LO 15.9: Explain the im pact o f a single asset price jum p on a volatility smile.

LO 15.9: Explain the im pact o f a single asset price jum p on a volatility smile.
Price jumps can occur for a number of reasons. One reason may be the expectation of a significant news event that causes the underlying asset to move either up or down by a large amount. This would cause the underlying distribution to become bimodal, but with the same expected return and standard deviation as a unimodal, or standard, price-change distribution.
Implied volatility is affected by price jumps and the probabilities assumed for either a large up or down movement. The usual result, however, is that at-the-money options tend to have a higher implied volatility than either out-of-the-money or in-the-money options. Away-from-the-money options exhibit a lower implied volatility than at-the-money options. Instead of a volatility smile, price jumps would generate a volatility frown, as in Figure 3.
Figure 3: Volatility Smile (Frown) With Price Jump Implied volatility
Strike price
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Topic 15 Cross Reference to GARP Assigned Reading – Hull, Chapter 20
K e y C o n c e p t s
LO 15.1
When option traders allow implied volatility to depend on strike price, patterns of implied volatility resemble volatility smiles.
LO 15.2
Put-call parity indicates that the deviation between market prices and Black-Scholes-Merton prices will be equivalent for calls and puts. Hence, implied volatility will be the same for calls and puts.
LO 15.3
Currency traders believe there is a greater chance of extreme price movements than predicted by a lognormal distribution. Equity traders believe the probability of large down movements in price is greater than large up movements in price, as compared with a lognormal distribution.
LO 15.4
The volatility pattern used by traders to price currency options generates implied volatilities that are higher for deep in-the-money and deep out-of-the-money options, as compared to the implied volatility for at-the-money options.
LO 15.5
The volatility smile exhibited by equity options is more of a smirk, with implied volatility higher for low strike prices. This has been attributed to leverage and crashophobia effects.
LO 15.6
Alternative methods to studying volatility patterns include: replacing strike price with strike price divided by stock price, replacing strike price with strike price divided by the forward price for the underlying asset, and replacing strike price with option delta.
LO 15.7
Volatility term structures and volatility surfaces are used by traders to judge consistency in model-generated option prices.
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LO 15.8
Volatility smiles that are not flat require the use of implied volatility functions or trees to correctly calculate option Greeks.
LO 15.9
Price jumps may generate volatility frowns instead of smiles.
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Topic 15 Cross Reference to GARP Assigned Reading – Hull, Chapter 20
C o n c e p t C h e c k e r s
1.
2.
3.
4.
5.
The market price deviations for puts and calls from Black-Scholes-Merton prices indicate: A. equivalent put and call implied volatility. B. equivalent put and call moneyness. C. unequal put and call implied volatility. D. unequal put and call moneyness.
An empirical distribution that exhibits a fatter right tail than that of a lognormal distribution would indicate: A. equal implied volatilities across low and high strike prices. B. greater implied volatilities for low strike prices. C. greater implied volatilities for high strike prices. D. higher implied volatilities for mid-range strike prices.
the same across maturities for given strike prices. the same for short time periods. The sticky strike rule assumes that implied volatility is: A. B. C. the same across strike prices for given maturities. D. different across strike prices for given maturities.
Compared to at-the-money currency options, out-of-the-money currency options exhibit which of the following volatility traits? A. Lower implied volatility. B. A frown. C. A smirk. D. Higher implied volatility.
Which of the following regarding equity option volatility is true? A. There is higher implied price volatility for away-from-the-money equity options. B. Crashophobia suggests actual equity volatility increases when stock prices
decline.
C. Compared to the lognormal distribution, traders believe the probability of large
down movements in price is similar to large up movements.
D. Increasing leverage at lower equity prices suggests increasing volatility.
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C o n c e p t C h e c k e r An s w e r s
1. A Put-call parity indicates that the implied volatility of a call and put will be equal for the same
strike price and time to expiration.
2. C An empirical distribution with a fat right tail generates a higher implied volatility for higher
strike prices due to the increased probability of observing high underlying asset prices. The pricing indication is that in-the-money calls and out-of-the-money puts would be expensive.
3. B The sticky strike rule, when applied to calculating option sensitivity measures, assumes
implied volatility is the same over short time periods.
4. D Away-from-the-money currency options have greater implied volatility than at-the-money
options. This pattern results in a volatility smile.
5. D There is higher implied price volatility for low strike price equity options. Crashophobia is based on the idea that large price declines are more likely than assumed in Black-Scholes- Merton prices, not that volatility increases when prices decline. Compared to the lognormal distribution, traders believe the probability of large down movements in price is higher than large up movements. Increasing leverage at lower equity prices suggests increasing volatility.
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S e l f -Te s t : M a r k e t R i s k M e a s u r e m e n t a n d M a n a g e m e n t
10 Q u e stio n s: 3 0 M in u te s
1.
2.
3.
4.
An analyst for Z Corporation is determining the value at risk (VaR) for the corporations profit/loss distribution that is assumed to be normally distributed. The profit/loss distribution has an annual mean of $3 million and a standard deviation of$3.3 million. Using a parametric approach, what is the VaR with a 99% confidence level? A. $0,775 million. B.$3,155 million. C. $5,775 million. D.$8,155 million.
The Basel Committee requires backtesting of actual losses to VaR calculations. How many exceptions would need to occur in a 250-day trading period for the capital multiplier to increase from three to four? two to five. A. B. five to seven. C. seven to nine. D. ten or more.
The top-down approach to risk aggregation assumes that a banks portfolio can be cleanly subdivided according to market, credit, and operational risk measures. In contrast, a bottom-up approach attempts to account for interactions among various risk factors. In order to assess which approach is more appropriate, academic studies evaluate the ratio of integrated risks to separate risks. Regarding studies of top-down and bottom-up approaches, which of the following statements is incorrect? A. Top-down studies suggest that risk diversification is present. B. Bottom-up studies sometimes calculate the ratio of integrated risks to separate
risks to be less than one.
C. Bottom-up studies suggest that risk diversification should be questioned. D. Top-down studies calculate the ratio of integrated risks to separate risks to be
greater than one.
Commercial Bank Z has a $3 million loan to company A and a$3 million loan to company B. Companies A and B each have a 5% and 4% default probability, respectively. The default correlation between companies A and B is 0.6. What is the expected loss (EL) for the commercial bank under the worst case scenario? a. b. c. d.
$83,700.$133,900. $165,600.$233,800.
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Book 1 Self-Test: Market Risk Measurement and Management
5.
6.
7.
8.
A risk manager should always pay careful attention to the limitations and advantages of applying financial models such as the value at risk (VaR) and Black-Scholes- Merton (BSM) option pricing model. Which of the following statements regarding financial models is correct? a. Financial models should always be calibrated using most recent market data
because it is more likely to be accurate in extrapolating trends.
b. When applying the VaR model, empirical studies imply asset returns closely
follow the normal distribution.
c. The Black-Scholes-Merton option pricing model is a good example of
the advantage of using financial models because the model eliminates all mathematical inconsistences that can occur with human judgment.
d. A good example of a limitation of a financial model is the assumption of
constant volatility when applying the Black-Scholes-Merton (BSM) option pricing model.
Assume that a trader wishes to set up a hedge such that he sells $100,000 of a Treasury bond and buys TIPS as a hedge. Using a historical yield regression framework, assume the DV01 on the T-bond is 0.072, the DV01 on the TIPS is 0.051, and the hedge adjustment factor (regression beta coefficient) is 1.2. What is the face value of the offsetting TIPS position needed to carry out this regression hedge? A.$138,462. B. $169,412. C.$268,499. D. $280,067. A constant maturity Treasury (CMT) swap pays ($1,000,000 / 2) x (yCMT 9%) every six months. There is a 70% probability of an increase in the 6-month spot rate and a 60% probability of an increase in the 1 -year spot rate. The rate change in all cases is 0.50% per period, and the initial yCMT is 9%. What is the value of this CMT swap? A. $2,325. B.$2,229. C. $2,429. D.$905.
