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CHAPTER 13
Measurement of Interest-Rate Risk for ALM
What is in this Chapter?
Introduction
Gap Reports
Contractual-Maturity Gap Reports
Estimating Economic Capital based
on Gap Reports
Sophisticated interest-rate models
INTRODUCTION
The purposes of measuring ALM interestrate risk
establish the amount of economic capital to be
held against such risks
 How to reduce the risks by buying or selling
interest-rate-sensitive instruments

Although ALM risk is a form of market risk,
it cannot be effectively measured using the
trading- VaR framework
This VaR framework is inadequate for
two reasons.
First, the ALM cash flows are complex
functions of customer behavior.
 Second, interest-rate movements over
long time horizons are not well modeled
by the simple assumptions used for VaR.

INTRODUCTION
Banks use three alternative approaches to
measure ALM interest-rate risk, as listed
below:
Gap reports （缺口報告）
 Rate-shift scenarios
 Simulation methods similar to Monte Carlo
VaR

GAP REPORTS
The "gap“ is the difference between the cash
flows from assets and liabilities
Gap reports are useful because they are relatively
easy to create
This measure is only approximate because gap
reports do not include information on the way
customers exercise their implicit options in
different interest environments
There are three types of gap reports:



contractual maturity
repricing frequency
effective maturity
Contractual-Maturity Gap Reports
A contractual-maturity gap report indicates
when cash flows are contracted to be paid
for liabilities, it is the time when payments
would be due from the bank, assuming that
customers did not roll over their accounts.
For example, the contractual maturity for
checking accounts is zero because
customers have the right to withdraw their
funds immediately.
Contractual-Maturity Gap Reports
The contractual maturity for a portfolio of
three-month certificates of deposit would
(on average) be a ladder of equal payments
from zero to three months.
The contractual maturity for assets may or
may not include assumptions about
prepayments.
In the most simple reports, all payments are
assumed to occur on the last day of the
contract
Repricing Gap Reports
Repricing Gap Reports
 Repricing
refers to when and how the
interest payments will be reset
Effective-Maturity Gap Reports
Although the repricing report includes the
effect of interest-rate changes, it does not
include the effects of customer behavior.
This additional interest-rate risk is captured
by showing the effective maturity.
For example, the effective maturity for a
mortgage includes the expected
prepayments, and may include an
adjustment to approximate the risk arising
from the response of prepayments to
changes in interest rates.
Effective-Maturity Gap Reports
 Gap reports give an intuitive view of
the balance sheet, but they represent
the instruments as fixed cash flows,
and therefore do not allow any
analysis of the nonlinearity of the
value of the customers' options.
 To capture this nonlinear risk requires
approaches that allow cash flows to
change as a function of rates.
Estimating Economic Capital based on Gap
Reports
Estimating Economic Capital based on Gap
Reports
Estimating Economic Capital based on Gap
Reports
 For
this analysis, we made several
significant assumptions:
 We assumed that value changes
linearly with rate changes
We also assumed that the duration
would be constant over the whole
year
Estimating Economic Capital based on Gap
Reports
 Finally,
we assumed that annual rate
changes were Normally distributed.
These assumptions could easily
create a 20% to 50% error in the
estimation of capital
The methods that do not require so
many assumptions (please refer to
Page 194 to 195)
SIMULATION METHODS
Models to Create Interest-Rate Scenarios
Randomly
 An important component in the simulation
approach is the stochastic (i.e., random
model used to generate interest-rate paths)
 This basic interest-rate model assumes that
the interest rate in the next period (rt+1) will
equal the current rate (rt), plus a random
number with a standard deviation of σ:
The basic interest-rate model
This is inadequate for ALM purposes because over
long periods, such as a year, the simulated interest
rate can become negative
 This model also lacks two features observed in
historical interest rates:

rates are mean reverting
 heteroskedastic (their volatility varies over time)

Sophisticated interest-rate models
Two classes of more sophisticated
models have been developed for interest
rates:
general-equilibrium (GE) models and
arbitrage-free (AF) models
A general model for the GE approach has
a mean-reverting term and a factor that
reduces the volatility as rates drop
Sophisticated interest-rate models
the level to which interest rates
tend to revert over time
the speed of reversion
The relative volatility of the
distributions of interest rate
>determines how significantly the
volatility will be reduced as rates drop
>If κ is close to 1, the rates revert
quickly
>If it was 0, the volatility would not
change if rates changed
> if it is close to 0, the model becomes
like a random walk
>0.5 for Cox-Ingersoll-Ross model
>1 for the Vasicek model
Sophisticated interest-rate models
Values
for the parameters θ, κ,
σ, and γ can be determined
from historical rate
information using maximum
likelihood estimation