I view this text as a complete outline or guide to the mathematics and ideas of financial calculus and derivative pricing.This is not meant disparagingly. The progression of concepts is clearly explained which is what the authors purport to do. Though discrete processes are discussed involving for instance binomial coefficients (combinations) in the beginning as examples, the real meat of the subject lies in probability applied to continuous processes. Hence knowledge of measure theoretic probability and martingales is required to rigorously complete the arguments. Brownian motion is used to model market fluctuation which stems from ideas of Bachelier. This motion has a Gaussian distribution as discovered by the eclectic genius of Einstein who had the insight to apply the heat equation in his solution. It models noise for instance in electrical engineering. Any differential equation containing this distribution term is referred to as a stochastic differential equation. A solution of...
Okay this is an intro, but you should have at least an understanding of Calculus. The purpose of this book is not to teach the fundamentals of the math, it teachs the financial pricing theorems, how they are applied to various assets and derivitives, and how to apply it to larger models.
The authors provide a very clear foundation of both discrete and continous processes. From Binomial to Brownian motion, this book packs in alot of material.
In the later chapters the authors cover the various derivative and asset pricing models, which really puts everything together in a context which will show you how to apply everything.
There is clear instruction for the novice in finance.
The only real issue I have with this book is that it does cover alot, but is not everything you will ever need to know. But it is a great intro which will enable you to move onto the advanced books on the subject.
Baxter/Renie's book makes it easier to understand Shreve's texts on stochastic calculus (vol.1,2). In particular, ch 2 (discrete) & ch. 3 (continuous) gives nice and simple descriptions of the essential concepts: filtration, measure, numeraire, drift, Ito formula. (These concepts can be difficult without a more detailed description of a stochastic process). The chapters 4,5,6 can be considered applying the concepts to SDE's in a number of cases, say, forex., equities, interest rates and multi-dimensional problems. These applications provide a good grasp of the mechanics to better understand the more detailed description of the same concepts in Shreve's texts.
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