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Springer

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

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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 studentsand researchers in mathematical finance and financial engineering will find this book useful. Read more

Publisher ‏ : ‎ Springer; First Edition (June 3, 2004)


Language ‏ : ‎ English


Hardcover ‏ : ‎ 569 pages


ISBN-10 ‏ : ‎ 0387401016


ISBN-13 ‏ : ‎ 10


Item Weight ‏ : ‎ 4.76 pounds


Dimensions ‏ : ‎ 6.5 x 1.25 x 9.5 inches


Best Sellers Rank: #169,651 in Books (See Top 100 in Books) #15 in Stochastic Modeling #120 in Calculus (Books) #205 in Probability & Statistics (Books)


#15 in Stochastic Modeling:


#120 in Calculus (Books):


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Top Amazon Reviews

    • Clear explanations Throughout. 10/10
So after trying to learn this subject from other sources (Evans, Klebaner, and perhaps a couple of others I cannot recall) I have determined that this is probably the only actual textbook that makes this subject understandable. The subject IS hard, there is no way around that, but Shreve is a master at explaining and reiterating ideas when he thinks that the reader might need it. You're still gonna spend hours/days between a page or two, but there's always progress being made. Even if something feels "iffy" that's the worst that you'll feel. Nothing from this book will ever make you feel like you don't have ANY understanding. For instance, the introduction of the Lebesgue integral was actually very simple and understandable. Something that you'll probably get no where else. A lot of other authors place unrealistic expectations/prerequisites on the reader stating that "probability and calculus" is all that's required to read their book, while it would be near impossible for a student that ONLY has probability and calculus under their belt to understand the sophistication, notation, etc. (mathematical maturity is required to see something purely in mathematical terms and understand it). Shreve states that calculus and probability based calculus is all that's required to read this text, and I do not think probability is even required (although I heavily recommend it)! If you have taken any course on probability and statistics, it should be sufficient. If not then you should still be able to read the text. You may struggle some through the exercises though and if you're learning the material for fun then it doesn't matter anyways. If you do not have any previous knowledge of probability then I would recommend that you have a probability book near by for reference (There are many great probability books, Taboga is a great reference.) If you are weak mathematically or have not seen probability in a while (like I had not) then Mikosch is a great prerequisite to the subject. Mikosch has no exercises, is simple, straightforward and can even be read in a few days. Even if you do not read Mikosch, Shreve is great. For other texts on the subject I would say that Mikosch is mandatory reading. I 100% recommend this book to anyone trying to learn the subject, you will not regret it. Also there are no solutions in the text, but just do a quick search and you'll find several manuals online. This text is gold in the set of all Stochastic Calculus textbooks where most everything else is garbage. UPDATE: I have been reading Calin's text for months now and it might be better than this one if you are struggling/not mathematically inclined. If you are struggling, then I recommend that you have this book, Mikosch, and Calin. I frequently reference Shreve and Mikosch as I have made Calin's text my primary book on the subject. Good luck on your journey! ... show more
Reviewed in the United States on July 13, 2021 by MJ
    • Shreve has done a tremendous job in communicating the concepts
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. ... show more
Reviewed in the United States on October 31, 2006 by Peter Haggstrom
    • Easily the best quantitative finance book ever made.
Every time I tried any other finance literature, I end up realizing Shreve's book is the only one that tell you all the truth. After analyzing some other alternatives out there, one should wonder whether all this math are necessary or not. Hull's and Wilmott's books give you a good amount of intuition and honest rules in order to avoid the fundamental theory behind stochastic calculus. Kerry Back and Thomas Mikosch, on the other hand, do not fear showing the math, but instead they give much more insight about the pricing theory without proving the most technical results. Finally, Shreve's books will tell you everything you need to know in order to master stochastic calculus. It's clear, very well written and cover every tiny subtle aspect underlying the theory. The only issue is: This is a Math book that frequently remembers it's solving finance problems, but it never forgets it's doing serious math. So, in my opinion, if you have strong knowledge in calculus and a good amount in probability, you should definitely try Shreve's books. Depending on your math background, it will hurt more or less. It hurt me a lot reading this book, but it is like any classical literature. The more you read, more you understand. And if you don't love math, books like Hull's will give you enough for your finance works. ... show more
Reviewed in the United States on August 26, 2016 by Danilo Elias Castro

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