Book Description
Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques.
This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios.
The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential.
The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry.
Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context."
Customer Reviews:
Review for Monte Carlo Methods... by P. Glasserman.......2007-07-16
The book is just right for a reader who is looking for state-of-the-art techniques in Monte-Carlo methods in general. The fact that the book is specific to financial systems does not limit the usability of the book in the manner it is written. There are a lots of useful references one can get out of this book.
The book is for advanced readers in the sense that it requires rigorous mathematical ability to understand all the concepts. It is by no means for a novice reader and requires background in computational mathematics.
Best financial engineering book on MC.......2007-06-29
This is like the bible of Monte Carlo methods in financing. Both a good read and a good reference book. Must have! for any quant on wall street.
good book on Monte Carlo in Finance.......2007-04-02
But it seems the author is a little focused on selling his ideas, but not a very subjective overview of all topics in M-C method in finance.
Excelent choice on finance Monte Carlo.......2007-03-08
Clear and sound theoretical background on applied Monte Carlo for finance.
Brilliant.......2006-12-26
Almost everything related to Monte Carlo in Financial Engineering is covered at just the right level of detail. Quite easy to read too.
Book Description
In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.
The theme of stochastic volatility also reappears systematically in the second part of the book, which has been revised fundamentally, presenting much more detailed analyses of the various interest-rate models available: the authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions, never neglecting to examine liquid primary and derivative assets and identifying the sources of trading risk associated. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on practical rather than theoretical aspects of financial modelling.
Customer Reviews:
Excellent introductory book to financial math.......2006-11-03
This book takes you through the math of finance step-by-step, passing through very simple examples first and then slowly adding complexity to the models studied. It is written very clearly and the prerequisites to reading this book are only some basic notions of probabilities (sigma-fields, probability measures).
Sometimes, the problem with math books is that they are "dry" and contain only a succession of theorems and proofs. In this one, the authors make a point of explaining in detail how different theorems and models relate to each other, and make extensive comparisons between them so that you get a better feel for how they work in practice.
The book is primarily a math book and can be light on market specifics. Do not buy this book as a practical "howto" in derivatives trading.
At the Forefront of Modern Mathematical Finance.......2005-05-23
This advanced text provides an excellent account of the current state-of-the art of options pricing/hedging models and interest rate term structure models. The book is accessible to both advanced practitioners of mathematical finance as well as to pure researchers in the field.
The book is in written in a mathematical style and contains rigorous proofs of many results. However, the main focus of the text is to describe the frontier of knowledge in the subject. Each section contains copious references to the literature and is so current that several references are to working papers. Many sections detail open problems and other areas suitable for scholarly research.
In their second edition, the authors provide an extremely useful critique of each modeling paradigm that they investigate. They also provide evidence for their position in the form of literature references which instruct the reader as to the shortcomings/limitations of a particular model. This information should prove quite valuable to model practitioners and implementers.
The authors assume an advanced background from the field of stochastic analysis, although they do provide an appendix which summarizes key results needed from the field. For the stochastic calculus prerequisites, I recommend Rogers & Williams "Diffusions, Markov Processes and Martingales" volumes I and II. Suitable prerequisites are also covered by Karatzas and Shreve in "Brownian Motion and Stochastic Calculus" 2nd edition. A good foundation in arbitrage pricing theory is also needed. I recommend the nice treatment by Bjork in "Arbitrage Theory in Continuous Time" 2nd edition.
The book is divided into two parts. The first part deals with options pricing in equity markets. Chapter 1 sets premlinaries required for the arbitrage theoretic framework, while Chapter 2 has a very nice treatment of discrete time models and finite financial markets.
In Chapter 3, the authors develop the Black-Scholes model along with the Bachelier model using arbitrage techniques. The models are compared and used as benchmark continuous time models and form the basis for all subsequent analysis.
Chapter 4 provides a nice survey of techniques used to price/hedge options in foreign equity and currency markets. The authors assume familarity of the basic workings of foriegn markets.
