Stochastic Calculus for Finance I: The Binomial Asset Pricing Model

by Steven E. Shreve

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

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

202 pages, Paperback

First published April 21, 2004

Reviews

[Stuart Baumann · Rating 5 out of 5]

These books are a great introduction to financial theory. They is very readable (which is unusual for a maths book) and focuses on intuition rather than focusing on the most general theorems or the shortest proofs. I found them much easier to read than other books on the topic such as that by Oksendal.

In terms of coverage there are two things to note. The first is that there are two general approaches to asset pricing. The most theoretical rigorous way is to make a model something like the Capital Asset Pricing Model (CAPM). This links the value of an asset to the concave utility function of a consumer. Risky assets are of less value than a riskfree assets due to Jensen's Inequality.
For an example consider an asset that will give you $0 with 50% probability and $1 billion dollars with 50% probability. Consider an alternative asset that gives you 500 million with 100% probability. Clearly the second asset will be of greater value because the utility of having 500 million dollars is nearly as much as the utility from having a billion dollars and is much much greater than t he utility of having no money. Thus the expected utility from owning the first asset is lower than the expected utility from owning the second.

The second approach is not as theoretically rigorous but is simpler and has been more accurate in some settings. We find risk-free probabilities which are the hypothetical probability of a payoff that a trader would factor into pricing the asset (with risk aversion built in). For instance the first asset above pays off with 50% probability but we may have a risk free probability where the asset pays off with probability 45%. This does not mean that the asset will pay off at 45% probability (it will pay off with 50% probability!) but it means that a trader with linear utility will act as though it will. In this way we can deal with traders with linear utility functions with (fictional) risk-free probabilities rather than true probabilities with concave utility functions. These books focus on this second approach with no more than a few pages on the first approach.

The second thing to note is that while both Shreve books are called "stochastic calculus for finance" the first book does not really deal with calculus and instead focuses on discrete time assets with binary payoffs. This is a good feature as it allows you to learn the financial theory without the complexities of stochastic calculus getting in the way. The second book is in fact the only book that actually deals with stochastic calculus however. This is a good approach and I would recommend learning this area by first reading the first book to get an overview of basic risk-free probability no-arbitrage financial theory before reading the second book which expands the analysis to account for assets in continuous time.

[Ahmed Bounadar · Rating 5 out of 5]

A masterpiece for anyone serious about quantitative finance. Shreve builds the entire framework of asset pricing from the ground up using the binomial model.
An essential first step before tackling Volume II and the continuous-time world, which I'm currently reading... Stay tuned for my review.

[Gabriel Tan · Rating 5 out of 5]

Throughout my current journey toward a Master's in Quantitative Finance, I have found this resource to be an excellent tool. In my opinion, the exercises are far more challenging than those typically assigned in class, but they are well worth the effort.

I also note that Shreve’s second book is especially useful for a Master’s in Quantitative Finance because of its focus on continuous-time models. It has more practical applications compared to discrete-time mathematics, which is largely theoretical, whereas continuous-time mathematics proves more valuable in practice. (or so i've been told)

[Calvin · Rating 3 out of 5]

This was the textbook I used to supplement my financial derivatives course this semester, it's quite meh, not a big fan of how it is written e.g., in terms of how it references equations excessively making the book hard to follow, and the notation used makes it needlessly annoying to go through.

[Medhat ullah · Rating 3 out of 5]

computational consideration ;P

[Denis Kuznetsov · Rating 5 out of 5]

It's one of the best books of its kind – very rigorous yet quite friendly

[Chico · Rating 5 out of 5]

Cum laude

[Szymon Woźniak · Rating 5 out of 5]

Good introduction to stochastic calculus in a discrete time setting. Much more accessible than most of the books on this topic.

[Sebestyén Máté Attila · Rating 5 out of 5]

The single clearest, most intuitive and most well motivated textbook on sctochastic finance there is.