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.
Table of Contents
Introduction and User Guide
Introduction and concept
How to use this book?
Generating Random Numbers
Examples of random number generators
Testing and analyzing RNGs
Generating random numbers with general distributions
Multivariate random variables
Quasi random sequences as a substitute for random sequences
The Monte Carlo Method: Basic Principles and Improvements
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
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
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
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
Merton’s jump diffusion model and stochastic volatility models with jumps
Special Lévy models and their simulation
Simulating Actuarial Models
Premium principles and risk measures
Some applications of Monte Carlo methods in life insurance
Simulating dependent risks with copulas
Markov chain Monte Carlo and Bayesian estimation
Asset-liability management and Solvency II
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.
The collection of topics covered is quite impressive. … this book should serve as a valuable reference provided that one has sufficient background in finance, probability theory, and stochastic processes. It is self contained, and the formal background for each model is carefully described. This work also does an excellent job of providing an accessible source for many of the most recent financial models and latest Monte Carlo methods for their application.
—Maria L. Rizzo, The American Statistician, November 2011
This book is a comprehensive canter through the various Monte Carlo methods and their application in numerous financial models before rounding off with a high level assessment of their role within the insurance industry. The book covers a wide range of methods and models from old favourites like the Black-Scholes model to recent developments such as the multilevel Monte Carlo method. … the authors cleverly weave in example algorithms throughout the book which allows the user to mock up simple examples of the method. … a good reference book which was comprehensive in its coverage of the methods and financial models available. The book certainly brought to my attention methods and applications I was unaware of with discussion of some very recent developments. … what stood out about the book for me (apart from the wide coverage) was the use of example algorithms and numbers by the authors.
—Annals of Actuarial Science, Vol. 5, June 2011
This book takes a straightforward line to discuss Monte Carlo experiments with financial and insurance applications, offering a step-by-step approach to Monte Carlo methods with extensive description of the algorithms required. … this book includes a rigorous and concise description of numerous financial models and offers an up-to-date survey of this literature. This thorough book can be seen as a handbook on Monte Carlo methods and models for practitioners in finance and can be used in graduate courses on simulation models, numerical methods, financial mathematics, actuarial models and financial econometrics. It is certainly a toolkit of models and their corresponding Monte Carlo algorithms for practitioners and researchers in finance and insurance.
—Journal of the Royal Statistical Society: Series A, July 2011