Suppose the market expects that the current 1-year rate for zero-coupon bonds with a face value of $1 will remain at 5%, but the 1-year rate in one year will be 3%. What is the 2-year spot rate for zero-coupon bonds? A. 3.995%. B. 4.088%. C. 4.005%. D. 4.115%. Page 200 2018 Kaplan, Inc. Book 1 Self-Test: Market Risk Measurement and Management 9. An analyst is modeling spot rate changes using short rate term structure models. The current short-term interest rate is 5% with a volatility of 80bps. After one month passes the realization of dw, a normally distributed random variable with mean 0 and standard deviation Vdt, is -0.5. Assume a constant interest rate drift, \ , of 0.36%. What should the analyst compute as the new spot rate? A. 5.37%. B. 4.63%. C. 5.76%. D. 4.24%. 10. Which of the following statements is incorrect regarding volatility smiles? A. Currency options exhibit volatility smiles because the at-the-money options have higher implied volatility than away-from-the-money options. B. Volatility frowns result when jumps occur in asset prices. C. Equity options exhibit a volatility smirk because low strike price options have greater implied volatility. D. Relative to currency traders, it appears that equity traders expectations of extreme price movements are more asymmetric. 2018 Kaplan, Inc. Page 201 S e l f -Te s t A n s w e r s : M a r k e t R i s k M e a s u r e m e n t a n d M a n a g e m e n t 1. B The population mean and standard deviations are unknown; therefore, the standard normal z-value of 2.33 is used for a 99% confidence level. VaR(l%) = -5.0 million + ($3.5 million)(2.33) = -5.0 million + 8.155 million = 3.155 million (See Topic 1)
2. D Ten or more backtesting violations require the institution to use a capital multiplier of four.
(See Topic 3)
3. D Top-down studies calculate this ratio to be less than one, which suggests that risk
diversification is present and ignored by the separate approach. Bottom-up studies also often calculate this ratio to be less than one; however, this research has not been conclusive, and has recently found evidence of risk compounding, which produces a ratio greater than one. Thus, bottom-up studies suggests that risk diversification should be questioned. (See Topic 5)
4. C The default probability of company A is 5%. Thus, the standard deviation for company A is:
^0.05(1 0.05) = 0.2179
Company B has a default probability of 4% and, therefore, will have a standard deviation of 0.1960. We can now calculate the expected loss under the worst case scenario where both companies A and B are in default. Assuming that the default correlation between A and B is 0.6, the joint probability of default is:
P(AB) = 0.6^0.05(0.95) x 0.04(0.96) + 0.05 x 0.04 = 0.6V0.001824 + 0.002 = 0.0276
Thus, the expected loss for the commercial bank is $165,600 (= 0.0276 x$6,000,000). (See Topic 6)
5. D The Black-Scholes-Merton (BSM) option pricing model assumes strike prices have a
constant volatility. However, numerous empirical studies find higher volatility for out-of- the-money options and a volatility skew in equity markets. Thus, this is a good example of a limitation of financial models. The choice of time period used to calibrate the parameter inputs for the model can have a big impact on the results. Risk managers used volatility and correlation estimates from pre-crisis periods during the recent financial crisis, and this resulted in significantly underestimating the risk for financial models. All financial models should be stress tested using scenarios of extreme economic conditions. VaR models often assume asset returns have a normal distribution. However, empirical studies find higher kurtosis in return distributions. High kurtosis implies a distribution with fatter tails than the normal distribution. Thus, the normal distribution is not the best assumption for the underlying distribution. Financial models contain mathematical inconsistencies. For example, in applying the BSM option pricing model for up-and-out calls and puts and down-and-out calls and puts, there are rare cases where the inputs make the model insensitive to changes in implied volatility and option maturity. (See Topic 8)
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Book 1 Self-Test Answers: Market Risk Measurement and Management
6. B Defining
and P * as the face amounts of the real and nominal bonds, respectively, and
their corresponding DVOls as DV01R and DV01N, a DV01 hedge is adjusted by the hedge adjustment factor, or beta, as follows:
RF = 100,000 x
xl.2 = 169,412
‘ d v o i n ‘ X 0 R DV01 \ / 0.072 .051 J
/ V0
FR = FN x
(See Topic 10)
7. A The payoff in each period is ($1,000,000 / 2) x (yCMT – 9%). For example, the 1-year payoff of$5,000 in the figure below is calculated as ($1,000,000 / 2) x (10% – 9%) =$5,000. The other numbers in the year one cells are calculated similarly.
In six months, the payoff if interest rates increase to 9.50% is ($1,000,000 / 2 ) x (9.5% – 9.0%) =$2,500. Note that the price in this cell equals the present value of the probability weighted 1 -year values plus the 6-month payoff:
months, U
($5,000×0.6)+ ($0x0.4)
+ 0.095 1
+ $2,500 =$5,363.96
The other cell value in six months is calculated similarly and results in a loss of $4,418.47. The value of the CMT swap today is the present value of the probability weighted 6-month values: ($5,363.96 x 0.7) + (-$4,418.47 x 0.3) + 0.09 1$2,324.62
yCMT=10% Price = $5,000 yCMT = 9 0 /0 Price =$0
yCMT = 8% Price = -$5,000 yCMT= 8*5% Price = -$4,418
T od ay
6 m on th s
1 year
Thus the correct response is A. The other answers are incorrect because they do not correctly discount the future values or omit the 6-month payoff from the 6-month values.
(See Topic 11)
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Book 1 Self-Test Answers: Market Risk Measurement and Management
8. A The 2-year spot rate is computed as follows:
f (2) = 2/(1.05) (1.03) – 1 = 3.995%
(See Topic 12)
9. B This short rate process has an annualized drift of 0.36%, so it requires the use of Model 2
(with constant drift). The change in the spot rate is computed as:
dr = Xdt + adw
dr = (0.36% / 12) + (0.8% x -0.5) = -0.37% = -37 basis points
Since the initial short-term rate was 5% and dr is -0.37%, the new spot rate in one month
5% – 0.37% = 4.63% (See Topic 13)
10. A Currency options exhibit volatility smiles because the at-the-money options have lower
implied volatility than away-from-the-money options.
Equity traders believe that the probability of large price decreases is greater than the probability of large price increases. Currency traders beliefs about volatility are more symmetric as there is no large skew in the distribution of expected currency values (i.e., there is a greater chance of large price movements in either direction).
(See Topic 15)
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delta-normal VaR: VaR(a%) = (p,r + a r x za ) x Pt_1
lognormal VaR: VaR(a%) = Pt_1 x ^1 e^R aRXZa j
standard error of a quantile: se (q)
V p ( l- p ) /n
f(q)
Topic 2
age-weighted historical simulation: w(i)
x ^ q – x )
l – X ”
Topic 3
model accuracy test: z
x – p T
V p (l- p )T
unconditional coverage test statistic:
LR = 2ln[(1 – p)TNpN] + 2ln{ [1 – (N/T)]t -n (N/T)nJ
Topic 4
V(Rp) is variance of portfolio return: V(Rp) = (3p x V(Rjyj) +
N
i= l
x CT,i
General market risk: (3p x V (Rm)
Specific risk:
N
i=l
wf x
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\ /
/
pt + p t v
pt-i
geometric return: R t = In
i
. i arithmetic return: rt = —————- = ———— 1
P t+ ^ t
Pt-1
p t- i
p t- i
F o r m u l a s
Topic 1
profit/loss data: P/Lt = P + D t Pt l
M arket R isk M easurem ent and M anagem ent
Book 1 Formulas
Undiversified VaR =
N
i=l
x Vj
Diversified VaR
a J x ‘ ^ x = ^ (x x V )’R (x x V )
Topic 6
portfolio mean return: pp = wxpx + wYPy
V 2 2
W
XCTX T Wytty + 2wyW y C O V y y
2 2
covariance: cov^y
n E ( X t – f e ) ( Y t – ^ Y) t=l__________________
n 1
correlation: PxY
CQVXY CTxCTy
realized correlation: Prealized
ZX
2 n – n i>] correlation swap payoff: notional amount x (preaBzej Pfixecj)
joint probability of default: P(AB) = pAB ^/PDA(1 PDa ) x PDb(1 PDB) + PDA x PDB
Topic 7
mean reversion rate: St S
j = a([i S
j)
autocorrelation: AC(pt,pt_i)
cov(pt,pt- 1) ff(pt)xof(Pt-i)
Topic 8
correlation with expectation values: PxY
E(XY) – E(X)E( Y)
E(X2)-(E (X ))2
E(Y2)-(E (Y ))2
n
i=l
n(n2 1)
Spearmans rank correlation: Ps
1 –
Kendalls t : t
n c ~ n d n(n 1) / 2
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Book 1 Formulas
Topic 12
2- year spot rate: r(2) = ^ (l + r1)(l +
~ 1
3- year spot rate: r (3) = ^ (l + q ) (l + ^ ) (l + ) 1
Jensens inequality: E
1 (i+0
1
> E[l + r
Topic 13
Model 1:
dr = crdw = annual basis-point volatility of rate changes where: dr = change in interest rates over small time interval, dt dt = small time interval (measured in years) o r = annual basis-point volatility of rate changes dw = normally distributed random variable with mean 0 and standard deviation Vdt
Model 2: dr = \d t + crdw
Vasicek model:
dr = k(0 – r)dt + crdw
where: k 0 r
= a parameter that measures the speed of reversion adjustment = long-run value of the short-term rate assuming risk neutrality = current interest rate level
long-run value of short-term rate:
X A
0 rj H k
where: ri = the long-run true rate of interest
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Book 1 Formulas
Topic 14
Model 3:
dr = \(t)dt + cre-atdw
where: a = volatility at t = 0, which decreases exponentially to 0 for a > 0
CIR model: dr = k(0 r)dt + a Vr dw
Model 4: dr = ardt + crrdw
Topic 13
put-call parity: c p = S PV(X)
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U s in g t h e C u m u l a t iv e Z-Ta b l e
Probability Example
Assume that the annual earnings per share (EPS) for a large sample of firms is normally distributed with a mean of $5.00 and a standard deviation of$1.50. What is the approximate probability of an observed EPS value falling between $3.00 and$7.25?
