Monte Carlo Methods and Models in Finance and Insurance

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.

Introduction and User GuideIntroduction and conceptContentsHow to use this book?Further literatureAcknowledgements Generating Random NumbersIntroductionExamples of random number generatorsTesting and analyzing RNGsGenerating random numbers with general distributionsSelected distributionsMultivariate random variablesQuasi random sequences as a substitute for random sequencesParallelization techniques The Monte Carlo Method: Basic Principles and ImprovementsIntroductionThe strong law of large numbers and the Monte Carlo methodImproving the speed of convergence of the Monte Carlo method: Variance reduction methodsFurther aspects of variance reduction methods Simulating Continuous-Time Stochastic Processes with Continuous PathsIntroductionStochastic processes and their paths: Basic definitionsThe Monte Carlo method for stochastic processesBrownian motion and the Brownian bridgeBasics of Itô calculusStochastic differential equationsSimulating solutions of stochastic differential equationsWhich simulation methods for SDE should be chosen? Simulating Financial Models and Pricing of Derivatives: Continuous PathsIntroductionBasics of stock price modelingA Black–Scholes type stock price frameworkBasic facts of optionsAn introduction to option pricingOption pricing and the Monte Carlo method in the Black–Scholes settingWeaknesses of the Black–Scholes modelLocal volatility models and the CEV modelAn excursion: Calibrating a modelOption pricing in incomplete markets: Some aspectsStochastic volatility and option pricing in the Heston modelVariance reduction principles in non-Black–Scholes modelsStochastic local volatility modelsMonte Carlo option pricing: American and Bermudan optionsMonte Carlo calculation of option price sensitivitiesBasics of interest rate modelingThe short rate approach to interest rate modelingThe forward rate approach to interest rate modelingLIBOR market models Simulating Continuous-Time Stochastic Processes: Discontinuous PathsIntroductionPoisson processes and Poisson random measures: Definition and simulationJump diffusions: Basics, properties, and simulationLévy processes: Definition, properties, and examplesSimulation of Lévy processes Simulating Financial Models: Discontinuous PathsIntroductionMerton’s jump diffusion model and stochastic volatility models with jumpsSpecial Lévy models and their simulation Simulating Actuarial ModelsIntroductionPremium principles and risk measuresSome applications of Monte Carlo methods in life insuranceSimulating dependent risks with copulasNon-life insuranceMarkov chain Monte Carlo and Bayesian estimationAsset-liability management and Solvency II References Index

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.