A Markov Chain Monte Carlo Method for Derivative Pricing and Risk Assessment

A Markov Chain Monte Carlo Method for Derivative Pricing and Risk Assessment
Author: Sanjiv Ranjan Das
Publisher:
Total Pages:
Release: 2009
Genre:
ISBN:

Derivative security pricing and risk measurement relies increasingly on lattice representations of stochastic processes, which are a discrete approximation of the movement of the underlying securities. Pricing is undertaken by summation of node values on the lattice. When the lattice is large (which is the case when high accuracy is required), exhaustive enumeration of the nodes becomes prohibitively costly. Instead, Monte Carlo simulation is used to estimate the lattice value by sampling appropriately from the nodes. Most sampling methods become extremely error-prone in situations where the node values vary widely. This paper presents a Markov chain Monte Carlo scheme, adapted from Sinclair and Jerrum (Information and Computation 82 (1989)), that is able to overcome this problem, provided some partial (possibly very inaccurate) information about the lattice sum is available. This partial information is used to direct the sampling, in similar fashion to traditional importance sampling methods. The key difference is that the algorithm allows backtracking on the lattice, which acts in a quot;self-correctingquot; manner to minimize the bias in the importance sampling.

The World of Risk Management

The World of Risk Management
Author: H. Gifford Fong
Publisher: World Scientific
Total Pages: 233
Release: 2006
Genre: Business & Economics
ISBN: 9812565175

Risk management is a foundation discipline for the prudent conduct of investment management. Being effective requires ongoing evolution and adaptation. In The World of Risk Management, an expert team of contributors addresses the important issues arising in the practice of risk management. A common thread among these distinguished articles is a rigorous theoretical or conceptual basis as well as their practical significance. The topics include not only broad policy considerations but also detailed how-to prescriptions.

Handbook in Monte Carlo Simulation

Handbook in Monte Carlo Simulation
Author: Paolo Brandimarte
Publisher: John Wiley & Sons
Total Pages: 688
Release: 2014-06-17
Genre: Business & Economics
ISBN: 1118593642

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 Simulation and Finance

Monte Carlo Simulation and Finance
Author: Don L. McLeish
Publisher: John Wiley & Sons
Total Pages: 308
Release: 2011-09-13
Genre: Business & Economics
ISBN: 1118160940

Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.

Monte Carlo Methods and Models in Finance and Insurance

Monte Carlo Methods and Models in Finance and Insurance
Author: Ralf Korn
Publisher: CRC Press
Total Pages: 485
Release: 2010-02-26
Genre: Business & Economics
ISBN: 1420076191

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 Rom

Monte Carlo Methods in Financial Engineering

Monte Carlo Methods in Financial Engineering
Author: Paul Glasserman
Publisher: Springer Science & Business Media
Total Pages: 603
Release: 2013-03-09
Genre: Mathematics
ISBN: 0387216170

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

Markov Chain Monte Carlo Simulations and Their Statistical Analysis

Markov Chain Monte Carlo Simulations and Their Statistical Analysis
Author: Bernd A Berg
Publisher: World Scientific Publishing Company
Total Pages: 380
Release: 2004-10-01
Genre: Science
ISBN: 9813106379

This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.

Lectures on Monte Carlo Methods

Lectures on Monte Carlo Methods
Author: Neal Noah Madras
Publisher: American Mathematical Soc.
Total Pages: 113
Release: 2002
Genre: Mathematics
ISBN: 0821829785

Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.

Monte Carlo Methods

Monte Carlo Methods
Author: Neal Noah Madras
Publisher: American Mathematical Soc.
Total Pages: 238
Release: 2000
Genre: Mathematics
ISBN: 0821819925

This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.

Markov Chain Monte Carlo Simulations and Their Statistical Analysis

Markov Chain Monte Carlo Simulations and Their Statistical Analysis
Author: Bernd A. Berg
Publisher: World Scientific
Total Pages: 380
Release: 2004
Genre: Science
ISBN: 9812389350

This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.