Stochastic Calculus Models for Finance II: Continuous Time Models

by Steven E. Shreve

Shastic 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 shastic 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 shastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.

Masters level students and researchers in mathematical finance and financial engineering will find this book useful.

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

Genres: Finance, Mathematics, Textbooks, Economics, Science, Business, Reference

569 pages, Hardcover

First published April 25, 2004

Reviews

[Gabriel Tan · Rating 5 out of 5]

I believe the greatest challenge for readers—especially those without a solid mathematical background—is the book’s dense mathematical content. Nevertheless, I thoroughly enjoyed the level of rigor in Shreve’s second volume, which, like the first, was highly recommended by my professor, who described stochastic calculus as the “bread and butter” of any quantitative finance professional.

Each chapter builds upon the previous one, covering what you’d expect from a comprehensive text on stochastic calculus, including martingale theory, the Black–Scholes framework, and Girsanov’s theorem. Similar to works by authors like Paolo Baldi, Shreve’s approach provides an in-depth exploration of these core topics.

I will certainly revisit this book, as I believe there is still more knowledge to extract from its pages.

[Daniel · Rating 5 out of 5]

Accessible and practical overview of modern stochastic finance: a deeper dive.

[Toivo Haapasaari · Rating 3 out of 5]

It’s alright, the book does what its supposed to but kind of fails to juggle both rigor and applications. I guess the books alright for the finance stuff and might be good for intuition.

Didn’t do the later chapters instead left for Protters stochastics book. Also studied some of Shreve’s other work with Karatzas namely Brownian mortion and Stochastic calculus which was in terms of rigor, very different.

The book might be a bit overhyped but it does what it promisses, I guess.

[Jing Ren · Rating 2 out of 5]

If not for the reason that there is no alternative, I really dislike the book. The author never says what he is doing before I have to go through a very long paragraph and figure it out myself. And he also seems to forget what he has written before. I particularly dislike the part solving stochastic PDE's when he is always like "This is the solution and now let's prove it is correct." even in the exercises. But there is no gain of conciseness. To me it seems he intentionally keeps things vague to avoid being criticized for lack of rigor.

[Joe Malicki · Rating 4 out of 5]

If I'm going to learn stochastic calculus this rigorously, I want more in-depth treatment of Ito's lemma and the like to know how much to believe it and what the proofs really depend on.

If you're not going to go full out, then why not just grab a quick primer on Ito's lemma without all the background?

(admittedly this book is probably better in that respect than just about any other finance-focused text I've seen, but still, what's the utility in the middle ground?)

[Austin · Rating 4 out of 5]

This is the best, most readable book on this topic (though make no mistake, it is still a graduate level mathematics text). The .pdf of Shreve's lecture notes that eventually became this book have had a loyal following on the net for years. This should be on every quant's shelf.

[Adam · Rating 5 out of 5]

The single book I have spent most time on. Steve Shreve is my professor of this course. He gives wonderful lectures. His understanding in math and finance helps a lot to understand the formulas of this book. His passion in teaching and skills in communication is truely inspiring.

[Peng Gao · Rating 3 out of 5]

Lacks depth once the author finishes borel algebras ;)) stochastic PDE is not developed in any way. Just remember Feynman-Kac and you are good to go lol