Financial Derivatives
Pricing, Applications, and Mathematics
Authors Baz and
Chacko have written what they seem to think is an accessible introduction to
financial engineering. The book has many merits, but I don't agree that
accessibility is one of them. Claiming that readers need only basic familiarity with
calculus, probability and statistics, the authors dive right in with stochastic
calculus in the opening chapter. Granted, their discussion is not rigorous, but
this hardly makes it accessible. We have all, at some point in our school years,
taken lectures from professors who were brilliant but difficult to follow. That is what reading this book is like.
You can learn a lot, but it will require some work.
An opening chapter primarily introduces Ito's
lemma, first in discrete time, then in one-dimensional continuous time, and
finally in two-dimensional continuous time. There is no motivation for the
profound importance of Ito's lemma, so you better come to the book with some
sense of why financial engineers care about it. The chapter closes with three
"paradoxes" of finance. As with many similar books on financial engineering, the
authors do a poor job of communicating exactly what a stochastic differential
equation is. Authors of so many books seem to think that simply using stochastic
differential equations over and over will breed, well, familiarity.
The next chapter is excellent. The authors
introduce a variety of sophisticated concepts: marginal rate of substitution,
risk neutrality, pricing kernels, etc. They then apply these in three distinct
derivations of the Black-Scholes formula. These lead to a discussion of pricing
for some exotic options: digitals, Asians, etc. The chapter is dense and
cryptic, but it is very rewarding for any reader who invests the considerable
effort required to get through it. The authors have a habit of not
telling the reader where they are going with a discussion until after they have
gotten there ... so plan on reading and rereading a few times. I recommend
reading Chriss (1997), and perhaps
Baxter and Rennie (1996)
or Neftci (2000), before attempting
this chapter.
Contents
Introduction
1. Preliminary Mathematics
2. Principles of Financial Valuation
3. Interest Rate Models
4. Mathematics of Asset Pricing
At this point, the
book gets a bit schizophrenic, following up on the sophisticated chapter 2 with
an extraordinarily simple discussion of fixed income pricing concepts and
duration in Chapter 3. Chapter 3 then introduces a variety of fixed income
derivatives: Eurodollar futures, swaptions, caps and floors, etc. The book's sophistication
soon returns with a discussion of standard yield curve models: Vasicek, Ho and
Lee, HJM, etc.
The book's last
chapter returns to the topic of stochastic calculus and continuous time
financial modeling, developing concepts in
greater depth than in Chapter 1. Topics include Ito calculus, jump processes,
mean reversion, etc.
I have mixed
feelings about this book. Unlike so many non-rigorous introductions to financial
engineering, this one offers a lot of substance. On the other hand, it is a
chore to read. It should definitely not be the only book you read on financial
engineering. Read as a supplement to other books, I think this one offers
valuable insights and alternative ways of thinking about concepts.
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