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Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
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"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM
Product details
Series: Springer Finance
Paperback: 550 pages
Publisher: Springer (December 1, 2010)
Language: English
ISBN-10: 144192311X
ISBN-13: 978-1441923110
Product Dimensions:
6.1 x 1.3 x 9.2 inches
Shipping Weight: 2.2 pounds (View shipping rates and policies)
Average Customer Review:
3.9 out of 5 stars
57 customer reviews
Amazon Best Sellers Rank:
#417,717 in Books (See Top 100 in Books)
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.
I have a lot of these 'introductory' books, and this one (and its companion Volume I), are by far the best set of introductory books to mathematical finance i have come across. It contains everything you need to get an entry level position as a quant - meaning that you will pass interview tests i if you understand the contents of this book, the portion of the test about stochastic calculus at least - provided you do all the exercises, and also are able to reproduce some of these proofs (eg the barrier option and lookback options analytical formulas in the exotic options chapter). If you want to make absolutely sure to pass the interview tests (again that section of the test focusing on stochastic calculus and derivative pricing), you could also buy Joshi's books, which are slightly more focused on the finance. [as an aside, interview tests are likely to contain more than just derivative pricing and stochastic calculus, you will need other books to cover these aspects]
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.
Being a lover of mathematics, I found this book very enjoyable to read. Stochastic calculus is pretty much what it says: deriving, integrating, etc. over processes that are stochastic ("random") instead of deterministic. You will be surprised about how many properties of stochastic processes you can nail down as a precise deterministic number.I haven't tried to make money off the ideas in this book, so I can't speak for whether that would work. However, keep in mind that it doesn't really have trading ideas per se but rather lays the foundation for some mathematical models which could be incorporated in such.
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