Labels
,
Edge Labels and Probability MeasuresSummary; Information Structures and Stochastic Processes; Stochastic Processes Adapted to a Filtration; Martingales; Characterizing Martingales; An Example; Exercises; Exercises on Submartingales and Supermartingales; Chapter 5 Discrete-Time Pricing Models; Assumptions; A Unit of Accounting; Assumption of a Risk-free Asset; Additional Assumptions; The Basic Model; Time; Assets; States of the Economy; Natural Probabilities; Asset Prices; Portfolios and Trading Strategies; Rolling Assets; Portfolio Rebalancing; Models are Two-Dimensional
,
The Valuation of Portfolios
Additional Edition:
ISBN 9781461435815
Additional Edition:
Erscheint auch als Druck-Ausgabe Roman, Steven Introduction to the mathematics of finance New York : Springer, 2012 ISBN 9781461435815
Language:
English
Subjects:
Economics
,
Mathematics
Keywords:
Finanzmathematik
;
Finanzmathematik
DOI:
10.1007/978-1-4614-3582-2
URL:
Volltext
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