Book Description
Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.
This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.
Master's level students and researchers in mathematical finance and financial engineering will find this book useful.
Customer Reviews:
Great, easy to understand introduction to mathematical finance.......2007-06-22
I say it's an "introduction" because I have little background in both stochastic calculus and finance but find this to be fairly easy to read. Unless other texts that present the material in a much more dense manner, i.e. skipping over the majority of derivations, Schreve goes through the derivation for even the most routine of derivations--which is actually great for a newbie like me.
The text is self-contained and covers a wide range of topics. I would like him to cover some practical aspects of modeling in finance, but that's really not what the text is about. For what it set out to explain, it does a great job. 5 stars.
Pre-digested chicken soup for the "aspiring quant".......2007-04-14
While writing a review for Hull's text, I suggested that an easier (than to start with Hull) way to learn quantitative finance is to pick up one of the more focused books on the subject. There is a huge deluge of these books - I think one comes out every few weeks. They all cover the same topics, in roughly the same manner, so there is little that distinguishes one from the other. There is certainly not much different in content in Shreve than in others - in fact you cannot go wrong by picking any well known book - just pick the cheapest.
What is different about Shreve is that he does not skimp on the details. As another reviewer pointed out, this is not an elegant book. For people new to quant finance, this is actually a good thing. There are pages after pages of ugly equations written in gory detail. In almost any other quantitative book (I don't mean quantitative finance book - but any book that is of a quantitative nature, be it wireless communications or information theory or what have you) these details would have been omited. But not here, and for a good reason: There are PhDs in areas that are only remotely quantitatve - who want to switch to quantitative finance just because they think there is money in the area. These people don't have the mathematical maturity or stamina required to actually go home and do the (mechanical!) math between equations themselves. They want to see it all done, served to them on a platter with fries and ketchup, please - because they haven't done math in a while but are "interested" in it. Shreve obliges. And succeeds beautifully in serving pre-digested food to those that need it.
Shreve even gives you a sense of having done something yourself through his exercies. Again the excercises in his book are unlike anything that I have see in any mathematically inclined text - they make up a whole section in each chapter. Again, Shreve is serving you things on a platter - the exercies essentially come with the equivalent of a verbose TA built-in - Shreve guides you to the solution, in a very tenderly-holding-your-hand manner. Of course, this is a good thing, for those that need it.
The chapters on SDEs and even on jump processes will make good chicken-soup introductions to these topics, and are written in a more rigorous (and, though I repeat myself, verbose) fashion than some of the other books I have seen. The book also strikes a good balance between the PDE approach and the martingale approach to pricing. The chapter on PDEs itself, in particular, is well written and does a good job of pointing out the Feynamn Kac connection between the two approaches. In general, this book covers everythying that my friends who are faculty in mathematical finance courses teach in a (continuous time finance course in a) typical MS in Qfin program.
While my review may sound negative, the verbosity of the book is its asset, because most people approaching it are looking for it. When grad students, who otherwise are not interested in talking to me, learn about what I do for a living and suddenly become extremely ingratiating, (and start drooling a bit from the side of their mouth) and go on to ask me for what to read, this is the book I recommend to them. It will take them from cluelessness to the point where they can actually see what Hull has been sweeping under the carpet.
Let me say it again, this is not a negative review for the book. The book does its job beautifully. But it doesnt have a soul. But then, nor does the greedy grad student who is suddenly interested in quantitative finance.
Good for introduction.......2007-01-10
This book introduced Symmetric Random Walk and then proved its properties before introducing Brownian Motion. More detailed proofs should be included in Ito integrals.
Shreve has done a tremendous job in communicating the concepts.......2006-10-31
Although I work in a major global bank at a senior level I don't use stochastic calculus in my job. My maths and physics background goes back to the 1970s when stochastic calculus was not part of undergraduate studies. Indeed, one usually did stochastic theory at postgraduate level. I have memories of reading Halmos for measure theory, Feller for probability theory, Wiener and others. None of this was easy.
Suffice it to say that there were a lot of abstract building blocks one had to erect first before one could actually do anything useful.
