FRM学习资料七：FRM Handbook 5th Edition E-Book

金融风险管理师（FRM）学习资料：FRM Handbook 5th Edition E-Book-非扫描版，超清晰PDF电子书

Preface ix

About the Author xi

About GARP xiii

Introduction xv

PART ONE

Quantitative Analysis

CHAPTER 1

Bond Fundamentals 3

CHAPTER 2

Fundamentals of Probability 31

CHAPTER 3

Fundamentals of Statistics 67

CHAPTER 4

Monte Carlo Methods 89

PART TWO

Capital Markets

CHAPTER 5

Introduction to Derivatives 111

CHAPTER 6

Options 127

CHAPTER 7

Fixed-Income Securities 161

CHAPTER 8

Fixed-Income Derivatives 195

CHAPTER 9

Equity, Currency, and Commodity Markets 217

PART THREE

Market Risk Management

CHAPTER 10

Introduction to Market Risk 247

CHAPTER 11

Sources of Market Risk 273

CHAPTER 12

Hedging Linear Risk 297

CHAPTER 13

Nonlinear Risk: Options 315

CHAPTER 14

Modeling Risk Factors 341

CHAPTER 15

VAR Methods 359

PART FOUR

Investment Risk Management

CHAPTER 16

Portfolio Management 383

CHAPTER 17

Hedge Fund Risk Management 401

PART FIVE

Credit Risk Management

CHAPTER 18

Introduction to Credit Risk 431

CHAPTER 19

Measuring Actuarial Default Risk 451

CHAPTER 20

Measuring Default Risk from Market Prices 479

CHAPTER 21

Credit Exposure 499

CHAPTER 22

Credit Derivatives and Structured Products 531

CHAPTER 23

Managing Credit Risk 561

PART SIX

Legal, Operational, and Integrated Risk Management

CHAPTER 24

Operational Risk 587

CHAPTER 25

Liquidity Risk 607

CHAPTER 26

Firm-Wide Risk Management 623

CHAPTER 27

Legal Issues 643

PART SEVEN

Regulation and Compliance

CHAPTER 28

Regulation of Financial Institutions 657

CHAPTER 29

The Basel Accord 667

CHAPTER 30

The Basel Market Risk Charge 699

About the CD-ROM 715

Index 717

Preface

T

he Financial Risk Manager Handbook provides the core body of knowledge

for ﬁnancial risk managers. Risk management has evolved rapidly over the past

decade and has become an indispensable function in many institutions.

This Handbook was originally written to provide support for candidates tak-

ing the FRM examination administered by GARP. As such, it reviews a wide

variety of practical topics in a consistent and systematic fashion. It covers quan-

titative methods and capital markets, as well as market, credit, operational, and

integrated risk management. It also discusses regulatory and legal issues essential

to risk professionals.

This edition has been thoroughly updated to reﬂect recent developments in

ﬁnancial markets. The unprecedented losses incurred by many institutions have

raised questions about risk management practices. These issues are now addressed

in various parts of the book, which also include lessons from recent regulatory

reports. The securitization process and structured credit products are critically

examined. A new chapter on liquidity risk has been added, given the importance

of this risk during the recent crisis. Finally, this Handbook incorporates the latest

questions from the FRM examinations.

Modern risk management systems cut across the entire organization. This

breadth is reﬂected in the subjects covered in this Handbook. The book was de-

signed to be self-contained, but only for readers who already have some exposure

to ﬁnancial markets. To reap maximum beneﬁt from this book, readers should

have taken the equivalent of an MBA-level class on investments.

Finally, I want to acknowledge the help received in writing this Handbook.

In particular, I thank the numerous readers who shared comments on previous

editions. Any comment or suggestion for improvement will be welcome. This

feedback will help us to maintain the high quality of the FRM designation.

Philippe Jorion

February 2009

KEY CONCEPT

When successive returns are uncorrelated, the volatility increases as the hori-

zon extends following the square root of time.

More generally, the variance can be added up from different values across

different periods. For instance, the variance over the next year can be computed as

the average monthly variance over the ﬁrst three months, multiplied by 3, plus the

average variance over the last nine months, multiplied by 9. This type of analysisP1: ABC/ABC P2: c/d QC: e/f T1: g

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70 QUANTITATIVE ANALYSIS

is routinely used to construct a term structure of implied volatilities, which are

derived from option data for different maturities.

It should be emphasized that this holds only if returns have constant parame-

ters across time and are uncorrelated. When there is non-zero correlation across

days, the two-day variance is

V(R2) = V(R1) + V(R1) + 2ρV(R1) = 2V(R1)(1 + ρ) (3.8)

Because we are considering correlations in the time series of the same variable, ρ

is called the autocorrelation coefﬁcient,orthe serial autocorrelation coefﬁcient.A

positive value for ρ implies that a movement in one direction in one day is likely to

be followed by another movement in the same direction the next day. A positive

autocorrelation signals the existence of a trend. In this case, Equation (3.8) shows

that the two-day variance is greater than the one obtained by the square root of

time rule.

A negative value for ρ implies that a movement in one direction in one day

is likely to be followed by a movement in the other direction the next day. So,

prices tend to revert back to a mean value. A negative autocorrelation signals

EXAMPLE 3.1: FRM EXAM 1999—QUESTION 4

A fundamental assumption of the random walk hypothesis of market returns

is that returns from one time period to the next are statistically independent.

