The Econometric Modelling of Financial Time Series

Book Description

Fully revised and updated, the second edition of the best-selling The Econometric Modelling of Financial Time Series provides comprehensive coverage of the variety of models currently used in the empirical analysis of financial markets. Covering bond, equity and financial markets, it is essential for scholars and practitioners wishing to acquire an understanding of the latest research techniques and findings in the field, and also graduate students wishing to research in financial markets. It provides many examples to illustrate techniques that are only just emerging in the technical literature.

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Customer Reviews:

Poorly Written and Unclear.......2001-01-10

Obviously patched together from topics written over a period of time, this book is not cohesive nor understandable. Mills doesn't spend any words developing his topics nor explaning the development. Spend your resources on Hamilton's classic and great definative bible, Time Series Analysis instead.

it's a terrific book for non-linear time series analysis.......2000-04-06

This is a very compact, practical book. It edits in a very readable way. What I like it most is that it contributes to non-linear time series analysis a lot, whereas not too many other time series related books do. The real data in the appendix can be downloaded and played around by the readers. You will really have a great time to read it.

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A great book
An excellent textbook!

Applied Stochastic Hydrogeology
Yoram Rubin
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 019513804X

Book Description

Stochastic Subsurface Hydrogeology is the study of subsurface, geological heterogeneity, and its effects on flow and transport process, using probabilistic and geostatistical concepts. This book presents a rational, systematic approach for analyzing and modeling subsurface heterogeneity, and for modeling flow and transport in the subsurface, and for prediction and decision-making under uncertainty. The book covers the fundamentals and practical aspects of geostatistics and stochastic hydrogeology, coupling theoretical and practical aspects, with examples, case studies and guidelines for applications, and provides a summary and review of the major developments in these areas.

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A great book.......2004-09-17

This is a great book, for sure the best and most comprehensive book on stochastic hydrogeology available today. It covers nearly all the fundamental and practical aspects of stochastic hydrogeology, with emphasis on both the theoretical and practical aspects of the discipline. The language is simple, with many examples and case studies. The book is a great reference for scientists who are familiar with stochastic hydrogeology as well as for students and/or practitioners who may get informed about the discipline and learn how to implement the various tools available. The book is at the same time a very good introduction to the matter and a reference book for people who are already familiar with stochastic hydrogeology and want to keep updated with the most recent developments. This is the kind of book to keep on the desk.

An excellent textbook!.......2004-06-20

Applied Stochastic Hydrogeology is easily the best book of this century in its field. Its intuitive and down-to-earth style makes even the most intricate aspects of stochastic analyses readily accessible to both graduate students and active researchers. The subjects the book covers range from stochastic site characterization and image reconstruction from sparse data to the concept of effective hydraulic parameters and probabilistic assessment of flow and transport in heterogeneous environments.

Mathematical Modeling, Volume 1: A Chemical Engineer's Perspective (Process Systems Engineering)

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Mathematical Modeling, Volume 1: A Chemical Engineer's Perspective (Process Systems Engineering)
Rutherford Aris
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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Elementary Chemical Reactor Analysis

ASIN: 0126045852

Book Description

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.
Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.

* Describes pitfalls as well as principles of mathematical modeling
* Presents twenty examples of engineering problems
* Features seventeen reprinted papers
* Presents personal reflections on some of the great natural philosophers
* Emphasizes modeling procedures that precede extensive calculations

Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Stochastic Modeling)

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Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Stochastic Modeling)
Gennady Samorodnitsky
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0412051710

Process Modelling and Model Analysis (Process Systems Engineering)

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Process Modelling and Model Analysis (Process Systems Engineering)
Ian T. Cameron , and Katalin Hangos
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0121569314

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This book describes the use of models in process engineering. Process engineering is all about manufacturing--of just about anything! To manage processing and manufacturing systematically, the engineer has to bring together many different techniques and analyses of the interaction between various aspects of the process. For example, process engineers would apply models to perform feasibility analyses of novel process designs, assess environmental impact, and detect potential hazards or accidents.

To manage complex systems and enable process design, the behavior of systems is reduced to simple mathematical forms. This book provides a systematic approach to the mathematical development of process models and explains how to analyze those models. Additionally, there is a comprehensive bibliography for further reading, a question and answer section, and an accompanying Web site developed by the authors with additional data and exercises.