Stochastic calculus is not easy. It is less intuitive than ordinary calculus. The vast majority of textbooks launch into a wall of definitions that seem divorced from the motivation for them. I am always suspicious of authors who do that. It's fine if you are writing for a very specialised audience but I am with Richard Feynman who reckoned that if you can't provide a simple explanation you don't really understand what is going on. In that context read his PhD thesis - it is most readable and understandable.
What Shreve has done - and this is a significant achievement in my view - is to present something that is rigorous enough (and we all know that in this and other areas of mathematics one can go on and on with minute points of detail all in the name of rigour) yet grounds the concepts in something that is understandable.
The simple pedagogical fact of life with this type of material is that there is a large overhead in getting to a particular point and Shreve had done a very good job in getting readers to a good standard without destroying their will to go on!
When one looks at areas of mathematics with much longer pedigrees - and Fourier Theory is an example - there are some extremely good presentations of the theory at both mathematical and physical levels. Elias Stein, for instance, has done some marvellous work in the area. Stochastic calculus is really very young in terms of mainstream appeal. I can recall actuarial subjects I did in the early 1980s that had no stochastic calculus at all in them. All that has changed and I think Shreve's attempts in this area can be improved upon too but this will only happen over time.
My colleagues in quant like Shreve's books so I guess that says something too.
Very good graduate text book.......2006-06-23
This book makes no claims to be the mathematical bible on stochastic calculus and I believe that the author refers (in a blatant piece of marketing) to the other Shreve book with Karatzas, which trust me IS a very intractable read.
This is a good book and covers all the topics in a well rounded manner, he also has a very good little section in which he addresses his competitors, such as Steele etc etc,
IF you want a really ridiculous read and to show off to your mates then I recommend Musiela and Rutkowski, which I use to prop my door open in hot weather, this book has pretty much everything but is written in a very dense and inaccessible manner, you get nervous opening it, as you find something new you didn't know every time, I don't like abook to make me feel that dumb and its not really an sde book!!!!!!
In summary I am happy with my purchase of Shreve, many moons ago, I will use it again to teach an MSc course and the students will again complain that its too hard, until I give them a few refs and they will understand that you can't just waltz into the city and say I wanna be a quantitative analyst it takes hard work. Reading Shreve puts you on the right road and you can't say anything more highly than that.
As to the discussion by previous reviewers on the Ito-Doebin formula I suggest Karatzas and Shreve will answer you arguments.
Book Description
The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Customer Reviews:
Nicely Prepared Intermediate-Level Treatment.......2005-05-06
The author has put together an excellent text that will take readers of an elementary text like Hull's "Options, Futures and Other Derivatives" to the next level. In the author's treatment, the power of stochastic calculus is brought to bear on the options pricing problem from the point of view of modern martingale theory, if not the complete mathematical rigor needed to establish all the results.
The text contains 26 chapters and 3 appendices. There is simply too much here to give a blow-by-blow account. So I'll try to hit the highlights.
The author gives intuitive definitions of some of the more heavy concepts from measure theory/Lebesgue integration, measure-theoretic probability theory and basic stochastic analysis. For the rigor, one need only look to the appendices, but the treatment is intuitive enough that can still follow along with only the occasionally glance to the back of the book.
Readers of Hull's text will find the first couple of chapters quite familiar, but starting in Chapter 4, stochastic integrals are (somewhat) formally introduced, along with the multi-dimensional version of Ito's change of variable rule. This is not overkill as the development of multi-factor term structure models later in the book benefits from this early development.
We note that these formulas are stated without proof, although they are motivated intuitively.
In the next chapter, stochastic differential equations are introduced and the Feynman-Kac representation is established as a nice application of Ito's rule. The chapter winds up with an intuitive treatment of Kolmogorov's forward & backward equations.
For the remainder of the first half of the text, readers of Hull will feel themselves in quite familiar territory, as the author develops the solution for the options pricing problem, studies the Greek letters and establishes parity using the now classical approach.
The second half of the text delves into martingale methods for mathematical finance. As a consequence, the sophistication level jumps considerably. The reader is well-advised to get the basic analytical toolkit in hand before delving too far into the second half of the book. I recommend Rudin's "Real and Complex Analysis" 3rd edition.
