Monte Carlo Methods and Models in Finance and Insurance

Author: Ralf Korn
Publisher: CRC Press
ISBN: 1420076191
Release Date: 2010-02-26
Genre: Mathematics

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.

Handbook in Monte Carlo Simulation

Author: Paolo Brandimarte
Publisher: John Wiley & Sons
ISBN: 9781118593646
Release Date: 2014-06-17
Genre: Business & Economics

An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.

Monte Carlo Methods in Finance

Author: Peter Jäckel
Publisher: Wiley
ISBN: 047149741X
Release Date: 2002-04-03
Genre: Business & Economics

An invaluable resource for quantitative analysts who need to run models that assist in option pricing and risk management. This concise, practical hands on guide to Monte Carlo simulation introduces standard and advanced methods to the increasing complexity of derivatives portfolios. Ranging from pricing more complex derivatives, such as American and Asian options, to measuring Value at Risk, or modelling complex market dynamics, simulation is the only method general enough to capture the complexity and Monte Carlo simulation is the best pricing and risk management method available. The book is packed with numerous examples using real world data and is supplied with a CD to aid in the use of the examples.

Computation and Modelling in Insurance and Finance

Author: Erik Bølviken
Publisher: Cambridge University Press
ISBN: 9780521830485
Release Date: 2014-04-10
Genre: Business & Economics

This practical introduction outlines methods for analysing actuarial and financial risk at a fairly elementary mathematical level suitable for graduate students, actuaries and other analysts in the industry who could use simulation as a problem solver. Numerous exercises with R-code illustrate the text.

Monte Carlo Simulation with Applications to Finance

Author: Hui Wang
Publisher: CRC Press
ISBN: 9781466566903
Release Date: 2012-05-22
Genre: Business & Economics

Developed from the author’s course on Monte Carlo simulation at Brown University, Monte Carlo Simulation with Applications to Finance provides a self-contained introduction to Monte Carlo methods in financial engineering. It is suitable for advanced undergraduate and graduate students taking a one-semester course or for practitioners in the financial industry. The author first presents the necessary mathematical tools for simulation, arbitrary free option pricing, and the basic implementation of Monte Carlo schemes. He then describes variance reduction techniques, including control variates, stratification, conditioning, importance sampling, and cross-entropy. The text concludes with stochastic calculus and the simulation of diffusion processes. Only requiring some familiarity with probability and statistics, the book keeps much of the mathematics at an informal level and avoids technical measure-theoretic jargon to provide a practical understanding of the basics. It includes a large number of examples as well as MATLAB® coding exercises that are designed in a progressive manner so that no prior experience with MATLAB is needed.

Introductory Stochastic Analysis for Finance and Insurance

Author: X. Sheldon Lin
Publisher: John Wiley & Sons
ISBN: 9780471793205
Release Date: 2006-04-21
Genre: Mathematics

Incorporates the many tools needed for modeling and pricing in finance and insurance Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory. Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers. This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested. Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics and Applications in Insurance, are devoted to more advanced topics. Readers learn the Feynman-Kac formula, the Girsanov's theorem, and complex barrier hitting times distributions. Finally, readers discover how stochastic analysis and principles are applied in practice through two insurance examples: valuation of equity-linked annuities under a stochastic interest rate environment and calculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplify complex theory and pro-cesses. An extensive bibliography opens up additional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, this text is recommended for one-semester courses in stochastic finance and calculus. It is also recommended as a study guide for professionals taking Causality Actuarial Society (CAS) and Society of Actuaries (SOA) actuarial examinations.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 9783642136948
Release Date: 2010-07-23
Genre: Mathematics

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Market Consistency

Author: Malcolm Kemp
Publisher: John Wiley & Sons
ISBN: 9780470684894
Release Date: 2009-09-10
Genre: Business & Economics

Achieving market consistency can be challenging, even for the most established finance practitioners. In Market Consistency: Model Calibration in Imperfect Markets, leading expert Malcolm Kemp shows readers how they can best incorporate market consistency across all disciplines. Building on the author's experience as a practitioner, writer and speaker on the topic, the book explores how risk management and related disciplines might develop as fair valuation principles become more entrenched in finance and regulatory practice. This is the only text that clearly illustrates how to calibrate risk, pricing and portfolio construction models to a market consistent level, carefully explaining in a logical sequence when and how market consistency should be used, what it means for different financial disciplines and how it can be achieved for both liquid and illiquid positions. It explains why market consistency is intrinsically difficult to achieve with certainty in some types of activities, including computation of hedging parameters, and provides solutions to even the most complex problems. The book also shows how to best mark-to-market illiquid assets and liabilities and to incorporate these valuations into solvency and other types of financial analysis; it indicates how to define and identify risk-free interest rates, even when the creditworthiness of governments is no longer undoubted; and it explores when practitioners should focus most on market consistency and when their clients or employers might have less desire for such an emphasis. Finally, the book analyses the intrinsic role of regulation and risk management within different parts of the financial services industry, identifying how and why market consistency is key to these topics, and highlights why ideal regulatory solvency approaches for long term investors like insurers and pension funds may not be the same as for other financial market participants such as banks and asset managers.

Monte Carlo Methods and Stochastic Processes

Author: Emmanuel Gobet
Publisher: CRC Press
ISBN: 9781498746250
Release Date: 2016-07-31
Genre: Mathematics

Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.

Monte Carlo Methods in Financial Engineering

Author: Paul Glasserman
Publisher: Springer Science & Business Media
ISBN: 9780387216171
Release Date: 2013-03-09
Genre: Mathematics

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

Rare Event Simulation using Monte Carlo Methods

Author: Gerardo Rubino
Publisher: John Wiley & Sons
ISBN: 047074541X
Release Date: 2009-03-18
Genre: Mathematics

In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.

Stochastic Finance

Author: Nicolas Privault
Publisher: CRC Press
ISBN: 9781466594036
Release Date: 2013-12-20
Genre: Business & Economics

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

Measuring Market Risk

Author: Kevin Dowd
Publisher: John Wiley & Sons
ISBN: 9780470016510
Release Date: 2007-01-11
Genre: Business & Economics

Fully revised and restructured, Measuring Market Risk, Second Edition includes a new chapter on options risk management, as well as substantial new information on parametric risk, non-parametric measurements and liquidity risks, more practical information to help with specific calculations, and new examples including Q&A’s and case studies.