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Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)

Average customer rating:

Great, easy to understand introduction to mathematical finance
Pre-digested chicken soup for the "aspiring quant"
Good for introduction
Shreve has done a tremendous job in communicating the concepts
Very good graduate text book

Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
Steven E. Shreve
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387401016

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.

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