Heavy machinery is pulled in from functional analysis to establish the first and second fundamental theorems of mathematical finance. Without some basic understanding of Hilbert and Banach space theory, the reader will understand very little of this treatment.
The next highlight is the Girsanov Theorem. The author actual provides a proof in the scalar case, and presents (without proof) the Novikov condition to test when the Girsanov transformation is indeed a martingale (so the theorem holds). As a nice application, the Black-Scholes theory is revisted and re-established via these martingale results.
Another highlight is the study of the Hamilton-Jacobi-Bellman model for stochastic control, along with a small catalogue of cases under which the HJB equations can be solved. As a nice application, Merton's mutual fund theorem is established.
The last several chapters of the book deal with martingale methods for term structure models. There is a nice survey and study of the 1-factor short rate models before loading up and doing the k-factor model framework of Heath-Jarrow-Morton.
The martingale setting makes for a very rigorous treatment.
The book ends with a really nice treatment of the Libor Market and Swap Market Models. Pure finance students may feel that the mathematics at the end unnecessarily overwhelms the intuition, but students of mathematical finance will appreciate the analytical treatment and may even feel inspired to implement their own LMM.
There are a ton of terrific exercises at the end of each chapter. The exercises really solidify the understanding of the presentation and they make great technical interview questions as well.
intuitive introduction to option pricing.......2004-11-10
I agree with several reviewers above that the book is written in a style very helpful for students to understand the material.
It doesn't contain a lot of small details of financial markets like Hull's book, but the approach is very systematic. The derivations of formula for Barrier options is a nice example, Hull only lists a set of formula. The focus is on the theory, not on the practice. (No numerical method in the book). Bjork's book is very valuable for a student with very good math skills but want to learn the reasoning style for option pricing. It is a quick and enjoyable read.
A huge plus side of the book is to describe strategy before writing down all the proofs. This helps greatly. It can be contrasted with Duffie's book "Dynamic Asset Pricing Theory", which is written like a dry math book (well, I have to admit that Duffie's book is not an intro book)
Only thing I can think of that can be improved is typo in the book, too many wrong formula, especially in the second half of the book, luckily enough, they are obviously wrong so that one can still understand the topics. I also find that using SEK and mentioning street name of Britain are amusing for a student in U.S.
Hell, I should have rated it 5 stars!.......2002-05-26
If you're going to be introduced to Derivatives pricing and Quantitative finance in continuous time, you need some basics in probability theory, an elementary introduction to stochastic calculus and you need "bjork". It tells you the equation and how to understand it.
It's the best source for a complete understanding of the basics of arbitrage free pricing in continuous time; whether it's in complete or incomplete markets.
The best feature of this book is how the author invariably provides an "intuitive interpretation or explanation" to convey critical concepts. {Things like market price of risk in the context of interest rate modelling, change of measure etc...}
Why I rated the book 4 instead of 5?
I will not forgive "Tomas bjork" not to have covered the Libor Market Model; it's "THE" model and therefore should be covered in great details by any book of this calibre. A new edition of this book with the libor market model is needed.
Having said that, the coverage he gives to the popular short rate models is worth every read!
Guy,
Msc Financial Engineering at ISMA Center, Reading - UK.
Good introductory book.......2002-05-25
It is a good book to read as an introduction to the field. The author is successful in conveying the intuition behind the models instead of striving for complete mathematical rigor. I recommend this book if you want to quickly get acquainted with derivatives pricing but are a bit afraid of the higher math seen in other books.
An FE Bible.......2001-11-08
The central text for IOE 552(financial Engineering I) at the University of Michigan. Halfway through the course and I really understand the application of Ito's Lemma and the Feynman-Kac stochastic representation theorem. This book has just the right mixture of narative story telling, and mathematical rigor. The derivations are accessible to those with a semester of advanced calculus and a semester of probability. Over and over, Bjork shows that the secret of success in Financial Engineering is "RAIL" which stands for the "Relentless Application of Ito's Lemma".