If EPS = x = $7.25, then z = (x – p)/a = ($7.25 – $5.00)/$1.50 = +1.50
If EPS = x = $3.00, then z = (x – p)/a = ($3.00 – $5.00)/$1.50 = -1.33
For z-value of 1.50: Use the row headed 1.5 and the column headed 0 to find the value 0.9332. This represents the area under the curve to the left of the critical value 1.50.
For z-value of1.33: Use the row headed 1.3 and the column headed 3 to find the value 0.9082. This represents the area under the curve to the left of the critical value +1.33. The area to the left o f1.33 is 1 0.9082 = 0.0918.
The area between these critical values is 0.9332 0.0918 = 0.8414, or 84.14%.
Hypothesis Testing One-Tailed Test Example
A sample of a stocks returns on 36 non-consecutive days results in a mean return of 2.0%. Assume the population standard deviation is 20.0%. Can we say with 95% confidence that the mean return is greater than 0%?
H q: p < 0.0%, Ha : p > 0.0%. The test statistic = ^-statistic = = (2.0 – 0.0) / (20.0 / 6) = 0.60.
x-po
The significance level = 1.0 0.95 = 0.05, or 5%.
Since this is a one-tailed test with an alpha of 0.05, we need to find the value 0.95 in the cumulative stable. The closest value is 0.9505, with a corresponding critical .z-value of 1.65. Since the test statistic is less than the critical value, we fail to reject H Q.
Hypothesis Testing Two-Tailed Test Example
Using the same assumptions as before, suppose that the analyst now wants to determine if he can say with 99% confidence that the stocks return is not equal to 0.0%.
H q: p = 0.0%, Ha : p ^ 0.0%. The test statistic (z-value) = (2.0 0.0) / (20.0 / 6) = 0.60. The significance level = 1.0 0.99 = 0.01, or 1%.
Since this is a two-tailed test with an alpha of 0.01, there is a 0.005 rejection region in both tails. Thus, we need to find the value 0.995 (1.0 0.005) in the table. The closest value is 0.9951, which corresponds to a critical .z-value of 2.58. Since the test statistic is less than the critical value, we fail to reject H Q and conclude that the stocks return equals 0.0%.
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C u m u l a t iv e Ta b l e P(Z < z) = N(z) for z > 0 P(Z < -z) = 1 - N(z) z 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 0 0.01 0.02 0.5000 0.5040 0.5080 0.03 0.5120 0.04 0.5160 0.05 0.06 0.07 0.08 0.09 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0 .5 5 1 7 0 .5 5 5 7 0 .5 5 9 6 0 .5 6 3 6 0.5675 0 .5 7 9 3 0 .5 8 3 2 0 .6 1 7 9 0 .6 2 1 7 0 .6 5 5 4 0.6591 0.5871 0.6255 0.6628 0.5910 0.5948 0 .5 9 8 7 0 .6 0 2 6 0 .6 0 6 4 0 .6 2 9 3 0.6331 0.6368 0 .6 4 0 6 0.6443 0.6664 0.6 7 0 0 0 .6 7 3 6 0 .6 7 7 2 0.6808 0.6 8 4 4 0 .5 7 1 4 0.6103 0.6480 0.5753 0.6141 0 .6 5 1 7 0 .6 8 7 9 0.6915 0.6950 0.6985 0.7019 0 .7 0 5 4 0 .7 0 8 8 0.7123 0 .7 1 5 7 0 .7 1 9 0 0 .7 2 2 4 0 .7 2 5 7 0.7291 0 .7 3 2 4 0 .7 3 5 7 0 .7 3 8 9 0 .7 4 2 2 0 .7 4 5 4 0 .7 4 8 6 0 .7 5 1 7 0 .7 5 4 9 0.7580 0.7611 0 .7 6 4 2 0.7673 0 .7 7 0 4 0 .7 7 3 4 0 .7 7 6 4 0 .7 7 9 4 0.7823 0 .7 8 5 2 0.7881 0.7910 0 .7 9 3 9 0 .7 9 6 7 0.7995 0.8023 0.8051 0 .8 0 7 8 0 .8 1 0 6 0.8133 0.8159 0 .8 1 8 6 0 .8 2 1 2 0 .8 2 3 8 0 .8 2 6 4 0.8289 0.8315 0.8340 0.8365 0.8389 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0 .8 5 5 4 0 .8 5 7 7 0 .8 5 9 9 0.8621 0.8643 0.8665 0 .8 6 8 6 0.8708 0 .8 7 2 9 0 .8 7 4 9 0.8770 0.8790 0.8810 0.8830 0 .8 8 4 9 0 .8 8 6 9 0.8888 0 .8 9 0 7 0.8925 0 .8 9 4 4 0 .8 9 6 2 0 .8 9 8 0 0 .9 0 6 6 0 .9 0 8 2 0 .9 0 9 9 0.9115 0.9131 0 .9 1 4 7 0 .9 2 2 2 0 .9 2 3 6 0.9251 0.9265 0.9279 0 .9 2 9 2 0 .9 3 0 6 0 .8 9 9 7 0 .9 1 6 2 0.9015 0 .9 1 7 7 0.9319 0 .9 0 3 2 0 .9 1 9 2 0 .9 0 4 9 0 .9 2 0 7 0 .9 3 3 2 0 .9 4 5 2 0.9345 0.9463 0 .9 3 5 7 0 .9 3 7 0 .9 3 8 2 0 .9 3 9 4 0 .9 4 0 6 0.9418 0.9429 0.9441 0 .9 4 7 4 0 .9 4 8 4 0.9495 0.9505 0.9525 0.9535 0.9545 0.9515 0.9608 0 .9 5 5 4 0 .9 5 6 4 0 .9 5 7 3 0 .9 5 8 2 0.9591 0 .9 5 9 9 0.9616 0.9625 0.9641 0 .9 6 4 9 0 .9 6 5 6 0 .9 6 6 4 0.9671 0.9678 0.9686 0.9693 0 .9 6 9 9 0.9713 0 .9 7 1 9 0 .9 7 2 6 0 .9 7 3 2 0 .9 7 3 8 0 .9 7 4 4 0 .9 7 5 0 0 .9 7 5 6 0.9761 0 .9 7 7 2 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0 .9 8 0 8 0 .9 8 1 2 0.9821 0.9861 0.9893 0 .9 8 2 6 0.983 0 .9 8 3 4 0.9838 0.9 8 4 2 0 .9 8 4 6 0.985 0 .9864 0.9868 0.9896 0.9898 0.9871 0.9901 0.9875 0 .9 9 0 4 0.9878 0.9881 0 .9 8 8 4 0 .9 9 0 6 0.9909 0.9911 0 .9 8 5 4 0 .9 8 8 7 0.9913 0.9633 0 .9 7 0 6 0 .9 7 6 7 0 .9 8 1 7 0 .9 8 5 7 0 .9 8 9 0 .9 9 1 6 0.9918 0.9920 0.9922 0.9925 0 .9 9 2 7 0 .9 9 2 9 0.9931 0 .9 9 3 2 0 .9 9 3 4 0 .9 9 3 6 0.9938 0 .9 9 5 3 0.9965 0 .9 9 7 4 0.9981 0 .9 9 4 0.9955 0 .9 9 6 6 0.9975 0 .9 9 8 2 0.9941 0 .9 9 5 6 0 .9 9 6 7 0 .9 9 7 6 0 .9 9 8 2 0.9943 0 .9 9 5 7 0.9968 0 .9 9 7 7 0.9983 0.9945 0 .9 9 5 9 0.9969 0 .9 9 7 7 0 .9 9 8 4 0.9960 0.9970 0.9978 0 .9 9 8 4 0.9949 0 .9 9 6 2 0 .9 9 7 2 0.9961 0.9971 0 .9 9 7 9 0 .9 9 7 9 0.9951 0.9963 0.9973 0.9980 0 .9 9 5 2 0 .9 9 6 4 0 .9 9 7 4 0.9981 0.9985 0.9985 0 .9 9 8 6 0 .9 9 8 6 0.9946 0.9948 0 .9 9 8 7 0 .9 9 8 7 0 .9 9 8 7 0.9988 0.9988 0.9989 0.9989 0.9989 0 .9 9 9 0 0 .9 9 9 0 Page 210 2018 Kaplan, Inc. 0.00 0.0000 0.01 0.02 0 .0 0 4 0 0 .0 0 8 0 0.03 0 .0 1 2 0 0.04 0 .0 1 6 0 0.05 0.0199 0.06 0.07 0.08 0.09 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 0 .0 5 1 7 0 .0 5 5 7 0 .0 5 9 6 0 .0 6 3 6 0.0675 0 .0 7 9 3 0 .0 8 3 2 0 .1 1 7 9 0 .1 2 1 7 0 .1 5 5 4 0.1591 0.0871 0.1255 0.1628 0.0910 0.0948 0 .0 9 8 7 0 .1 0 2 6 0 .1 0 6 4 0 .1 2 9 3 0.1331 0.1368 0 .1 4 0 6 0.1443 0.1664 0.1700 0 .1 7 3 6 0 .1 7 7 2 0.1808 0.1 8 4 4 0 .0 7 1 4 0.1103 0.1480 0.0753 0.1141 0 .1 5 1 7 0 .1 8 7 9 0.1915 0 .1 9 5 0 0.1985 0.2019 0 .2 0 5 4 0 .2 0 8 8 0.2123 0 .2 1 5 7 0 .2 1 9 0 0 .2 2 2 4 0 .2 2 5 7 0.2291 0 .2 3 2 4 0 .2 3 5 7 0 .2 3 8 9 0 .2 4 2 2 0 .2 4 5 4 0 .2 4 8 6 0 .2 5 1 7 0 .2 5 4 9 0 .2 5 8 0 0.2611 0 .2 6 4 2 0.2673 0 .2 7 0 4 0 .2 7 3 4 0 .2 7 6 4 0 .2 7 9 4 0.2823 0 .2 8 5 2 0.2881 0.2910 0 .2 9 3 9 0 .2 9 6 7 0.2995 0.3023 0.3051 0.3078 0.3106 0.3159 0 .3 1 8 6 0 .3 2 1 2 0.3238 0.3 2 6 4 0.3289 0.3315 0 .3 3 4 0 0 .3 3 5 6 0.3133 0 .3 3 8 9 0.3413 0.3643 0.3438 0.3461 0.3485 0.3508 0.3531 0 .3 5 5 4 0 .3 5 7 7 0 .3 5 9 9 0.3621 0.3665 0 .3 6 8 6 0.3708 0 .3 7 2 9 0 .3 7 4 9 0.3770 0.3790 0.3810 0.3830 0 .3 8 4 9 0 .3 8 6 9 0.3888 0 .3 9 0 7 0.3925 0 .3 9 4 4 0 .3 9 6 2 0 .3 9 8 0 0 .4 0 6 6 0 .4 0 8 2 0 .4 0 9 9 0.4115 0.4131 0 .4 1 4 7 0 .4 2 2 2 0 .4 2 3 6 0.4251 0.4265 0.4279 0 .4 2 9 2 0 .4 3 0 6 0 .3 9 9 7 0 .4 1 6 2 0.4015 0 .4 1 7 7 0.4319 0 .4 3 5 7 0 .4 3 7 0 0 .4 3 8 2 0 .4 3 9 4 0 .4 4 0 6 0.4418 0.4429 0.4441 0 .4 4 7 4 0 .4 4 8 4 0.4495 0.4505 0.4525 0.4535 0.4545 0.4515 0.4608 0 .4 5 5 4 0 .4 5 6 4 0.4573 0 .4 5 8 2 0.4591 0 .4 5 9 9 0.4616 0.4625 0.4641 0 .4 6 4 9 0 .4 6 5 6 0 .4 6 6 4 0.4671 0.4678 0.4686 0.4693 0 .4 6 9 9 0 .4 7 1 3 0.4719 0 .4 7 2 6 0 .4 7 3 2 0 .4 7 3 8 0 .4 7 4 4 0 .4 7 5 0 0 .4 7 5 6 0.4761 0 .4 0 3 2 0 .4 1 9 2 0.4049 0 .4 2 0 7 0 .4 3 3 2 0 .4 4 5 2 0.4345 0.4463 0 .4 7 7 2 0.4778 0.4783 0.4788 0 .4 8 2 6 0 .4 8 3 0 0 .4 8 3 4 0.4864 0.4868 0 .4 8 9 6 0.4898 0.4871 0.4901 0.4793 0.4838 0.4875 0.4798 0 .4 8 0 3 0.4808 0.4812 0.4842 0 .4 8 4 6 0 .4 8 5 0 0 .4 8 5 4 0.4878 0.4881 0 .4 8 8 4 0.4 9 0 4 0 .4 9 0 6 0.4 9 2 0 0 .4 9 2 2 0.4925 0 .4 9 2 7 0 .4 9 2 9 0 .4 9 4 0 0.4941 0.4955 0 .4 9 6 6 0.4975 0 .4 9 8 2 0 .4 9 5 6 0 .4 9 6 7 0 .4 9 7 6 0 .4 9 8 2 0.4943 0 .4 9 5 7 0.4968 0 .4 9 7 7 0.4983 0.4945 0.4959 0.4969 0 .4 9 7 7 0 .4 9 8 4 0.4946 0.4960 0.4970 0.4978 0 .4 9 8 4 0.4909 0.4931 0.4911 0 .4 9 3 2 0.4948 0.4961 0.4971 0 .4 9 4 9 0 .4 9 6 2 0 .4 9 7 2 0 .4 9 7 9 0 .4 9 7 9 0 .4 8 8 7 0.4913 0 .4 9 