Monte Carlo Methods and Models in Finance and Insurance

ISBN: 9781420076189 出版年：2010 页码：485 Korn, Ralf Korn, Elke Kroisandt, Gerald CRC Press

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 Ito 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 Levy processes: Definition, properties, and examples Simulation of Levy processes Simulating Financial Models: Discontinuous Paths Introduction Merton's jump diffusion model and stochastic volatility models with jumps Special Levy 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