Chapter 5 is a terrific chapter on valuing American-style options. The American call option is thoroughly studied and approximation techniques for the American put option are introduced. The explicit derivations of the formulas are referenced to the literature.
Chapter 6 provides an introduction to exotic options, although the authors vary their use of the term 'exotic' to meaning 'not a standard European-style or American-style' in this chapter to meaning 'no readily available liquid market' in Chapter 7. The descriptions are quite accessible and the basic properties of the options are described along with pricing formulas (assuming the Black-Scholes framework).
Chapter 7 provides as complete an accounting as I have ever seen of the generalizations of the Black-Scholes model and motivates this from the point of view of volatility surfaces. Many of the well-known models are studied in detail, such as CEV, local volatility, and mixture models. The strengths and weaknesses of each model are analyzed. The stochastic volatility models of Wiggins (via Orenstien-Uhlenbeck processes), Hull-White, and Heston are studied, as is the SABR model. The chapter wraps up with a study of the SIV models, describes how the stochastic volatility models can be obtained via limits of GARCH models and surveys Jump-diffusion processes and Levy processes.
The second part of the book is concerned with term structure models and interest rate derivatives. The authors are quite well-know for their many contributions to this study and their treatment is authoritative.
Martingales & Finance.......2003-04-12
I have used this book for two courses in my MSc degree in Financial Maths...well this book is hard to understand at first glance, but, once you are introduced with a good course on stochastic analysis and applied probability, this is an illuminating book...I particularly enjoyed the part on foreing equity derivatives and exotic derivatives.....Harmed with patience this is definitely the book by which you can effectively gain a sound a knowledge on modern mathematical finance theory....reading in conjunction with Bingham-Kiesel book, could help understanding the foundation of the subject.
yes, but ..........2000-03-17
I've been using this book on and off over the last year. At first I was very impressed with the level of detail in the mathematics, especially as it was the only book at the time focussing on risk-neutral methods and covering BGM. But I've become increasing disillusioned with it of late. It's difficult to explain, but although the whole book is written in traditional theorem-proof style, there are no real proofs! (I have a PhD in math and have done research for 10 years so I should know a little about proofs.) The only "proofs" provided are basically symbol shifting, but the heart of the math is strangely absent. This is especially strange given the Springer series in which it appears.
In short, if you want a catalogue of methods this book does the job, but if you want a deeper understanding try Lars Nielsens book.
excellent book for post-John-Hull readers.......1999-08-17
This book covers essentially everything needed for a serious financial math study. It captures the spirit of modern financial math. For people with math, physics or engineering background, when you feel comfortable woth John Hull's books, then this book is right one, and a must one.
Book Description
This book is an introduction to financial mathematics for mathematicians. It is intended both for graduate students with a certain background in probability theory as well as for professional mathematicians in industry and academia. In contrast to many textbooks on mathematical finance, only discrete-time stochastic models are considered. This setting has the advantage that the text can concentrate from the beginning on typical problems which are suggested by financial applications. Moreover, certain principles, such as the general incompleteness of realistic market models, become thus more transparent and visible. On the other hand, all models are based on general probability spaces, and so the text captures the interplay between probability theory and functional analysis which is typical for modern mathematical finance.
The first part of the book contains a study of financial investments in a static one-period market model. Here, an investor faces intrinsic risk and uncertainty, which cannot be hedged away. The tools presented to deal with this situation range from the classical theory of expected utility until the more recent development of measures of risk.
In the second part of the book, the idea of dynamic hedging and arbitrage-free pricing of contingent claims is developed in a multi-period framework. Such market models are typically incomplete, and particular focus is given to
methods combining the dynamic hedging of a risky position with the tools of assessing risk and uncertainty as presented in part.