3 4 0.4951 0.4963 0.4973 0.4980 0.4985 0.4985 0 .4 9 8 6 0 .4 9 8 6 0.4633 0 .4 7 0 6 0 .4 7 6 7 0 .4 8 1 7 0 .4 8 5 7 0.4890 0 .4 9 1 6 0 .4 9 3 6 0 .4 9 5 2 0 .4 9 6 4 0 .4 9 7 4 0.4981 A l t e r n a t iv e .Z-Ta b l e P(Z < z) = N(z) for z > 0 P(Z < -z) = 1 - N(z) z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 0.4821 0.4861 0.4893 0.4918 0.4939 0 .4 9 5 3 0.4965 0 .4 9 7 4 0.4981 0 .4 9 8 7 0 .4 9 8 7 0 .4 9 8 7 0.4988 0.4988 0.4989 0.4989 0.4989 0 .4 9 9 0 0 .4 9 9 0 2018 Kaplan, Inc. Page 211 S t u d e n t s T -D i s t r i b u t i o n df df 1 2 3 4 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 o o Level of Significance for One-Tailed Test 0.100 0.050 0.025 0.01 0.005 0.0005 Level of Significance for Two-Tailed Test 0.20 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 0.10 6.314 2.920 2 .3 5 3 2 .1 3 2 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 0.05 12.706 4 .3 0 3 3 .1 8 2 2 .7 7 6 2.571 2 .4 4 7 2.365 2 .3 0 6 2 .2 6 2 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2 .1 1 0 2.101 2 .0 9 3 2 .0 8 6 2 .0 8 0 2 .0 7 4 2 .0 6 9 2 .0 6 4 2.060 2 .0 5 6 2 .0 5 2 2.048 2.045 2 .0 4 2 2.021 2 .0 0 0 1.980 1.960 0.02 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2 .8 9 6 2.821 2.764 2.718 2.681 2.650 2 .6 2 4 2 .6 0 2 2 .5 8 3 2 .5 6 7 2 .5 5 2 2 .5 3 9 2.528 2.518 2.508 2.500 2 .4 9 2 2.485 2.479 2.473 2 .4 6 7 2 .4 6 2 2 .4 5 7 2 .4 2 3 2 .3 9 0 2.358 2 .3 2 6 0.01 6 3 .6 5 7 9.925 5.841 4.604 4 .0 3 2 3.707 3.499 3.355 3.250 3.169 3 .1 0 6 3.055 3.012 2 .9 7 7 2 .9 4 7 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2 .8 0 7 2 .7 9 7 2 .7 8 7 2.779 2.771 2.763 2 .7 5 6 2 .7 5 0 2 .7 0 4 2 .6 6 0 2 .6 1 7 2 .5 7 6 0.001 6 3 6 .6 1 9 31.599 12.294 8.610 6.869 5.959 5.408 5.041 4.781 4 .5 8 7 4 .4 3 7 4.318 4.221 4 .1 4 0 4 .0 7 3 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3 .6 7 4 3.659 3 .6 4 6 3.551 3.460 3.373 3.291 Page 212 2018 Kaplan, Inc. 2018 Kaplan, Inc. Page 213 diversified VaR 44 duration mapping 41 DV01 -neutral hedge 121 dynamic financial correlations 65 mbedded options 143 endogenous liquidity 57 exception 26 exogenous liquidity 57 expected shortfall 6, 58, 76 E e actor exposures 38 failure rate 26 filtered historical simulation 19 F f aussian copula 112 Gaussian default time copula 113 generalized extreme value distribution 92 general risk factors 39 G G edge adjustment factor 123 historical scenarios 58 historical simulation approach 2 Ho-Lee model 168 H h ntegrated risk measurement 58 interest rate drift 135 interest rate expectations 149 interest rate tree 132 interest rate volatility 151 I i ensens inequality 153 Johnson SB distribution 92 J J endalls 103 K K everage 192 L l ge-weighted historical simulation 17 arbitrage-free models 168 autocorrelation 91 A a acktesting 25 backward induction 133 balance sheet management 60 Basel penalty zones 33 best-fit distributions 92 binomial interest rate model 132 Black-Karasinski model 184 bootstrap historical simulation 15 bottom-up approach 59 B b allable bonds 143 cash flow mapping 41 Cholesky decomposition 115 cleaned returns 26 coherent risk measure 6 compartmentalized approach 59 concentration ratio 78 concentration risk 78 conditional coverage 32 constant drift 167 constant maturity Treasury swap 139 convexity effect 153 copula function 111 correlation coefficient 67, 100 correlation copula 111 correlation options 68 correlation risk 64 correlation swap 70 correlation trading strategies 68 correlation-weighted historical simulation 18 covariance 67 Cox-Ingersoll-Ross (CIR) model 181 crashophobia 192 credit default swaps 65 cyclical feedback loop 60 c c efault correlation 76 default time 115 D d In d e x pearmans rank correlation 101 specific risks 39 spectral risk measures 58 standard deviation 66 state-dependent volatility 138 static financial correlations 65 statistical correlation measures 100 sticky delta rule 194 sticky strike rule 193 stressed VaR 58 stress testing 58, 99 surrogate density function 16 systemic risk 77 s S ime-dependent volatility 179 time-varying volatility 56 top-down approach 59 tracking error VaR 45 true probabilities 135 Type I error 28 Type II error 28 u unconditional coverage 32 undiversified VaR 43, 44 unified approach 59 T t alue at risk 1, 56, 71 Value at risk (VaR) mapping 38 variance-covariance method 72 Vasicek model 169 volatility skew 190 volatility smiles 190 volatility surface 193 volatility term structure 193 volatility-weighted historical simulation 18 V v wrong-way risk 65 mean reversion 89 mean reversion rate 89 mean-reverting process 169 mechanical-search stress tests 58 migration risk 76 Model 1 164 Model 2 167 Model 3 180 Model 4 182 ean 66 M m egative convexity 143 nonmonotonous 65 nonrecombining trees 138 N n ption-adjusted spread 141 ordinal risk measures 104 o o P Pearson correlation 67, 100 positions 38 predefined scenarios 58 price jumps 194 primitive risk factors 39 principal components analysis 125 principal mapping 41 putable bonds 144 put-call parity 189 uantile 4 quantile-quantile plot 9 quanto option 69 Q q recombining tree 138 regression hedge 122 risk-averse investor 157 risk diversification 59 risk engine 39 risk factors 38 risk-neutral investor 157 risk-neutral pricing 135 risk-neutral probabilities 135 risk premium 157 Book 1 Index lognormal model 182 lognormal VaR 5 Page 214 2018 Kaplan, Inc. Notes Notes Notes Required Disclaimers: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Kaplan. CFA Institute, CFA, and Chartered Financial Analyst are trademarks owned by CFA Institute. Certified Financial Planner Board of Standards Inc. owns the certification marks CFP, CERTIFIED FINANCIAL PLANNER, and federally registered CFP (with flame design) in the U.S., which it awards to individuals who successfully complete initial and ongoing certification requirements. Kaplan does not certify individuals to use the CFP, CERTIFIED FINANCIAL PLANNER1", and CFP (with flame design) certification marks. CFP certification is granted only by Certified Financial Planner Board of Standards Inc. to those persons who, in addition to completing an educational requirement such as this CFP Board-Registered Program, have met its ethics, experience, and examination requirements. Kaplan is a review course provider for the CFP Certification Examination administered by Certified Financial Planner Board of Standards Inc. CFP Board does not endorse any review course or receive financial remuneration from review course providers. GARP does not endorse, promote, review, or warrant the accuracy of the products or services offered by Kaplan of FRM related information, nor does it endorse any pass rates claimed by the provider. Further, GARP is not responsible for any fees or costs paid by the user to Kaplan, nor is GARP responsible for any fees or costs of any person or entity providing any services to Kaplan. FRM, GARP, and Global Association of Risk Professionals are trademarks owned by the Global Association of Risk Professionals, Inc. CAIAA does not endorse, promote, review or warrant the accuracy of the products or services offered by Kaplan, nor does it endorse any pass rates claimed by the provider. CAIAA is not responsible for any fees or costs paid by the user to Kaplan nor is CAIAA responsible for any fees or costs of any person or entity providing any services to Kaplan. GAIA, CAIA Association, Chartered Alternative Investment Analyst, and Chartered Alternative Investment Analyst Association are service marks and trademarks owned by CHARTERED ALTERNATIVE INVESTMENT ANALYST ASSOCIATION, INC., a Massachusetts non-profit corporation with its principal place of business at Amherst, Massachusetts, and are used by permission. 