Book Description
Based on his extensive experience Sandras reveals a complete procedure for successfully managing all of the challenges and possible obstacles in an actual implementation. Organizing the implementation team, developing a working Kanban system, restructuring the shop floor, creating efficient connections between suppliers and customers, measuring performance and integrating JIT with TQM are among the issues discussed.
Customer Reviews:
waste of money.......2005-08-24
Don't buy this book. The book doesn't have any new insights. I found the book very useless.
A great introduction to JIT world.......2000-08-02
This is a great introduction to JIT. It covers main issues as the core knowlodge of this technique as well as the implementation cornerstones. It's an easy to read way to get a handle on this planning and production control. It has also tried to get a compromise with MRP without forgeting currently popular topics as the link to suppliers and customers. As a plus, there are some chapters for problem solving using quality control techniques as storyboards which are actually useful in many others environments and areas.
The book is an excellent guide to JIT implementation........1999-05-25
Just-In-Time:Making It Happen can be an invaluable guide to implementing JIT principles in the manufacturing environment. Although it is not a cookbook, it does provide a comprehensive step-by-step to understanding and implementing a workable JIT process. Perhaps the most valuable contribution of the book is the way it demonstrates that JIT processes can coexist with MRP effectively. Sandras defines those functions that need to be incorporated in the MRP System to most effectively interface with and support JIT. However, he also describes how the MRP System can be manually augmented to allow their coexistence. But what I liked best was the practitioner's understanding of the problems facing the JIT implementer.
Good, mostly based on real life experiences.......1999-01-23
Gives a very good insight into JIT, making you aware of the zillion things manufacturing companies can (still!!) do to avoid waste. The book, however, does not prepare you for actual implementation. For that to happen, there is nothing to replace being an 'insider' in the manufacturing environment.
Book Description
Most of the current books on stochastic control theory are written for students in mathematics or finance. This introduction is designed, however, for those interested in the relevance and applications of the theory's mathematical principles to economics. Therefore, mathematical methods are discussed intuitively and illustrated with economic examples. More importantly, mathematical concepts are introduced in language and terminology familiar to graduate students in economics.
Customer Reviews:
A good book that brings out the economic intuition.......2007-07-31
This is a nice book for optimization in continuous time. I see why somebody could be frustrated with lack of "Proof", however a book with hard-core proofs can miss the forest for the trees. This book strikes a good balance. The author is helpful in admitting where the proof is a mere outline and provides detailed references on where to look. The style of the book is very clear. I will recommend it very highly to economics and finance PhD students. The author provides nuggets of intuition which are very valuable.
The book is different from Shreve's book, which picks the examples from finance and serves a different purpose.
Perfect tradeoff between intuition and rigor.......2006-04-11
This book covers the theory and application of dynamic programming in continuous time. It is the perfect mix of intuition and rigor, for someone who is working on applications of stochastic control. It explains enough theory and methods to get you going...
Great for macro in continuous time.......2005-10-03
This book is very well written, the most prestine text about this subject I have ever laid eyes on. The best thing about this book is its focus on macroeconomics, books on this subject are normally focused on finance. I recommend this book for those who want to study macro in continuous time under uncertainty.
lack of precision.......2005-05-19
When you would like to learn the basic issues of stochastic optimization in continuous time, and you are rather unfamiliar with probability theory, then this book is a bad choice. The treatment is far less rigorous then promised by the praise at the back cover of the book. The proofs are often not that rigorous to deserve the name of proof. As in so many books the author invokes the so-called principle of optimality, suggesting that it is an eternal truth. As a heuristic principle this is fine, it is only a theorem, when properly phrased, under certain conditions, see for instance the works of Bertsekas. Furtheron the notation is now and then misleading.
It is quite well possible, that in the hands of a good teacher this is a valuable book, but someone, who would like to learn the trade on her own, by using this book, is strongly advised not to do so, and instead start with a mathematically sound introduction to stochastic processes. Someone, who would like to have a good intro in the context of finance is strongly advised to consult the two latest books by Shreve. These books are in my view exemplary for a thorough introduction to stochastic processes in an applied context.
Book Description
Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual financial choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance. For this revised edition a new section on managing university endowments has been added. The book begins with a foreword by Paul Samuelson.
