data does not start until 1996 and b) I wanted to relate the real world default rates to
Table 19.1. I stopped collecting credit spreads at the start of the credit crisis. If the crisis
period had been included for the risk-neutral default rate estimates, the difference between
real world and risk-neutral default probabilities would have been much greater. Table 19.4
has been included in the fourth edition to help students see how calculations have been
done.
Some instructors may wish to use the material in Sections 7.7 and 7.8 when covering
this chapter.
This chapter incorporates material on credit default swaps. It also explains asset
swap spreads which are used by the market to calculate credit spreads relative to the
LIBOR/swap curve. The typical asset swap is a deal where the coupon on a bond is
exchanged for LIBOR plus a spread and the coupon is paid regardless of whether the bond
defaults. The present value of the asset swap spread provides a convenient quick estimate
of the present value of losses on the underlying bond. (See Problem 19.16 for a proof of
this.) Equation (19.3) is a widely used way of converting a credit spread to an average
hazard rate. Some instructors will also wish to go through the more exact calculation given
after this equation is introduced. I usually skip it.
Any of the Problems 19.23, 19.24 and 19.25 can be used as assignment questions.
Chapter 20: CVA and DVA
This chapter contains some of the same material as Chapter 17 or the third edition,
but the presentation of the material has been improved. The material on bilateral and
central clearing has been moved to the new Chapter 18 of the fourth edition.
The chapter first explains how the exposure on a derivatives portfolio with a particular
counterparty is calculated. If Vis the value of the portfolio with the counterparty and
no collateral is posted the exposure at any given time (i.e., the maximum amount that
can be lost) is max(V, 0). When collateral is posted, the calculation of the exposure at a
time is more complicated because it depends on the collateral available at the time. The
calculations must take account of the fact that the counterparty is likely to have stopped
posting collateral a number of days before defaulting.
Calculating CVA involves a) dividing the life of the derivatives portfolio into a number
of time steps b) carrying out a Monte Carlo simulation to calculate the expected exposure
at the mid point of each time step and c) using credit spreads to calculate the probability
of default during each time step. The CVA is
X
i
(1 −R)qivi
where Ris the recovery rate, qiis the probability of default during the ith time and viis
the present value of the expected exposure at the mid point of the ith time step.
The chapter discusses how the impact of a new transaction can be calculated, how
CVA risk is calculated for Basel III, and issues concerning wrong-way/right-way risk. It
also covers DVA (the mirror image of CVA).
The chapter concludes with some simple examples where it is not necessary to use
Monte Carlo simulation to get results.
12
Problems 20.13 to 20.16 are possible assignment questions of varying difficulty.
Chapter 21: Credit Value at Risk
This chapter is a update to Chapter 18 of the third edition. The chapter starts by
explaining what rating transitions matrices are and how they can be manipulated. (The
manipulation of credit transition matrices is explained in Appendix J and software for doing
it is provided on my web site.) It then discusses three different approaches for calculating
VaR for the banking book. Vasicek’s model is the one used by regulators. Credit Risk
Plus corresponds to an approach widely used by the insurance industry . Creditmetrics
is most commonly used by banks when they calculate economic capital. More details on
both credit risk plus and creditmetrics are given in the fourth edition.
The chapter then moves on to calculate credit VaR for items in the trading book. In
particular it discusses how the specific risk charge and the incremental risk charge can be
computed.
Any of the three further questions can be used as assignments.
Chapter 22: Scenario Analysis and Stress Testing
This chapter is an update to Chapter 19 of the third edition. More material has been
included on regulatory stress testing. Stress testing has clearly become a more important
topic as a result of the credit crisis. The chapter discusses a) how the scenarios are
generated, b) how the scenarios are evaluated, and c) how the results should be used. It
emphasizes the importance of senior management involvement in the generation of the
scenarios. It also makes the point that the evaluation of the scenarios is not a mechanistic
exercise because the market’s reaction to the scenario and the consequences of that reaction
need to be considered. The technique of reverse stress testing is explained and Berkowitz’s
procedure for integrating VaR with stress testing is outlined.
Problems 22.10 and 22.11 can be used as assignment questions. 22.10 requires an
understanding of the DerivaGem Applications Builder.
Chapter 23: Operational Risk
This chapter is an update to Chapter 20 of the third edition. With the advent of
Basel II, there has been a big increase in the resources devoted to measuring operational
risk at banks and other financial institutions. The estimation of operational risk is less
quantitative than the estimation of other risks. The different approaches are outlined in
the chapter. I generally spend about 1.5 hours on the chapter.
By the end of a class based on the chapter students should understand a) the dis-
tinction between loss frequency and loss severity and how they are combined to calculate
a loss distribution, b) the ways in which internal and external data are used, c) the role
of scenario analysis, d) the importance of BEICFs, e) self assessment and f) the moral
hazard/adverse selection issues in insurance.
Problem 23.13 can be used for class discussion. Problems 23.12 and 23.14 are potential
hand-in assignments.
Chapter 24: Liquidity Risk
13