2018 SchweserNotes Part Credit Risk Measurement and Management eBook 2 K A P L A N ' ) S C H W E S E R Getting Started FRM Exam Part II Welcome As the VP of Advanced Designations at Kaplan Schweser, I am pleased to have the opportunity to help you prepare for the 2018 FRM Exam. Getting an early start on your study program is important for you to sufficiently prepare, practice, and perform on exam day. Proper planning will allow you to set aside enough time to master the learning objectives in the Part II curriculum. Now that you've received your SchweserNotes, here's how to get started: Step 1: Access Your Online Tools Visit www.schweser.com/frm and log in to your online account using the button located in the top navigation bar. After logging in, select the appropriate part and proceed to the dashboard where you can access your online products. Step 2: Create a Study Plan Create a study plan with the Schweser Study Calendar (located on the Schweser dashboard). Then view the Candidate Resource Library on-demand videos for an introduction to core concepts. Step 3: Prepare and Practice Read your SchweserNotes Our clear, concise study notes will help you prepare for the exam. At the end of each reading, you can answer the Concept Checker questions for better understanding of the curriculum. Attend a Weekly Class Attend our Live Online Weekly Class or review the on-demand archives as often as you like. Our expert faculty will guide you through the FRM curriculum with a structured approach to help you prepare for the exam. (See our instruction packages to the right. Visit www.schweser.com/frm to order.) Practice with SchweserPro QBank Maximize your retention of important concepts and practice answering exam-style questions in the SchweserPro QBank and taking several Practice Exams. Use Schweser's QuickSheet for continuous review on the go. (Visit www.schweser.com/frm to order.) Step 4: Final Review A few weeks before the exam, make use of our Online Review Workshop Package. Review key curriculum concepts in every topic, perform by working through demonstration problems, and practice your exam techniques with our 8-hour live Online Review Workshop. Use Schweser's Secret Sauce for convenient study on the go. Step 5: Perform As part of our Online Review Workshop Package, take a Schweser Mock Exam to ensure you are ready to perform on the actual FRM Exam. Put your skills and knowledge to the test and gain confidence before the exam.. Again, thank you fortrusting Kaplan Schweser with your FRM Exam preparation! Sincerely, Derek Burkett, CFA, FRM, CAIA VP, Advanced Designations, Kaplan Schweser The Kaplan Way Acquire new knowledge through demonstration and examples. Practice < ?xl-----bs Apply new knowledge through simulation and practice. Evaluate mastery of new knowledge and identify achieved outcomes. FRM Instruction Packages: PremiumPlus Package Premium Instruction Package Live Instruction*: Remember to join our Live Online Weekly Class. Register online today at www.schweser.com/frm. *Dates, times, and instructors subject to change MKT-005736 Contact us for questions about your study package, upgrading your package, purchasing additional study materials, or for additional information: www.schweser.com/frm Toll-Free: 888.325.5072 International: +1 608.779.8397 FRM Pa r t II B o o k 2: C r e d i t R i s k M e a s u r e m e n t a n d M a n a g e m e n t R e a d i n g A s s i g n m e n t s a n d L e a r n i n g O b j e c t i v e s C r e d i t R i s k M e a s u r e m e n t a n d M a n a g e m e n t 16: The Credit Decision 17: The Credit .Analyst 18: Classifications and Key Concepts of Credit Risk 19: Rating Assignment Methodologies 20: Credit Risks and Credit Derivatives 21: Spread Risk and Default Intensity Models 22: Portfolio Credit Risk 23: Structured Credit Risk 24: Counterparty Risk 25: Netting, Close-out and Related Aspects 26: Collateral 27: Credit Exposure and Funding 28: Counterparty Risk Intermediation 29: Default Probabilities, Credit Spreads and Funding Costs 30: Credit and Debt Value Adjustment 31: Wrong-way Risk 32: The Evolution of Stress Testing Counterparty Exposures 33: Credit Scoring and Retail Credit Risk Management 34: The Credit Transfer Markets and Their Implications 35: An Introduction to Securitization 36: Understanding the Securitization of Subprime Mortgage Credit S e l f -Te s t : C r e d i t R i s k M e a s u r e m e n t a n d M a n a g e m e n t F o r m u l a s A p p e n d i x In d e x v 1 15 28 38 63 90 107 122 143 153 161 173 193 205 219 231 242 254 265 281 301 311 316 320 323 2018 Kaplan, Inc. Page iii FRM 2018 PART II BOOK 2: CREDIT RISK MEASUREMENT AND MANAGEMENT 2018 Kaplan, Inc. All rights reserved. Published in 2018 by Kaplan, Inc. Printed in the United States of America. ISBN: 978-1-4754-7031-4 Required Disclaimer: GARP does not endorse, promote, review, or warrant the accuracy of the products or services offered by Kaplan of FRM related information, nor does it endorse any pass rates claimed by the provider. Further, GARP is not responsible for any fees or costs paid by the user to Kaplan, nor is GARP responsible for any fees or costs of any person or entity providing any services to Kaplan. FRM, GARP, and Global Association of Risk Professionals are trademarks owned by the Global Association of Risk Professionals, Inc. These materials may not be copied without written permission from the author. The unauthorized duplication of these notes is a violation of global copyright laws. Your assistance in pursuing potential violators of this law is greatly appreciated. Disclaimer: The SchweserNotes should be used in conjunction with the original readings as set forth by GARP. The information contained in these books is based on the original readings and is believed to be accurate. However, their accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam success. Page iv 2018 Kaplan, Inc. R e a d in g A s s i g n m e n t s a n d L e a r n in g O b j e c t i v e s The following material is a review of the Credit Risk Measurement and Management principles designed to address the learning objectives set forth by the Global Association of Risk Professionals. R e a d i n g A s s i g n m e n t s Jonathan Golin and Philippe Delhaise, The Bank Credit Analysis Handbook, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2013). 16 The Credit Decision, Chapter 1 17. The Credit Analyst, Chapter 2 (page 1) (page 13) Giacomo De Laurentis, Renato Maino, and Luca Molteni, Developing, Validating and Using Internal Ratings (West Sussex, UK: John Wiley & Sons, 2010). 18. Classifications and Key Concepts of Credit Risk, Chapter 2 19. Rating Asignment Methodologies, Chapter 3 (page 28) (page 38) Rene Stulz, Risk Management & Derivatives (Florence, KY: Thomson South-Western, 2002). 20. Credit Risks and Credit Derivatives, Chapter 18 (page 63) Alan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011). 21. Spread Risk and Default Intensity Models, Chapter 7 22. Portfolio Credit Risk, Chapter 8 23. Structured Credit Risk, Chapter 9 (page 90) (page 107) (page 122) Jon Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd Edition (West Sussex, UK: John Wiley & Sons, 2013). 