Steven Shreve is a
mathematics professor at Carnegie-Mellon University who has a reputation for
co-authoring impenetrable texts on stochastic calculus and financial engineering.
This independent effort is his most penetrable to date, so it may be worth checking out. The
book is the first in a two-volume introduction to financial engineering that is
based on courses offered at Carnegie-Mellon. Volume I develops concepts in
discrete time. Volume II is longer and does so in continuous time. You don't
need to read Volume I in order to read Volume II. The two book are independent.
However, one purpose of Volume I is to familiarize readers with important
concepts before they progress to a more technical continuous-time treatment.
Volume I starts
off considering a single-time step binomial tree and uses is to develop
replicating portfolios and the notion of risk neutral probabilities. It then
extends the discussion to multiple time steps, which permits the pricing of path
dependent instruments and leads naturally to the notion of dynamic replication.
This is a familiar approach to developing concepts. It is employed in other
financial engineering books. Later chapters discuss random walks, stochastic
interest rates and other topics. The entire book assumes complete markets, but
it does acknowledge the challenges posed by incomplete markets in the context of
a nice capital asset pricing model (CAPM) application.
I like several
things about Shreve's treatment. It is mathematically elegant. He has a depth
of knowledge that other authors cannot match, and this shines through clearly in
these pages. Without getting bogged down along the way, Shreve points out
insights and important generalizations that other books never pick up on.
Reading this book is going to leave you hungry for more. Finally, Shreve chooses
his words carefully. In many elementary texts, you will find authors saying
things that aren't exactly true or are otherwise unfortunate. This never happens
with Shreve. His writing is accessible but impeccably precise.
Contents
1. The Binomial No-Arbitrage Pricing
Model
2. Probability Theory on Coin-Toss
Space
3. State Prices
4. American Derivative Securities
5. Random Walk
6. Interest Rate
Dependent Assets
The book is not
for everyone. It is elementary, but it is also mathematically rigorous. Shreve
is a mathematician, and he develops arguments through formulas. To benefit from
his book, you will have to slow down and decipher what the formulas are telling
you. There are wonderful exercises at the end of each chapter. Readers who take
the time to do them will benefit enormously. Readers who can't be bothered
should probably read a more informal text. The author promises that the book can
be read by anyone with knowledge of calculus and calculus-based probability, and
for the most part he delivers on that promise. However, I do feel that this book
should be read only by readers who have some familiarity with financial
engineering or derivatives markets. Some exposure to more advanced mathematics
will also be useful. For example, Shreve assumes familiarity with the method of proof
by induction in one derivation. This is a concept that is not generally covered
in introductory calculus or probability courses.
For readers who want to master the mathematics of
financial engineering, I highly recommend this book. It is not an end in itself,
but as the author intends, it builds a firm foundation from which to advance to
continuous time finance. It is a short book, so you can get through it in a few
weeks. For some readers, proceeding to Volume II will then be a logical next
step.
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