Stochastic Calculus for Finance II:
Continuous-Time Models (Springer
Finance) (v. 2) by Steven E. Shreve
Great, Easy To Understand Introduction To Mathematical Finance
Stochastic Calculus for Finance evolved from the first ten years of the
Carnegie Mellon Professional Masters 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 stochastic 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 stochastic 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.
Personal Review: Stochastic Calculus for Finance II:
Continuous-Time Models (Springer Finance) (v. 2) by Steven E.
Shreve
As one of my Math professors put it, "a mathematician will never ever
dream of coming up with Black-Scholes formula". The key here is to
understand why Fischer Black and Myron Scholes were forced to make the
kind of assumptions they have made to price an option contract. The
adapted processes, the sigma algebras and several such seemingly
abstract concepts are hard to understand or even teach in one or two
semesters. It seems the accepted pedagogical approach in teaching this
subject has been to skim the surface and focus on the senseless
derivation and application of this now infamous formula. You were told that
somehow (magically) Black-Scholes works. You were also told to take
many things on faith. But for those you who are not willing to surrender that
easily, Steven Shreve can be your savior. The author meticulously proved
everything. He explains (in amazingly concise format), the most basic
ingredients of continuous time finance. There is undoubtedly a
philosophical bent to the whole approach and that becomes apparent as
you read the book.
The best part is that you could start almost anywhere and work your way
backwards through easily navigable theorems and definitions. The notation
is straightforward; however it does take some time to get used to.
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