24. Counterparty Risk, Chapter 4 25. Netting, Close-out and Related Apects, Chapter 5 26. Collateral, Chapter 6 27. Credit Exposure and Funding, Chapter 7 (page 143) (page 153) (page 161) (page 173) 2018 Kaplan, Inc. Page v Book 2 Reading Assignments and Learning Objectives 28. Counterparty Risk Intermediation, Chapter 9 (page 193) 29. Default Probabilities, Credit Spreads and Funding Costs, Chapter 12 (page 203) 30. Credit and Debt Value Adjustment, Chapter 14 31. Wrong-way Risk, Chapter 17 (page 219) (page 231) Stress Testing: Approaches, Methods, and Applications, Edited by Akhtar Siddique and Iftekhar Hasan (London, UK: Risk Books, 2013). 32. The Evolution of Stress Testing Counterparty Exposures, Chapter 4 (page 242) Michel Crouhy, Dan Galai, and Robert Mark, The Essentials of Risk Management, 2nd Edition (New York, NY: McGraw-Hill, 2014). 33. Credit Scoring and Retail Credit Risk Management, Chapter 9 (page 234) 34. The Credit Transfer Markets and Their Implications, Chapter 12 (page 265) Moo rad Choudhry, Structured Credit Products: Credit Derivatives & Synthetic Securitization, 2nd Edition (New York, NY: John Wiley & Sons, 2010). 35. An Introduction to Securitization, Chapter 12 (page 281) 36. Adam Ashcraft and Til Schuermann, Understanding the Securitization of Subprime Mortgage Credit, Federal Reserve Bank of New York Staff Reports, No. 318 (March 2008). (page 301) Page vi 2018 Kaplan, Inc. Book 2 Reading Assignments and Learning Objectives L e a r n i n g O b j e c t i v e s 16. The Credit Decision After completing this reading, you should be able to: 1. Define credit risk and explain how it arises using examples, (page 1) 2. Explain the components of credit risk evaluation, (page 2) 3. Describe, compare and contrast various credit risk mitigants and their role in credit analysis, (page 2) 4. Compare and contrast quantitative and qualitative techniques of credit risk evaluation, (page 4) 3. Compare the credit analysis of consumers, corporations, financial institutions, and sovereigns, (page 3) 6. Describe quantitative measurements and factors of credit risk, including probability of default, loss given default, exposure at default, expected loss, and time horizon, (page 7) 7. Compare bank failure and bank insolvency, (page 9) 17. The Credit Analyst After completing this reading, you should be able to: 1. Describe, compare and contrast various credit analyst roles, (page 15) 2. Describe common tasks performed by a banking credit analyst, (page 20) 3. Describe the quantitative, qualitative, and research skills a banking credit analyst is expected to have, (page 21) 4. Assess the quality of various sources of information used by a credit analyst. (page 22) 18. Classifications and Key Concepts of Credit Risk After completing this reading, you should be able to: 1. Describe the role of ratings in credit risk management, (page 28) 2. Describe classifications of credit risk and their correlation with other financial risks (page 28) Define default risk, recovery risk, exposure risk and calculate exposure at default, (page 29) Explain expected loss, unexpected loss, VaR, and concentration risk, and describe the differences among them, (page 30) Evaluate the marginal contribution to portfolio unexpected loss, (page 32) Define risk-adjusted pricing and determine risk-adjusted return on risk-adjusted capital (RARORAC). (page 32) 3. 4. 5. 6. 19. Rating Assignment Methodologies .After completing this reading, you should be able to: 1. Explain the key features of a good rating system, (page 38) 2. Describe the experts-based approaches, statistical-based models, and numerical approaches to predicting default, (page 39) 3. Describe a rating migration matrix and calculate the probability of default, cumulative probability of default, marginal probability of default, and annualized default rate, (page 40) 4. Describe rating agencies assignment methodologies for issue and issuer ratings, (page 41) 2018 Kaplan, Inc. Page vii Book 2 Reading Assignments and Learning Objectives 5. Describe the relationship between borrower rating and probability of default. (page 42) 6. Compare agencies ratings to internal experts-based rating systems, (page 42) 7. Distinguish between the structural approaches and the reduced-form approaches to predicting default, (page 43) 8. Apply the Merton model to calculate default probability and the distance to default and describe the limitations of using the Merton model, (page 44) 9. Describe linear discriminant analysis (LDA), define the Z-score and its usage, and apply LDA to classify a sample of firms by credit quality, (page 43) 10. Describe the application of logistic regression model to estimate default probability, (page 48) 11. Define and interpret cluster analysis and principal component analysis, (page 49) 12. Describe the use of a cash flow simulation model in assigning rating and default probability, and explain the limitations of the model, (page 32) 13. Describe the application of heuristic approaches, numeric approaches, and artificial neural network in modeling default risk and define their strengths and weaknesses, (page 53) 14. Describe the role and management of qualitative information in assessing probability of default, (page 56) 20. Credit Risks and Credit Derivatives After completing this reading, you should be able to: 1. Using the Merton model, calculate the value of a firms debt and equity and the volatility of firm value, (page 63) 2. Explain the relationship between credit spreads, time to maturity, and interest rates, and calculate credit spread, (page 68) 3. Explain the differences between valuing senior and subordinated debt using a contingent claim approach, (page 71) 4. Explain, from a contingent claim perspective, the impact of stochastic interest rates on the valuation of risky bonds, equity, and the risk of default, (page 71) 5. Compare and contrast different approaches to credit risk modeling, such as those related to the Merton model, CreditRisk+, CreditMetrics, and the KMV model, (page 75) 6. Assess the credit risks of derivatives, (page 80) 7. Describe a credit derivative, credit default swap, and total return swap, (page 80) 8. Explain how to account for credit risk exposure in valuing a swap, (page 83) 21. Spread Risk and Default Intensity Models After completing this reading, you should be able to: 1. Compare the different ways of representing credit spreads, (page 90) 2. Compute one credit spread given others when possible, (page 90) 3. Define and compute the Spread 01. (page 91) 4. Explain how default risk for a single company can be modeled as a Bernoulli trial, (page 92) 5. Explain the relationship between exponential and Poisson distributions, (page 93) 6. Define the hazard rate and use it to define probability functions for default time and conditional default probabilities, (page 93) 7. Calculate the conditional default probability given the hazard rate, (page 93) 8. Calculate risk-neutral default rates from spreads, (page 95) 9. Describe advantages of using the CDS market to estimate hazard rates, (page 96) Page viii 2018 Kaplan, Inc. Book 2 Reading Assignments and Learning Objectives 10. Explain how a CDS spread can be used to derive a hazard rate curve, (page 97) 11. Explain how the default distribution is affected by the sloping of the spread curve. (page 99) 12. Define spread risk and its measurement using the mark-to-market and spread volatility, (page 100) 22. Portfolio Credit Risk After completing this reading, you should be able to: 1. Define and calculate default correlation for credit portfolios, (page 107) 2. Identify drawbacks in using the correlation-based credit portfolio framework. (page 108) 3. Assess the impact of correlation on a credit portfolio and its Credit VaR. (page 