CDO were often only 1% wide. As the BBB tranches used to make ABS CDOs become
thinner, the tranches of ABS CDOs begin to look more and more similar to each other.
(See the two Business Snapshots in this chapter.) I like to get students to work this out
for themselves by asking leading questions.
Many of the points made in Section 6.5 will be returned to later in the course.
Problem 6.14 can be set as a (fairly straightforward) assignment question. Problem
6.15 can be discussed in class to illustrate the thin tranches point mentioned above.
Chapter 7: Valuation and Scenario Analysis: The Risk Neutral and Real World
This is a new chapter for the fourth edition. It covers some key theoretical ideas
relevant to risk management. The material is somewhat technical and some instructors
may wish skip the chapter covering the concepts when they are needed for later chapters.
The chapter explains using simple examples how a risk-neutral world is used for val-
uation while a real world is used for scenario analysis. It points out that sometimes risk
managers have to use both the real-world and risk-neutral world because a portfolio has
to be valued on the horizon date in a scenario analysis. It explains (without stochastic
calculus) the processes that can be assumed in a Monte Carlo simulation for asset prices
and interest rates, distinguishing between the drift and volatility. Girsanov’s theorem is
explained. The difference between the drift in real world and risk neutral processes is tied
back to the material in Chapter 1.
The last part of the chapter discusses how the risk-neutral valuation arguments work
when there are a number of discrete outcomes that can occur in the future. An important
example concerns the default/no-default outcomes in credit risk
The Further Questions contain straightforward examples that can be used as assign-
ment questions.
Chapter 8: How Traders Manage Their Risks
This material is similar to the material in Chapter 7 of the third edition. If students
are required to take a course on derivatives prior to the course based on this book relatively
little time needs to be spent on this chapter. But in other situations instructors may want
to spend two to three hours of classroom on the chapter.
The focus in the chapter is on a trader working for a financial institution. The trader
might have a position such as that shown in Table 8.1 and is faced with the problem of
hedging his or her exposures to changes in the price of the underlying asset, changes in its
volatility, and changes in interest rates. The Greek letters are measures of these exposures.
The chapter distinguishes between linear and non-linear products as far as delta is
concerned. A “hedge-and-forget” strategy can be used for linear products. Non-linear
products require the hedge position to be continually rebalanced. The way the rebalancing
works is illustrated in Table 8.2 and 8.3.
When discussing gamma I spend some time on Figure 8.4 to show the problem created
by non-linearity. I emphasize that changing the gamma or vega of a position requires a
trade in an option or similar derivative. Trading the underlying asset has no effect on these
Greek letters.
When teaching students about Greek letters I find it useful to show students some
output from DerivaGem. The mechanics of the calculation of the Greek letters is discussed
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