E-Book, Englisch, 254 Seiten
Lamberton / Lapeyre Introduction to Stochastic Calculus Applied to Finance, Second Edition
2. Auflage 2011
ISBN: 978-1-4200-0994-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 254 Seiten
Reihe: Chapman & Hall/CRC Financial Mathematics Series
ISBN: 978-1-4200-0994-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, Introduction to Stochastic Calculus Applied to Finance, Second Edition incorporates some of these new techniques and concepts to provide an accessible, up-to-date initiation to the field.
New to the Second Edition
- Complements on discrete models, including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete markets
- Discussions on local volatility, Dupire's formula, the change of numéraire techniques, forward measures, and the forward Libor model
- A new chapter on credit risk modeling
- An extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategies
- Additional exercises and problems
Providing all of the necessary stochastic calculus theory, the authors cover many key finance topics, including martingales, arbitrage, option pricing, American and European options, the Black-Scholes model, optimal hedging, and the computer simulation of financial models. They succeed in producing a solid introduction to stochastic approaches used in the financial world.
Zielgruppe
Advanced undergraduate and graduate students of mathematical finance, statistics, and economics; quantitative finance practitioners and researchers; and risk analysis professionals.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
INTRODUCTION
DISCRETE-TIME MODELS
Discrete-time formalism
Martingales and arbitrage opportunities
Complete markets and option pricing
Problem: Cox, Ross and Rubinstein model
OPTIMAL STOPPING PROBLEM AND AMERICAN OPTIONS
Stopping time
The Snell envelope
Decomposition of supermartingales
Snell envelope and Markov chains
Application to American options
BROWNIAN MOTION AND STOCHASTIC DIFFERENTIAL EQUATIONS
General comments on continuous-time processes
Brownian motion
Continuous-time martingales
Stochastic integral and Itô calculus
Stochastic differential equations
THE BLACK-SCHOLES MODEL
Description of the model
Change of probability: Representation of martingales
Pricing and hedging options in the Black-Scholes model
American options
Implied volatility and local volatility models
The Black-Scholes model with dividends and call/put symmetry
Problems
OPTION PRICING AND PARTIAL DIFFERENTIAL EQUATIONS
European option pricing and diffusions
Solving parabolic equations numerically
American options
INTEREST RATE MODELS
Modeling principles
Some classical models
ASSET MODELS WITH JUMPS
Poisson process
Dynamics of the risky asset
Martingales in a jump-diffusion model
Pricing options in a jump-diffusion model
CREDIT RISK MODELS
Structural models
Intensity-based models
Copulas
SIMULATION AND ALGORITHMS FOR FINANCIAL MODELS
Simulation and financial models
Introduction to variance reduction methods
Computer experiments
APPENDIX
Normal random variables
Conditional expectation
Separation of convex sets
BIBLIOGRAPHY
INDEX
Exercises appear at the end of each chapter.