109) 4. Describe the use of a single factor model to measure portfolio credit risk, including the impact of correlation, (page 111) 3. Define and calculate Credit VaR. (page 109) 6. Describe how Credit VaR can be calculated using a simulation of joint defaults. (page 116) 23. Structured Credit Risk After completing this reading, you should be able to: 1. Describe common types of structured products, (page 122) 2. Describe tranching and the distribution of credit losses in a securitization. (page 123) 3. Describe a waterfall structure in a securitization, (page 124) 4. Identify the key participants in the securitization process, and describe conflicts of interest that can arise in the process, (page 127) 3. Compute and evaluate one or two iterations of interim cashflows in a three-tiered securitization structure, (page 128) 6. Describe a simulation approach to calculating credit losses for different tranches in a securitization, (page 131) 7. Explain how the default probabilities and default correlations affect the credit risk in a securitization, (page 132) 8. Explain how default sensitivities for tranches are measured, (page 134) 9. Describe risk factors that impact structured products, (page 134) 10. Define implied correlation and describe how it can be measured, (page 135) 11. Identify the motivations for using structured credit products, (page 135) 24. Counterparty Risk After completing this reading, you should be able to: 1. Describe counterparty risk and differentiate it from lending risk, (page 143) 2. Describe transactions that carry counterparty risk and explain how counterparty 3. risk can arise in each transaction, (page 144) Identify and describe institutions that take on significant counterparty risk. (page 145) 4. Describe credit exposure, credit migration, recovery, mark-to-market, replacement 5. cost, default probability, loss given default, and the recovery rate, (page 146) Identify and describe the different ways institutions can quantify, manage and mitigate counterparty risk, (page 147) 2018 Kaplan, Inc. Page ix Book 2 Reading Assignments and Learning Objectives 25. Netting, Close-out and Related Aspects After completing this reading, you should be able to: 1. Explain the purpose of an ISDA master agreement, (page 153) 2. Summarize netting and close-out procedures (including multilateral netting), explain their advantages and disadvantages, and describe how they fit into the framework of the ISDA master agreement, (page 153) 3. Describe the effectiveness of netting in reducing credit exposure under various scenarios, (page 156) 4. Describe the mechanics of termination provisions and trade compressions and 5. explain their advantages and disadvantages, (page 156) Identify and describe termination events and discuss their potential effects on parties to a transaction, (page 156) 26. Collateral After completing this reading, you should be able to: 1. Describe the rationale for collateral management, (page 161) 2. Describe the terms of a collateral and features of a credit support annex (CSA) within the ISDA Master Agreement including threshold, initial margin, minimum transfer amount and rounding, haircuts, credit quality, and credit support amount, (page 161) 3. Describe the role of a valuation agent, (page 162) 4. Describe the mechanics of collateral and the types of collateral that are typically used, (page 163) 5. Explain the process for the reconciliation of collateral disputes, (page 163) 6. Explain the features of a collateralization agreement, (page 164) 7. Differentiate between a two-way and one-way CSA agreement and describe how collateral parameters can be linked to credit quality, (page 166) 8. Explain how market risk, operational risk, and liquidity risk (including funding liquidity risk) can arise through collateralization, (page 166) 27. Credit Exposure and Funding After completing this reading, you should be able to: 1. Describe and calculate the following metrics for credit exposure: expected mark-to- market, expected exposure, potential future exposure, expected positive exposure and negative exposure, effective exposure, and maximum exposure, (page 173) 2. Compare the characterization of credit exposure to VaR methods and describe 3. 4. additional considerations used in the determination of credit exposure, (page 176) Identify factors that affect the calculation of the credit exposure profile and summarize the impact of collateral on exposure, (page 176) Identify typical credit exposure profiles for various derivative contracts and combination profiles, (page 177) 5. Explain how payment frequencies and exercise dates affect the exposure profile of various securities, (page 180) 6. Explain the impact of netting on exposure, the benefit of correlation, and calculate the netting factor, (page 181) 7. Explain the impact of collateralization on exposure, and assess the risk associated with the remargining period, threshold, and minimum transfer amount, (page 182) Page x 2018 Kaplan, Inc. Book 2 Reading Assignments and Learning Objectives 28. Counterparty Risk Intermediation After completing this reading, you should be able to: 1. Identify counterparty risk intermediaries including central counterparties (CCPs), derivative product companies (DPCs), special purpose vehicles (SPVs), and monoline insurance companies (monolines) and describe their roles, (page 193) 2. Describe the risk management process of a CCP and explain the loss waterfall structure of a CCP. (page 196) 3. Compare bilateral and centrally cleared over-the-counter (OTC) derivative markets, (page 198) 4. Assess the capital requirements for a qualifying CCP and discuss the advantages and disadvantages of CCPs. (page 199) 3. Discuss the impact of central clearing on credit value adjustment (CVA), funding value adjustment (FVA), capital value adjustment (KVA), and margin value adjustment (MVA). (page 200) 29. Default Probabilities, Credit Spreads and Funding Costs After completing this reading, you should be able to: 1. Distinguish between cumulative and marginal default probabilities, (page 203) 2. Calculate risk-neutral default probabilities, and compare the use of risk-neutral and real-world default probabilities in pricing derivative contracts, (page 206) 3. Compare the various approaches for estimating price: historical data approach, equity based approach, and risk neutral approach, (page 207) 4. Describe how recovery rates may be estimated, (page 209) 5. Describe credit default swaps (CDS) and their general underlying mechanics. (page 210) 6. Describe the credit spread curve and explain the motivation for curve mapping, (page 211) 7. Describe types of portfolio credit derivatives, (page 211) 8. Describe index tranches, super senior risk, and collateralized debt obligations (CDOs), (page 212) 30. Credit and Debt Value Adjustments After completing this reading, you should be able to: 1. Explain the motivation for and the challenges of pricing counterparty risk. (page 219) 2. Describe credit value adjustment (CVA). (page 219) 3. Calculate CVA and the CVA spread with no wrong-way risk, netting, or collateralization, (page 219) 4. Evaluate the impact of changes in the credit spread and recovery rate assumptions on CVA. (page 221) 5. Explain how netting can be incorporated into the CVA calculation, (page 222) 6. Define and calculate incremental CVA and marginal CVA, and explain how to convert CVA into a running spread, (page 222) 7. Explain the impact of incorporating collateralization into the CVA calculation. (page 222) 8. Describe debt value adjustment (DVA) and bilateral CVA (BCVA). (page 223) 9. Calculate BCVA and BCVA spread, (page 223) 2018 Kaplan, Inc. Page xi Book 2 Reading Assignments and Learning Objectives 31. Wrong-way Risk After completing this reading, you should be able to: 1. Describe wrong-way risk and contrast it with right-way risk, (page 231) 2. 