Contents: Mathematical finance in one period: Arbitrage theory. Expected utility. Optimal investments. Measures of risk Dynamic Arbitrage Theory: Dynamic hedging of contingent claims. American contingent claims. Optional decomposition and super-hedging. Efficient hedging in incomplete markets. Minimizing the hedging error. Hedging under constraints References. Index
Customer Reviews:
Excellent book on mathematical finance.......2004-04-20
It is well-known that the mathematical study of finance has, over the last two decades, led to a number of discoveries in stochastic analysis whose import extends beyond the boundaries of finance to other areas of mathematics. There are, currently, many good text-books which treat the mathematics of financial markets (e.g. Pliska, Bingham&Kiesel, Elliott&Kopp, Musiela&Rutkowski, Karatzas&Shreve, roughly in increasing order of difficulty. Pliska's text works only in the discrete-time framework, whereas the others move quickly to continuous-time). The text by Follmer and Schied deals only with the discrete-time case, but covers a large amount of material which you won't find in any of the other books: A thorough introduction to utility theory, excellent coverage of coherent and convex risk measures, and various approaches to hedging in incomplete markets. Each chapter quickly brings the reader close to the frontiers of research. Future research in these areas also promises to overflow the boundaries, providing new applications to other branches of functional analysis.
A word of caution: Though the text restricts itself to the "simpler" discrete-time case, thus avoiding stochastic integration, it nevertheless demands a solid background in analysis, including graduate level probability theory and functional analysis. Though not technically a requirement, some background in mathematical finance is necessary in order to understand what this book is about.
In conclusion, therefore, don't make this your first book on mathematical finance -- get Bingham&Kiesel instead. But if you have the mathematical background, and are analytically inclined, do buy it. This book is a phenomenal achievement.
Book Description
Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. Many mathematical tools are needed to solve these models. The book presents various methods for computing the dynamics of general equilibrium models. In part I, the representative-agent stochastic growth model is solved with the help of value function iteration, linear and linear quadratic approximation methods, parameterised expectations and projection methods. In order to apply these methods, fundamentals from numerical analysis are reviewed in detail. Part II discusses methods for solving heterogeneous-agent economies. In such economies, the distribution of the individual state variables is endogenous. This part of the book also serves as an introduction to the modern theory of distribution economics. Applications include the dynamics of the income distribution over the business cycle or the overlapping-generations model. Through an accompanying home page to this book, computer codes to all applications can be downloaded.
Book Description
Efficient Methods for Valuing Interest Rate Derivatives provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore the practical issues, such as the implementation of models, and model selection.
Aimed at people with a solid quantitative background, this book will be of particular interest to risk managers, interest rate derivative traders, quantitative researchers, portfolio and fund managers, and students of mathematics and economics, but it will also prove invaluable to anyone looking for a good overview of interest rate derivative modelling.
Customer Reviews:
Finally... a road map to interest rate models!!!.......2003-08-07
I had a strong background in equity derivative models but found the leap to interest rate models difficult. What are the relationships between short rates, forward rates, and term structure? How do assumptions translate into restrictions on our ability to model the "stylized facts" of interest rates? How are assumption violations "corrected" by practitioners?
This book answers all of these questions in a straightforward yet rigorous manner. Explanations are supplemented with simple examples.
After reading this book, I had the roadmap and analytical context I needed to tackle implementation focused books like Brigo and Mercurio.
As a bonus, this book provides a very nice summary of major valuation tools. (Monte Carlo simulation of martingale processes, development of pricing PDE via Feynman-Kac, development of fundamental solutions, etc.)
Begin your BGM, Libor & Swap market model journey here........2003-03-02
If you want a concise, clearly written and excellently explained introduction to the cutting edge interest rate models used in dealing rooms today. Look no further. With an elementary stochastic calculus background from Rennie & Baxter, this book is very readable, even on a crowded train! For those who want more details & case studies, have Interest Rate Models by Brigo & Mercurio as a companion text. With useful tips on Libor & swap market model implementation, and a whole chapter devoted to convexity correction. One of the best texts on the subject I have read.
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Stochastic Optimization Methods
Kurt Marti
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Introduction to Stochastic Search and Optimization
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Numerical Optimization (Springer Series in Operations Research and Financial Engineering)
ASIN: 3540222723 |
Book Description
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Book Description
This book--an overview of contemporary topics related to the modelling of financial time series--is set against a backdrop of rapid expansions of interest in both the models themselves and the financial problems to which they are applied.