This assumption implies

a. Returns from one time period to the next can never be equal.

b. Returns from one time period to the next are uncorrelated.

c. Knowledge of the returns from one time period does not help in predict-

ing returns from the next time period.

d. Both b) and c) are true.

EXAMPLE 3.2: FRM EXAM 2002—QUESTION 3

Consider a stock with daily returns that follow a random walk. The annual-

ized volatility is 34%. Estimate the weekly volatility of this stock assuming

that the year has 52 weeks.

a. 6.80%

b. 5.83%

c. 4.85%

d. 4.71%P1: ABC/ABC P2: c/d QC: e/f T1: g

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Fundamentals of Statistics 71

EXAMPLE 3.3: FRM EXAM 2002—QUESTION 2

Assume we calculate a one-week VAR for a natural gas position by rescal-

ing the daily VAR using the square-root rule. Let us now assume that we

determine the true gas price process to be mean-reverting and recalculate the

VAR.

Which of the following statements is true?

a. The recalculated VAR will be less than the original VAR.

b. The recalculated VAR will be equal to the original VAR.

c. The recalculated VAR will be greater than the original VAR.

d. There is no necessary relation between the recalculated VAR and the

original VAR.

mean reversion. In this case, the two-day variance is less than the one obtained by

the square root of time rule.

3.1.3 Portfolio Aggregation

Let us now turn to aggregation of returns across assets. Consider, for example, an

equity portfolio consisting of investments in N shares. Deﬁne the number of each

share held as qi with unit price Si . The portfolio value at time t is then

Thus, derivatives valuation focuses on the discounted center of the distribution,

while VAR focuses on the quantile on the target date.

Monte Carlo simulations have been long used to price derivatives. As will

be seen in a later chapter, pricing derivatives can be done by assuming that the

underlying asset grows at the risk-free rate r (assuming no income payment).

For instance, pricing an option on a stock with expected return of 20% is done

assuming that (1) the stock grows at the risk-free rate of 10%and (2) we discount

at the same risk-free rate. This is called the risk-neutral approach.

In contrast, riskmeasurement deals with actual distributions, sometimes called

physical distributions. For measuring VAR, the risk manager must simulate asset

growth using the actual expected return µ of 20%. Therefore, risk management

uses physical distributions, whereas pricingmethods use risk-neutral distributions.

It should be noted that simulation methods are not applicable to all types

of options. These methods assume that the value of the derivative instrument at

expiration can be priced solely as a function of the end-of-period price ST,and

perhaps of its sample path. This is the case, for instance, with an Asian option,

where the payoff is a function of the price averaged over the sample path. Such an

optionissaidtobe path-dependent.

Simulation methods, however, are inadequate to price American options, be-

cause such options can be exercised early. The optimal exercise decision, however,

is complex to model because it should take into account future values of the op-

tion. This cannot be done with regular simulation methods, which only consider

present and past information. Instead, valuing American options requires a back-

ward recursion, for example with binomial trees. This method examines whether

the option should be exercised or not, starting fromthe end andworking backward

in time until the starting time.

4.2.3 Accuracy

Finally, we shouldmention the effect of sampling variability. Unless K is extremely

large, the empirical distribution of ST will only be an approximation of the trueP1: ABC/ABC P2: c/d QC: e/f T1: g

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100 QUANTITATIVE ANALYSIS

distribution. There will be some natural variation in statistics measured from

Monte Carlo simulations. Since Monte Carlo simulations involve independent

draws, one can show that the standard error of statistics is inversely related to the

square root of K. Thus more simulations will increase precision, but at a slow

rate. For example, accuracy is increased by a factor of ten going from K = 10

to K = 1,000, but then requires going from K = 1,000 to K = 100,000 for the

same factor of 10.

This accuracy issue is worse for risk management than for pricing, because

the quantiles are estimated less precisely than the average. For VAR measures,

the precision is also a function of the selected conﬁdence level. Higher conﬁ-

dence levels generate fewer observations in the left tail and hence less-precise

VAR measures. A 99% VAR using 1,000 replications should be expected to have

only 10 observations in the left tail, which is not a large number. The VAR

estimate is derived from the tenth and eleventh sorted number. In contrast, a

95% VAR is measured from the ﬁftieth and ﬁfty-ﬁrst sorted numbers, which is

more precise. In addition, the precision of the estimated quantile depends on the

shape of the distribution. Relative to a symmetric distribution, a short option

position has negative skewness, or a long left tail. The observations in the left

tail therefore will be more dispersed, making is more difﬁcult to estimate VAR

precisely.

Various methods are available to speed up convergence:

Antithetic Variable Technique. This technique uses twice the same sequence

of random draws from t to T. It takes the original sequence and changes the

sign of all their values. This creates twice the number of points in the ﬁnal

distribution of FT without running twice the number of simulations.

Control Variate Technique. This technique is used to price options with trees

when a similar option has an analytical solution. Say that fE is a European

option with an analytical solution. Going through the tree yields the values

of an American and European option, FA and FE. We then assume that the

error in FA isthesameasthatin FE, which is known. The adjusted value is

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