3. Discuss the impact of wrong-way risk on collateral and central counterparties. Identify examples of wrong-way risk and examples of right-way risk, (page 232) (page 237) 32. The Evolution of Stress Testing Counterparty Exposures After completing this reading, you should be able to: 1. Differentiate among current exposure, peak exposure, expected exposure, and expected positive exposure, (page 242) 2. Explain the treatment of counterparty credit risk (CCR) both as a credit risk and as a market risk and describe its implications for trading activities and risk management for a financial institution, (page 243) 3. Describe a stress test that can be performed on a loan portfolio and on a derivative portfolio, (page 244) 4. Calculate the stressed expected loss, the stress loss for the loan portfolio and the stress loss on a derivative portfolio, (page 243) 3. Describe a stress test that can be performed on CVA. (page 246) 6. Calculate the stressed CVA and the stress loss on CVA. (page 246) 7. Calculate the DVA and explain how stressing DVA enters into aggregating stress tests of CCR. (page 248) 8. Describe the common pitfalls in stress testing CCR. (page 249) 33. Credit Scoring and Retail Credit Risk Management After completing this reading, you should be able to: 1. 2. Explain the differences between retail credit risk and corporate credit risk. .Analyze the credit risks and other risks generated by retail banking, (page 254) (page 255) 3. Discuss the dark side of retail credit risk and the measures that attempt to address the problem, (page 255) 4. Define and describe credit risk scoring model types, key variables, and applications, (page 256) 5. Discuss the key variables in a mortgage credit assessment and describe the use of cutoff scores, default rates, and loss rates in a credit scoring model, (page 257) 6. Discuss the measurement and monitoring of a scorecard performance including the use of cumulative accuracy profile (CAP) and the accuracy ratio (AR) techniques, (page 258) 7. Describe the customer relationship cycle and discuss the trade-off between creditworthiness and profitability, (page 259) 8. Discuss the benefits of risk-based pricing of financial services, (page 260) 34. The Credit Transfer Markets and Their Implications After completing this reading, you should be able to: 1. Discuss the flaws in the securitization of subprime mortgages prior to the financial 2. crisis of 2007. (page 265) Identify and explain the different techniques used to mitigate credit risk, and describe how some of these techniques are changing the bank credit function, (page 267) Page xii 2018 Kaplan, Inc. Book 2 Reading Assignments and Learning Objectives 3. Describe the originate-to-distribute model of credit risk transfer and discuss the two ways of managing a bank credit portfolio, (page 268) 4. Describe the different types and structures of credit derivatives including credit default swaps (CDS), first-to-default put, total return swaps (TRS), asset-backed credit-linked note (CLN), and their applications, (page 269) 3. Explain the credit risk securitization process and describe the structure of typical collateralized loan obligations (CLOs) or collateralized debt obligations (CDOs). (page 273) 6. Describe synthetic CDOs and single-tranche CDOs. (page 273) 7. Assess the rating of CDOs by rating agencies prior to the 2007 financial crisis. (page 275) 35. An Introduction to Securitization After completing this reading, you should be able to: 1. Define securitization, describe the securitization process and explain the role of participants in the process, (page 281) 2. Explain the terms over-collateralization, first-loss piece, equity piece, and cash waterfall within the securitization process, (page 283) 3. Analyze the differences in the mechanics of issuing securitized products using a trust versus a special purpose vehicle (SPV) and distinguish between the three main SPV structures: amortizing, revolving, and master trust, (page 284) 4. Explain the reasons for and the benefits of undertaking securitization, (page 286) 5. Describe and assess the various types of credit enhancements, (page 287) 6. Explain the various performance analysis tools for securitized structures and identify the asset classes they are most applicable to. (page 288) 7. Define and calculate the delinquency ratio, default ratio, monthly payment rate (MPR), debt service coverage ratio (DSCR), the weighted average coupon (WAC), the weighted average maturity (WAM), and the weighted average life (WAL) for relevant securitized structures, (page 290) 8. Explain the prepayment forecasting methodologies and calculate the constant prepayment rate (CPR) and the Public Securities Association (PSA) rate, (page 293) 9. Explain the decline in demand in the new-issue securitized finance products following the 2007 financial crisis, (page 295) 36. Understanding the Securitization of Subprime Mortgage Credit .After completing this reading, you should be able to: 1. Explain the subprime mortgage credit securitization process in the United States. 2. (page 301) Identify and describe key frictions in subprime mortgage securitization, and assess the relative contribution of each factor to the subprime mortgage problems. (page 301) 3. Describe the characteristics of the subprime mortgage market, including the creditworthiness of the typical borrower and the features and performance of a subprime loan, (page 304) 4. Describe the credit ratings process with respect to subprime mortgage backed securities, (page 305) 5. Explain the implications of credit ratings on the emergence of subprime related mortgage backed securities, (page 305) 6. Describe the relationship between the credit ratings cycle and the housing cycle. (page 305) 2018 Kaplan, Inc. Page xiii Book 2 Reading Assignments and Learning Objectives 7. Explain the implications of the subprime mortgage meltdown on portfolio management, (page 306) 8. Compare predatory lending and borrowing, (page 306) Page xiv 2018 Kaplan, Inc. The following is a review of the Credit Risk Measurement and Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in: T h e C r e d i t D e c i s i o n Topic 16 E x a m F o c u s This topic provides an overview of the credit analysis process. Credit risk can arise from multiple sources, including default, an increased probability of default, failure to perform on a prepaid obligation, more severe losses than forecasted resulting from greater exposure than expected, or smaller recoveries than expected given a default. For the exam, be able to compare and contrast the credit analysis process for consumers (i.e., individuals), nonfinancial firms, financial firms, and to a lesser degree sovereigns. Also, be able to distinguish between the probability of default (PD), the loss given default (LGD), the exposure at default (EAD), and the overall expected loss (EL). Understand that it is simple to measure these factors after the fact but difficult to forecast losses in advance. Finally, understand that outside of times of stress or crisis, banks rarely fail. Credit analysts must determine where a financial institution falls on a continuum between perfectly creditworthy and bankrupt. C r e d i t R i s k