* Introduces a structured modeling methodology emphasizing the importance of the modeling goal and including key steps such as model verification, calibration, and validation.
* Focuses on novel and advanced modeling techniques such as discrete, hybrid, hierarchical, and empirical modeling
* Illustrates the notions, tools, and techniques of process modeling with examples and advances applications

Continuous Stochastic Calculus with Applications to Finance

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Material every quantitative financial analyst should know.
Good Treatment of Continuous Time Martingales
Elegant Math Book on Finance - you need the math to read
It is indeed meant for learning
Not meant for learning

Continuous Stochastic Calculus with Applications to Finance
Michael Meyer
Manufacturer: Chapman & Hall/CRC
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Binding: Hardcover

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ASIN: 1584882344

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The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale. The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives. Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.

Customer Reviews:

Material every quantitative financial analyst should know........2006-01-25

Time spent to read the book in detail: Four weeks
The book, 295 pages, is ordered as follows:

Chapter 1 (First 50 pages):
These cover discreet time martingale theory.

Expectation/Conditional expectation: The coverage here is unusual and I found it irritating. The author defines conditional expectation of variables in e(P) - the space of extended random variables for which the expectation is defined - i.e. either E(X+) or E(X-) is defined - rather than the more traditional space L^1(R) - the space of integrable random variables. The source of irritation is that the former is not a vector space. Thus given a variable X in e(P) and another variable Y, in general X+Y will not be defined, for example if EX+ = infinity, EY= - infinity. As a result, one is constantly having to worry about whether one can add variables or not, a real pain. Perhaps an example might help:

Suppose I have two variables X1 AND X2. If I am in the space L^1 then I know both are finite almost everywhere (a.e) and so I can create a third variable Y through addition by setting say Y = X1+X2. In the treatment here however, I have to be careful since it is not a priori clear that X1+X2 is defined a.e. What I need is - one of the proofs in the book - that E(X1)+E(X2) be defined (i.e. it is not the case that one is + infinity the other -infinity). If both E(X1)and E(X2) are finite this reduces to the L^1 case. However, because the Author chooses to work in e(P), we still have, in order to show even this basic result, quite a bit of boring work to do. Specifically: if E(X1) = +infinity then we must have, recall the definition of e(P), that E(X1^+)= +infinity AND E(X1-) < -infinity and also, because E(X1)+E(X2) is defined E(X2)> -infinity and so , since X2 is in e(P), that E(X2^-) < -infinity. Now since,
(X1+X2)^- <= (X1)^- +(X2)^-, we have
E(X1+X2)- less than infinity which shows that a)X1+X2 is defined a.e. and b) it is in e(P).A little more work shows that, E(X1)+E(X2) =E(X1)+E(X2).

When one introduces conditioning the above irritation continues. We have that if X is in e(P) that the conditional expectation E(X|L) exist and is in , not as is standard in the literatureL^1, but rather, in e(P). Consequently we can no longer carry out simple operations, normally done without thinking, such as E(X1|L)+ E(X2|L)= E(X1+X2|L), but rather have to pause to check if as in the example above that E(X1|L)+ E(X2|L) is defined etc, etc.

Submartingale , Supermartingales ,Martingales: The definitions here again are a little unusual. The variables for both Sub and Super martingales are taken to be, yet again, in e(P). This in turn forces the definition:

A submartingale is an adapted process X = (Xn,Fn) such that:

1) E(Xn^+) <¥ ( The Standard in the literature is to have E(Xn) <¥
2) E( Xn+1|Fn)>=Xn
Likewise for a supermartingale we get:

A supermartingale is an adapted process X = (Xn,Fn) such that:
1) E(Xn^-) <¥ ( The Standard in the literature is to have E(Xn) <¥
2) E( Xn+1|Fn) <=Xn

These definitions, along with the fact that a martingale is both a supermartingale and submartingale, lead then to the standard - as appears in the literature - definition of a martingale.

Stopping Times, Upcrossing Lemmas, Modes of Convergence: The treatment here is quite nice - modulo the e(P)- inconvenience. The proofs are all given in detail. And the level is at that of Chung's "A Course in Probability Theory", Chapter 9.

Optional Sampling Theorem, Maximal Inequalities: A very rigorous treatment of the Optional Sampling Theorem (OST) is given. The need for closure is emphasized in order for OST to be applied in its full generality. In the absence of closure - the author emphasizes why - it is shown how the OST still applies if the optional times are taken to be bounded. The author then uses these results to show how stopped smartingales - super, sub and marts - are smartingales. Finally, Doobs, submartingle and L^p inequalities are derived.

Chapter 1 (Next 50 pages)

These cover continuous time martingale theory under the assumption that the probability space is complete and the filtration augmented and right continuous.

The treatment here - most of the hard work has already been done in the discreet case - uses the standard bootstrapping technique based on sequences of optional times taking only countable values, along with the assumption of right continuity of paths to generalize the discreet time results - through passing to limits - to analogous ones for a continuous time, i.e. where the index set is a subset of [0, ¥], setting. The Upcrossing lemmas, Convergence results, OST and Doobs inequalities are all derived

Next follows a superb treatment of local martingales.

