Stochastic Calculus and Financial Applications
Author: J. Michael Steele
List Price: $79.95
Our Price: Click to see the latest and low price
ISBN: 0387950168
Publisher: Springer Verlag (12 October, 2000)
Sales Rank: 71,592
Average Customer Rating: 3.93 out of 5
Customer Reviews
Rating: 5 out of 5
The book I wish I had 5 years ago!
Written in an unassuming and humorous style with practical examples and interesting excercises. If you want to learn Stochastic Calculus without forgetting why you wanted to learn it, this is the book. After wading through the books by Durrett, Oksendal and Revuz & Yor, I can say with confidence that for those whose first interest is finance, but who want to actually use Stochastic Calculus, this is the place to start. That is not to say that it is light on the mathematics side, but where possible the financial applications drive the discourse. From a mathematical standpoint, this book covers much of the same material as the delightful "Probability With Martingales", by David Williams. From among finance books I am familiar with, "Financial Calculus : An Introduction to Derivative Pricing" by Rennie & Baxter takes a similar, but less mathematical approach, however I find the explanations in this book more transparent and the excercises more relevant--In the end you will know much more about Stochastic Calculus if you choose Steele.
Rating: 4 out of 5
graduate course taught at Wharton
Mike Steele has used the material in this text to teach stochastic calculus to business students. The text presupposes knowledge of calculus and advanced probability. However the students are not expected to have had even a first course in stochastic processes. The book introduces the Ito calculus by first teaching about random walks and other discrete time processes. Steele uses a lecturing style and even brings in some humor and philosophy. He also presents results using more than one approach or proof. This can help the student get a deeper appreciation for the probabilitist concepts.The gambler's ruin problem is one of the first problems that Steele tackles and he uses recursive equations as his way to introduce it.
Brownian Motion, Skorohod embedding and other advanced mathematics is introduced and emphasized. After motivating the stochastic calculus and developing martingales Steele covers arbitrage and stochastic differential equations leading up to the fundamental Black-Scholes theory that is important in financial applications. It is not fair to criticize this book for lack of applicability. It is strickly intended to develop a firm theoretical background for the students that will prepare them for a deep understanding of financial models important in applications.
I am not enough of an expert in this area to know if Professor McCauley's criticism in another amazon review of this book is valid, but I do think he is a little too harsh in criticizing the ideology that Steele presents. The ideology is what makes Steele's lectures stimulating and interesting to the students.
Rating: 2 out of 5
I Hate It When Books Lie About Mathematical Requriements
The book says that its only prerequisites are calculus and probability. This is not true. To be able to understand everything that's going on, you'll need to have a very good grasp of subjects like measure-theoretic probability, Hilbert spaces, and functional analysis. I quit reading the book in the early chapters, when Steele starts talking about things like "spans" and "denseness" for function spaces. I don't know where you went to school, but at my school, I didn't learn these subjects in my intro calculus and probability classes. To summarize, don't buy this book if you don't know measure theory.If you want to learn quant finance at an elementary level, Baxter and Rennie is much, much better. Moreover, if you're comfortable with measure theory,and you want to learn the math that's necessary for option pricing, you'd be better off buying Oksendal's excellent book, which is at least as rigorous as Steele's book but much more clear.
Similar Products
Financial Calculus : An Introduction to Derivative Pricing
Options, Futures, and Other Derivatives (5th Edition)
Introduction to the Mathematics of Financial Derivatives
Elementary Stochastic Calculus With Finance in View
A Course in Financial Calculus
Book Index