Customer Reviews:
Collection of past papers.......2000-02-26
This book is a collection of thier(most of the parts are Merton's) papers written during the past 25 years. The papers are little bit changed so as to be cross-referenced through the book. Also You can find some comments in the book for the recent literatures. As you know, Dr. Merton introduced continuous-time approaches into the finance. This book deals with basic mathematics for the continuous time finance, portfolio selection, option pricing, and theory of intertemporal equilibrium. The value of this book is greater than that of papers copied separately in the library. Also it is a great pleasure to see how his theory has been evolved through the book.
The bible of continuous time approach to financial theory.......1999-10-08
I think the Nobel Prize was not enough to thank Professor Merton for his thought. The absolute and necessary book to approach continuous time Finance.
Average customer rating:
- Reinvention of Published Work
|
Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance (Springer Finance)
Alexandre Ziegler
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
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Book Description
This book considers the impact of incomplete information and heterogeneous beliefs on investor's optimal portfolio and consumption behavior and equilibrium asset prices. After a brief review of the existing incomplete information literature, the effect of incomplete information on investors' exptected utility, risky asset prices, and interest rates is described. It is demonstrated that increasing the quality of investors' information need not increase their expected utility and the prices of risky assets. The impact of heterogeneous beliefs on investors' portfolio and consumption behavior and equilibrium asset prices is shown to be non-trivial. Heterogeneous beliefs can explain a number of observed phenomena, such as the fact that equilibrium state-price densities are not log-normal, the "smile" in option implied volatility, and the patterns of implied risk aversion reported recently in the literature. It is also demonstrated that financial markets in general do not aggregate information efficiently, a fact that can explain the equity premium puzzle.
Customer Reviews:
Reinvention of Published Work.......2004-01-13
The book has deficiencies that I am sorry to report in the following.
The book is about heterogeneous beliefs. Therefore, a discussion of the
relevant literature would have been appropriate. Unfortunately, the au-
thor does not mention important contributions. I highlight a few omissions.
Mordecai Kurz and his coauthors (1997) have developed a fascinating theory
of heterogeneous, yet rational beliefs. This approach should be part of a
book about the economic implications of heterogeneous beliefs. Stochastic
volatility, to mention just one point that plays also a role in Ziegler's book,
has been shown to arise endogenously in the literature on rational beliefs.
Another approach to heterogeneous beliefs is provided by the recent liter-
ature on 'ambiguity', see Gilboa and Schmeidler (1989), Dow and Werlang
(1992), Epstein and Chen (2002). There, agents are uncertain or ambiguous
about the exact distribution of asset returns. Therefore, they use a whole
class of possible priors and maximize the expected utility under the worst be-
lief. The home bias puzzle, e.g., can be explained by ambiguity, see Epstein
and Miao (2003). Both Kurz's approach as well as the ambiguity literature
have the advantage of having a sound decision theoretic foundation whereas
the assumption of heterogeneous priors is somewhat ad hoc.
Chapter 2 of Ziegler's book has been published before { but not by the
author. In fact, it is the sad reviewer who has published not only that chap-
ter (Riedel (2000a)) but related work earlier(Riedel (2000b), Riedel (2001)).
Parts of Chapter 5 are easy corollaries to Chapter 1 in Riedel (2000b). Un-
fortunately, Ziegler has not read these contributions.
References
Detemple, J. (1986): Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, 41, 383-391.
Detemple, J., and R. Kihlstrom (1987): Acquisition d'Information
dans un Modle Intertemporel en Temps Continu," L'Actualite Economique,
63, 118-137.
Dothan, M. U., and D. Feldman (1986): Equilibrium Interest Rates
and Multiperiod Bonds in a Production-Exchange Economy," Journal of
Finance, 41, 369-382.
Dow, J., and S. Werlang (1992): Uncertainty Aversion, Risk Aversion,
and the Optimal Choice of Portfolio," Econometrica, 60(1), 197-204.
Epstein, L., and Z. Chen (2002): Ambiguity, Risk and Asset returns in
Continuous Time," Econometrica, 70, 14031443.
3
Epstein, L., and J. Miao (2003): A Two-Person dynamic Equilibrium
under Ambiguity," Journal of Economic Dynamics and Control, 27, 1253-
1288.
