Option Theory with Stochastic Analysis
An Introduction to Mathematical Finance
Published on 26. November 2003
Book
Paperback/Softback
X, 162 pages
978-3-540-40502-3 (ISBN)
Description
Since 1972 and the appearance of the famous Black & Scholes option pric ing formula, derivatives have become an integrated part of everyday life in the financial industry. Options and derivatives are tools to control risk ex posure, and used in the strategies of investors speculating in markets like fixed-income, stocks, currencies, commodities and energy. A combination of mathematical and economical reasoning is used to find the price of a derivatives contract. This book gives an introduction to the theory of mathematical finance, which is the modern approach to analyse options and derivatives. Roughly speaking, we can divide mathematical fi nance into three main directions. In stochastic finance the purpose is to use economic theory with stochastic analysis to derive fair prices for options and derivatives. The results are based on stochastic modelling of financial as sets, which is the field of empirical finance. Numerical approaches for finding prices of options are studied in computational finance. All three directions are presented in this book. Algorithms and code for Visual Basic functions are included in the numerical chapter to inspire the reader to test out the theory in practice. The objective of the book is not to give a complete account of option theory, but rather relax the mathematical rigour to focus on the ideas and techniques.
Reviews / Votes
From the reviews:
"This is a . book concerned solely with describing the mathematics of option pricing and I found it a delight to read. It is very well written, quite comprehensive and non-rigorous so that it can be used on courses aimed at a variety of students. . The book includes a healthy number of exercises and there are fully worked solutions to most of these." (David Applebaum, The Mathematical Gazette, Vol. 90 (517), 2006)
"The book provides an introduction to the basic ideas of the mathematical theory of financial options valuation, or, more concretely, to the Black-Scholes theory of pricing contingent claims on equity. . The text is a brief, neat, carefully written introduction to the fundamentals of the mathematics and the modelling of the analysis of options pricing." (José Lúis Fernandez Perez, Zentralblatt MATH, Vol. 1042 (17), 2004)
More details
Series
Edition
Softcover reprint of the original 1st ed. 2004
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
1 s/w Abbildung
X, 162 p. 1 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 11 mm
Weight
283 gr
ISBN-13
978-3-540-40502-3 (9783540405023)
DOI
10.1007/978-3-642-18786-5
Schweitzer Classification
Other editions
Additional editions
E-Book
12/2012
Springer
€64.19
Available for download
Person
Ole Barndorff-Nielsen is well known for his manifold contributions to the theory and applications of probability and mathematical statistics, as described in the introductions of The Fascination of Probability, Statistics and Their Applications, Springer 2016. He has contributed to various fields, including statistical inference, sedimentology, infinite divisibility and Levy theory, homogeneous turbulence, and financial econometrics. Together with Jürgen Schmiegel he has founded the field of ambit stochastics.
Fred Espen Benth's research focuses on stochastic analysis and its applications to energy and finance. He has contributed to risk management analysis of financial markets for weather and energy, as well as theoretical developments of stochastic calculus, including non-semimartingale stochastic integration. Recently he has developed stochastic volatility models and autoregressive processes in the infinite dimensional context.
Almut E. D. Veraart is a statistician and probabilist with an interest in developing stochastic models and statistical methods for finance, energy markets and weather and environmental variables. Her main methodological contributions are in statistical finance focusing on stochastic volatility modelling and estimation based on high-frequency data and in spatio-temporal statistics dealing with simulation and inference for ambit fields.
Content
1 Introduction.- 1.1 An Introduction to Options in Finance.- 1.2 Some Useful Material from Probability Theory.- 2 Statistical Analysis of Data from the Stock Market.- 2.1 The Black & Scholes Model.- 2.2 Logarithmic Returns from Stocks.- 2.3 Scaling Towards Normality.- 2.4 Heavy-Tailed and Skewed Logreturns.- 2.5 Logreturns and the Normal Inverse Gaussian Distribution.- 2.6 An Alternative to the Black & Scholes Model.- 2.7 Logreturns and Autocorrelation.- 2.8 Conclusions Regarding the Choice of Stock Price Model.- 3 An Introduction to Stochastic Analysis.- 3.1 The Itô Integral.- 3.2 The Itô Formula.- 3.3 Geometric Brownian Motion as the Solution of a Stochastic Differential Equation.- 3.4 Conditional Expectation and Martingales.- 4 Pricing and Hedging of Contingent Claims.- 4.1 Motivation from One-Period Markets.- 4.2 The Black & Scholes Market and Arbitrage.- 4.3 Pricing and Hedging of Contingent Claims X= f(S(T)).- 4.4 The Girsanov Theorem and Equivalent Martingale Measures.- 4.5 Pricing and Hedging of General Contingent Claims.- 4.6 The Markov Property and Pricing of General Contingent Claims.- 4.7 Contingent Claims on Many Underlying Stocks.- 4.8 Completeness, Arbitrage and Equivalent Martingale Measures.- 4.9 Extensions to Incomplete Markets.- 5 Numerical Pricing and Hedging of Contingent Claims.- 5.1 Pricing and Hedging with Monte Carlo Methods.- 5.2 Pricing and Hedging with the Finite Difference Method.- A Solutions to Selected Exercises.- References.