At this point, and for what follows, the treatment switches to smartingales, with continuous paths.

It is now shown that for any bounded - continuous - martingale M, there exists a unique continuous bounded variation (increasing) process starting at 0 -denoted by [M], such that the process M^2-[M] is a closed martingale. Moreover, it is shown that this process is the limit in L^2 of the Quadratic variation of M. This result is then generalized to the case where M is a local martingale where it is shown that M^2-[M] is also a local martingale and where [M] is now only the limit in probability of the quadratic variation. Next the covariation process for two local martingales [M N] is defined and it is shown that MN -[MN] is again a local martingale.
Finally, integration with respect to integrators of bounded variation is defined for a suitable class of integrands and the "Kunita Watanabe", inequality derived.

All of the above is then extended to the case of Semi Martingales.

Chapter 2 (29 Pages) Brownian Motion
Definition of. Existence is shown. The Weak Markov properties derived. I found the notation in this chapter to be rather cumbersome. One would be better served by skipping this chapter, replacing it instead, by chapter 2 in Karatzas and Shreve's "Brownian Motion and Stochastic Calculus" (KS).

Chapter 3 (80 Pages) Stochastic Integration
This chapter, my favourite in the book, is a detailed discussion of integration with respect to continuous semi-martingales. The approach is modern. The chapter starts with a detailed definition of stochastic integration with respect to a continuous local martingale M. The level of rigour, is at the level of sections 3.1 and 3.2 of KS. However, the approach is different and in my opinion more elegant. Leveraging on the material in chapter 1 the stochastic integral for a square integrable - with respect to the induced product measure-progressively measurable, r.v X is defined to be the unique square integrable local martingale, starting at 0, I, such that for any other continuous local martingale N we have:

[I, N] = X DOT [M,N].

This is then extended to the case where X is only locally pathwise integrable with respect to [M], which is then extended to the case where M is a continuous semi martingale.
It is then shown how in the case where X is simple predictable the above definition yields that suggested by one's intuition, that the space of simple predictable variables is dense in the space of square integrable - with respect to the induced product measure - predictable processes, and that I in this case is an L^2 - this is the usual approach - limit of , with respect to P, of simple integrals.

Following this, is a derivation of Ito's lemma - this says that semimartingales are preserved under smooth transformation. It is then shown that given a P semimartingale X, a probability measure Q equivalent to P, X is a Q semi martingale and its Compensator under Q given by Uq = Up + [logM,X], where M is the Radoyn Nikodym derivative of Q with respect to P. It is then an easy step to conclude that the local martingale component of X under Q is related to that under P by:
LMq = LMp - [logM,X].
Thus the Girsanov theorem is proved. In the case where M is of the form,
M = exp( L - [L]/2), where L is a continuous local martingale, conditions on L , those of Novikov and other weaker one, necessary to make M a martingale are given and proven.

Finally, the Chapter concludes with a detailed section on the Martingale representation theorem. Most of this section is very similar to that in section 3.4 of KS. However, while the treatment there leaves a lot of work for the reader, many of the key results are buried in the exercises, the results here are all spelled out and detailed proofs furnished.

Chapter 4 (84 Pages) Applications to Finance:
I only read, the first 40 pages - the section dealing with the Black and Scholes Economy and that with The General Market Model. The treatment of the Black and Scholes economy - 17 pages -is standard and concise. The General Market model is at the level of chapters 4 and 5 in Nielson Pricing and Hedging of Derivatives Securities"(N). Because however, the Author has spent the time to develop the machinery in detail, unlike in the case Nielsen's 106 pages of "hand waving", the pace is a lot faster and the treatment more general. Moreover, results like, no free lunch with limited risk implying the existence of local martingale measure, based the work of Schaechermayer, something not alluded to in Nielson, are covered here The final 40 or so- which I have not read-pages are devoted to applications of the general theory to pricing specific derivatives.

Good Treatment of Continuous Time Martingales .......2005-06-10

Chapter 1: This is a summary of what every probabilist should know about Continuous Time Martingales. Essentially it does, although in a rather terse fashion, and with no examples, for Continuous Time Martingales, what David Williams book, "Probability and Martingales", does for the discreet time case. By restricting himself to the continuous case, as opposed to the more general cadlag processes, the author is able to provide a simple proof of the Doob Meyer Decomposition. The coverage in this chapter is more extensive than that of Chapter 1 in Karatzas and Shreeve and perhaps closer to ChapterII in Rogers and Williams.

