Korn / Kroisandt Monte Carlo Methods and Models in Finance and Insurance

1. Auflage 2010
ISBN: 978-1-4200-7619-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 484 Seiten

Reihe: Chapman & Hall/CRC Financial Mathematics Series

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath–Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models.

The authors separately discuss Monte Carlo techniques, stochastic process basics, and the theoretical background and intuition behind financial and actuarial mathematics, before bringing the topics together to apply the Monte Carlo methods to areas of finance and insurance. This allows for the easy identification of standard Monte Carlo tools and for a detailed focus on the main principles of financial and insurance mathematics. The book describes high-level Monte Carlo methods for standard simulation and the simulation of stochastic processes with continuous and discontinuous paths. It also covers a wide selection of popular models in finance and insurance, from Black–Scholes to stochastic volatility to interest rate to dynamic mortality.

Through its many numerical and graphical illustrations and simple, insightful examples, this book provides a deep understanding of the scope of Monte Carlo methods and their use in various financial situations. The intuitive presentation encourages readers to implement and further develop the simulation methods.

Zielgruppe

Graduate and advanced undergraduate students in financial mathematics and economics; researchers and practitioners in finance, insurance, and economics.

Autoren/Hrsg.

Korn, Ralf

Korn, Elke

Kroisandt, Gerald

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines

Inhaltsverzeichnis

Introduction and User Guide
Introduction and concept
Contents
How to use this book?
Further literature
Acknowledgements

Generating Random Numbers
Introduction
Examples of random number generators
Testing and analyzing RNGs
Generating random numbers with general distributions
Selected distributions
Multivariate random variables
Quasi random sequences as a substitute for random sequences
Parallelization techniques

The Monte Carlo Method: Basic Principles and Improvements
Introduction
The strong law of large numbers and the Monte Carlo method
Improving the speed of convergence of the Monte Carlo method: Variance reduction methods
Further aspects of variance reduction methods

Simulating Continuous-Time Stochastic Processes with Continuous Paths
Introduction
Stochastic processes and their paths: Basic definitions
The Monte Carlo method for stochastic processes
Brownian motion and the Brownian bridge
Basics of Itô calculus
Stochastic differential equations
Simulating solutions of stochastic differential equations
Which simulation methods for SDE should be chosen?

Simulating Financial Models and Pricing of Derivatives: Continuous Paths
Introduction
Basics of stock price modeling
A Black–Scholes type stock price framework
Basic facts of options
An introduction to option pricing
Option pricing and the Monte Carlo method in the Black–Scholes setting
Weaknesses of the Black–Scholes model
Local volatility models and the CEV model
An excursion: Calibrating a model
Option pricing in incomplete markets: Some aspects
Stochastic volatility and option pricing in the Heston model
Variance reduction principles in non-Black–Scholes models
Stochastic local volatility models
Monte Carlo option pricing: American and Bermudan options
Monte Carlo calculation of option price sensitivities
Basics of interest rate modeling
The short rate approach to interest rate modeling
The forward rate approach to interest rate modeling
LIBOR market models

Simulating Continuous-Time Stochastic Processes: Discontinuous Paths
Introduction
Poisson processes and Poisson random measures: Definition and simulation
Jump diffusions: Basics, properties, and simulation
Lévy processes: Definition, properties, and examples
Simulation of Lévy processes

Simulating Financial Models: Discontinuous Paths
Introduction
Merton’s jump diffusion model and stochastic volatility models with jumps
Special Lévy models and their simulation

Simulating Actuarial Models
Introduction
Premium principles and risk measures
Some applications of Monte Carlo methods in life insurance
Simulating dependent risks with copulas
Non-life insurance
Markov chain Monte Carlo and Bayesian estimation
Asset-liability management and Solvency II

References
Index

Über Autor(innen)

Ralf Korn is a professor of financial mathematics at the University of Kaiserslautern and a member of the scientific advisory board of Fraunhofer ITWM in Kaiserslautern, Germany.
Elke Korn is an independent financial mathematics consultant in Kaiserslautern, Germany.
Gerald Kroisandt is a financial mathematician at Fraunhofer ITWM, in Kaiserslautern, Germany.