The book forms part of a new series of upper level textbooks, Routledge Advanced Texts in Economics and Finance and includes the following features:
* an exposition of the use of three popular computer packages used for econometric estimation - including Microfit
* end of chapter points for discussion
* contexts that provide background.
Customer Reviews:
Financially Viable.......2003-03-14
This is the first book of its kind on the market and it was a real relief to see it when it came out. It covers everything an advanced student of financial econometrics needs to know and does so with impressive mathematical clarity.
I can see this book doing very well indeed, and the contents list alone should be enough to recommend it.
Book Description
In 1958, Stanford University Press published Studies in the Mathematical Theory of Inventory and Production (edited by Kenneth J. Arrow, Samuel Karlin, and Herbert Scarf), which became the pioneering road map for the next forty years of research in this area. One of the outgrowths of this research was development of the field of supply-chain management, which deals with the ways organizations can achieve competitive advantage by coordinating the activities involved in creating products—including designing, procuring, transforming, moving, storing, selling, providing after-sales service, and recycling. Following in this tradition, Foundations of Stochastic Inventory Theory has a dual purpose, serving as an advanced textbook designed to prepare doctoral students to do research on the mathematical foundations of inventory theory and as a reference work for those already engaged in such research.
The author begins by presenting two basic inventory models: the economic order quantity model, which deals with “cycle stocks,” and the newsvendor model, which deals with “safety stocks.” He then describes foundational concepts, methods, and tools that prepare the reader to analyze inventory problems in which uncertainty plays a key role. Dynamic optimization is an important part of this preparation, which emphasizes insights gained from studying the role of uncertainty, rather than focusing on the derivation of numerical solutions and algorithms (with the exception of two chapters on computational issues in infinite-horizon models).
All fourteen chapters in the book, and four of the five appendixes, conclude with exercises that either solidify or extend the concepts introduced. Some of these exercises have served as Ph.D. qualifying examination questions in the Operations, Information, and Technology area of the Stanford Graduate School of Business.
Customer Reviews:
Excellent Review of the Stochastic Inventory Theory.......2007-02-13
This book provides a good path to learn the theory of stochastic inventory control. The first few chapters and the appedices are pretty useful.
Stochastic Inventory Mathematical Formulations.......2007-01-12
This book is not suitable for practitioner looking for methodologies on how to solve real-world stochastic inventory problems. However, it is suitable for someone interest on mathematical formulations, research...etc.; perhaps a graduate IE/OR student working on inventory models.
A great overview of stocahstic inventory theory........2004-09-12
Begining from early day in 1950, the Inventory theory is mathematically rich and widely applicable field of Operations Research. This books provides an excellent overview of the development in this direction so far. It teaches many very important concept without getting tedious in technical details. This also serves as a very good text for students interested in learning dynamic programming and structured policies. This book falls short of (my) expectations as its approach in describing the problem solving is very legality oriented. In other words, though this informs a reader why certain things are true by presenting mathematical proofs, it doesn't tell how do one arrives at the proof. However there are very few books which really do that.
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Average-Cost Control of Stochastic Manufacturing Systems (Stochastic Modelling and Applied Probability)
Suresh P. Sethi ,
Han-Qin Zhang , and
Qing Zhang
Manufacturer: Springer
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ASIN: 0387219471 |
Book Description
Most manufacturing systems are large, complex, and operate in an environment of uncertainty. It is common practice to manage such systems in a hierarchical fashion. This book articulates a new theory that shows that hierarchical decision making can in fact lead to a near optimization of system goals. The material in the book cuts across disciplines. It will appeal to graduate students and researchers in applied mathematics, operations management, operations research, and system and control theory.
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Dynamic and Stochastic Efficiency Analysis: Economics of Data Envelopment Analysis
Jati K. Sengupta
Manufacturer: World Scientific Publishing Company
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