Despite its title,
this is an introductory financial engineering text. The author is a math
professor who, with this book, makes financial engineering concepts accessible
to readers with a strong background in basic calculus and probability theory but
with little other background in math. In this respect, the book competes with
the likes of Baxter and Rennie (1996),
Chriss (1997), Neftci (2000)
and Joshi (2003). Before I describe the
book itself, let me position the book relative to this competition.
Baxter and Rennie
(1996) and Neftci (2000)
discuss a lot of sophisticated concepts, but they are "hand waving" treatments.
You can't implement what they teach you. Neither builds a foundation for further
study. Chriss (1997) is less
ambitious about the concepts he covers, but he does an excellent job of
explaining the mathematics he does use. He builds a foundation for further
study. Joshi (2003) falls between these
two extremes.
Roman's book is in
the tradition of Chriss. Of the two, his is the more up to date book, since
Chriss was written just when the fundamental theorem of asset pricing was being
developed. Chriss focuses more on finance. Roman focuses more on mathematics.
What Roman does is
develop the theory of asset pricing, first in discrete time and then in
continuous time. Intermingled with the financial engineering chapters are
chapters on probability theory. As a mathematician, he does an excellent job of
getting the reader's understanding of probability to the "next level,"
explaining concepts such as partitions, sigma algebras, conditional
expectations, filtrations, etc. He mentions stochastic calculus but does little
with it. It is quite impressive how he develops continuous time pricing theory
largely without it.
Contents
1. Probability I
2. Portfolio management and the capital asset pricing model
3. Background on options
4. An aperitif on arbitrage
5. Probability II : more discrete probability
6. Discrete-time pricing models
7. The Cox-Ross-Rubinstein model
8. Probability III : continuous probability
9. The Black-Scholes option pricing formula
10. Optimal stopping and American options
Only one of the
book's chapters is not on probability theory or financial engineering. This is a
somewhat quixotic second chapter that looks at portfolio theory. The author approaches the
topic from a purely mathematical standpoint, deriving some interesting results. For example, he derives for us the exact shape of Markowitz's efficient frontier in return-volatility space. In case you are
wondering, it is not a parabola. The author uses some non-standard terminology
and changes definitions to suit the discourse. For example, he defines the
market portfolio as Tobin's super-efficient portfolio. Historically, Sharpe
actually derived the conclusion that the super efficient portfolio must be the
market portfolio. For someone who really knows portfolio theory well, this is a
nice chapter to glean a mathematician's insights into aspects of the subject.
Others may want to skip it and head straight for the financial engineering.
In summary,
despite its modest idiosyncrasies, this is an excellent introduction to
financial engineering. For quantitative professionals who want to understand
financial engineering theory, it is excellent. The treatment is quite abstract,
so some general familiarity with financial instruments and financial engineering
will be invaluable. Other than that, if you are comfortable with elementary
calculus and probability, you will find this an excellent and highly accessible
text. It definitely builds a foundation for further study.
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