Chapter 2: Essentially a brief introduction to Brownian Motion. I would advize the reader to skip this Chapter and replace it with chapter 2 of Karatzas and Shreves "Stochastic Calculus and Brownian Motion". The coverage there is more rigorous.

Chapter 3:This chapter covers Stochatic Integration with respect to a Continous Time Local Martingales. The coverage here mirrors that of chapter three in Karatazs and Shreve though the notation is perhaps closer in spirit to Chapter 4 of Rogers and Williams, Diffusions, Markhov Processes and Martingales. The construction of the Stochastic Integral is then followed by the usual suspects: Ito's Lemma which says that the SemiMartingale property is preserved under smooth transformations. The Martingale Representation Theorem this says that in the case where the integral is with respect to Brownian Motion, then the integral viewed as a mapping from the space of measurable adapted processes that are square integrable with respect to the product measure onto the space of continuous square integrable martingales is surjective. And last but not least Girsanovs theorem which allows one, modulu the satisfaction of the Novikov Condition, to alter the "drift term" in semi martingales through changing to an equivalent measure.

Chapter 4: I would advice the reader to replace this with chapters 4 and 5 in Nielsen's "Pricing and Hedging of Derivative Securities" for the general theory and chapter 6 for the Black and Scholes Economy. The coverage there is the best I have seen.

Elegant Math Book on Finance - you need the math to read.......2004-01-22

This is a math book first and foremost. It uses advanced mathematical techniques to discuss aspects of randomness that can be used to understand finance. Please don't mistake it for a course to teach concepts in basic finance.

It is a very elegant and sophisticated book for those who are very well versed in the necessary mathematics in stochastic calculus and in particular Martingale theory to show them how these tools can be applied to problems in finance.

If you have the math background and are interested in this topic you will get a lot from this book. If you don't have the math, don't bother. This book will be opaque.

It is indeed meant for learning.......2004-01-02

I completely disagree with Student.

This book is indeed meant for learning. Just do not take it as your first entry into Stochastic Calculus. Take it as a second reading. It is complete, thorough and well, very well written.

It will teach you. A lot. All theorems are cross-referenced, so you will not have any "it is obvious that" etc. Theorems are proved, over and over again, until they hammer themselves in your head.

It is a fine achievement, if you want something quick and dirty read something else.

Not meant for learning.......2001-02-03

Some books are meant to teach, and to elucidate new material; this book is not one of them. It seems the purpose of this book was rather to record for prosperity all theorems related to Stochastic Calculus. Instead of developing any intuition on the subject, the author seems to think the purpose of writing is to use the most elegant proofs with the most modern of mathematical jargon. In short, the book consists of stated lemmas and theorems with terse, undeveloped proofs. This book will not teach you anything.

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Elements of Stochastic Modeling
K. A. Borovkov
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Paperback

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ASIN: 9812383018

Book Description

This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments — with indications as to why a particular result holds, and also how it is connected with other results — and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered.

Advances in Stochastic Modelling and Data Analysis

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Advances in Stochastic Modelling and Data Analysis

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792335643

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Advances in Stochastic Modelling and Data Analysis presents the most recent developments in the field, together with their applications, mainly in the areas of insurance, finance, forecasting and marketing. In addition, the possible interactions between data analysis, artificial intelligence, decision support systems and multicriteria analysis are examined by top researchers. Audience: A wide readership drawn from theoretical and applied mathematicians, such as operations researchers, management scientists, statisticians, computer scientists, bankers, marketing managers, forecasters, and scientific societies such as EURO and TIMS.

Applied and Industrial Mathematics (Mathematics and Its Applications)

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Applied and Industrial Mathematics (Mathematics and Its Applications)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0792305213

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This book presents the state of the art in applied and industrial mathematics, updating the earlier Kluwer publication Applied and Industrial Mathematics, Venice-1, 1989. The current work includes a selection of main invited papers as well as conference contributions from a number of leading scientists working in the areas of applied mathematics, industrial mathematics applied analysis, numerical mathematics, mathematical physics and applied probability.

Audience: This volume will be of interest to researchers and advanced graduate students whose work involves mathematical modelling and industrial mathematics, numerics and computation, mathematics of science, mathematical physics, mathematical analysis in general and partial differential equations in particular.

Applied Stochastic Models and Data Analysis: Proceedings of the Sixth International Symposium, Chania, Crete, Greece May 3-6, 1993

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Applied Stochastic Models and Data Analysis: Proceedings of the Sixth International Symposium, Chania, Crete, Greece May 3-6, 1993
Crete) International Symposium on Asmda 1993 (Chaina , and Jacques Janssen
Manufacturer: World Scientific Pub Co Inc
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Binding: Hardcover

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