Gilboa, I., and D. Schmeidler (1989): Maxmin Expected Utility with
Non-Unique Prior," Journal of Mathematical Economics, 18, 141{153.
Kurz, M. (ed.) (1997): Endogenous Economic Fluctuations: Studies in the
Theory of Rational Beliefsvol. 6 of Springer Series in Economic Theory,
Heidelberg, New York. Springer.
Riedel, F. (2000a): Decreasing Yield Curves in a Model with an Unknown
Constant Growth Rate," European Finance Review, 4, 51-67.
(2000b): Imperfect Information and Investor Heterogeneity in the
Bond Market. Physica, Heidelberg.
(2001): Existence of Arrow{Radner Equilibrium with Endoge-
nously Complete Markets under Incomplete Information," Journal of Economic Theory, 97, 109-122.
Average customer rating:
- A good cookbook for the maths of derivatives
|
Finance in Continuous Time: A Primer
David C. Shimko
Manufacturer: Blackwell Pub
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The Little SAS Book: A Primer, Third Edition
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Introduction to the Mathematics of Financial Derivatives
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Asset Pricing: (Revised)
ASIN: 1878975072 |
Customer Reviews:
A good cookbook for the maths of derivatives.......2000-04-16
This thin book explain modern finance methods in a concise way, and is useful for both financial and real investment applications. The book is divided into four chapters, with lots of exercises at the ending of each chapter. In contrast with most other texts, this one frequently uses Laplace transformations to solve the differential equations (used also in Cox & Miller, 1965, a book about stochastic processes).
The first chapter is an overview of stochastic processes (arithmetic and geometric Brownian, mean-reversion, jump process), stochastic tools (Ito Lemma), and correlations between two stochastic process (see the table at p.16, for a summary of multiplication for differential variables).
In the second chapter, the frequently occurring differential equations is presented, which has the same general format in financial derivatives problems, and also important questions such as the homogeneity of these equations, the discount rate for the assets (showing that the solution is of the same form in risk-averse and risk-neutral economies), and an introduction of recursive techniques in asset valuation is also presented.
The third chapter explain the arbitrage principle with applications for asset valuation. European and American options are analysed, and the "smooth pasting" (or "high contact") optimal condition is presented for the American one.
The last chapter deals with optimal as a maximation of present values, first with the time-homogeneous problem (a infinitely lived asset or project), followed by extensions: the multiple state variables case, and the time non-homogeneous case. Closing the book is presented some aspects of the classic Merton (1971) optmization problem for comsuption and portfolio rules.
In short a good "cookbook" for the experts on financial and real derivatives, and a complementary literature for introductory courses on financial derivatives.
Average customer rating:
- Compact And a little profound
|
Stochastic Volatility in Financial Markets: Crossing the Bridge to Continuous Time (Dynamic Modeling and Econometrics in Economics and Finance)
Antonio Mele , and
Fabio Fornari
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 0792378423 |
Book Description
Stochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurrence of sudden and persistent changes of financial markets volatility. This phenomenon, technically termed `stochastic volatility', or `conditional heteroskedasticity', has been well known for at least 20 years; in this part, further, useful theoretical properties of conditionally heteroskedastic models are uncovered. The second part goes beyond the statistical aspects of stochastic volatility models: it constructs and uses new fully articulated, theoretically-sounded financial asset pricing models that allow for the presence of conditional heteroskedasticity. The third part shows how the inclusion of the statistical aspects of stochastic volatility in a rigorous economic scheme can be faced from an empirical standpoint.
Customer Reviews:
Compact And a little profound.......2001-06-09
Just as the title, it is a compact book and not so easy to read. It is a technic book for us to understand how to measure the volitility in the financial market.It takes me a lot of time to read this one.I think it would be better for people to know a little stochastic calculus at first and then try to read it.... It is a good book I think and suits for the one who wants to know the topic more deeply.
Average customer rating:
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Financial Markets in Continuous Time
Rose-Anne Dana , and
Monique Jeanblanc
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ASIN: 3540434038 |
Book Description
In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.
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