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Stochastic Calculus for Finance: Continuous Time Mode

Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
By Steven E. Shreve
* Publisher: Springer
* Number Of Pages: 550
* Publication Date: 2008-04-25
* ISBN-10 / ASIN: 0387401016
* ISBN-13 / EAN: 9780387401010
* Binding: Hardcover
Product 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.
Summary: Good and rigourous intro to financial maths
Rating: 5
This is definitely one of the best introductory books on financial mathematics. The book starts to make sense after a summer course in discrete-time martingale course (using william’s blue book). Shreve’s book gives a general introduction to Brownian motion and Ito stochastic calculus. At the same time, he shows how to apply these theoreis into financial maths, equity or interest rate etc. If you want to learn financial mathematics at a relatively more rigourous level (yet still not too difficult), this is the book to read. If you want intuition and implementation, I strongly recommend Mark Joshi’s concepts and practice of mathematical finance.
Summary: excellent book on quantitative finance
Rating: 5
Nicely written. Shreve is the one of the best authors in mathematical writings(another one I like is milnor). Worth buying one.
Summary: The definitive word
Rating: 5
This is the most fundamental word in mathematical finance. Those with a background in math will benefit most: ordinary differential equations, probability theory, statistics and multivariable calculus prerequisites. This is a very mathematical approach. Don’t look to it for computational implementations of the financial models it covers. But for the mathematical foundations of the models, this is THE book.
Summary: Great, easy to understand introduction to mathematical finance
Rating: 5
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. Unlike 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.
Summary: Pre-digested chicken soup for the "aspiring quant"
Rating: 5
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

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