xVA Challenge

Fourth Edition

p. 61 Under the bullet point ‘Funding’ the correct text should be “this will not be the case”.
p. 227
Figure 9.4 caption should refer to a long equity position.
p. 295
Figure 11.8 caption should read “The latter corresponds to a swap where the cash flows are received semi-annually and paid annually”. 
p. 298
The discussion at the bottom of the page suggests that the cross-currency swap exposure will be large when the correlation is low. This depends on the FX pair with +100% or -100% being the largest depending of the directionality. In the spreadsheet example, positive correlation leads to a higher exposure. 
p. 314
Second sentence should read (numbers changed) “The amount that has to be funded is 8, which is partially uncollateralised value (5) and partly the initial margin that is posted (3).”
p. 319
bad wording under the four bullets at the top of the page: “the CDS market represents probably the most clean and directly available quotes”
p. 362
The value of $249,182 should read $259,182.
p. 364
First bullet point should read “defined by the term V-C”.
p. 403
RDR should be RFR.
p. 442
Reference to Andersen et al (2015) should be same authors (2017a) and (2017b).
p. 450
In the caption of Figure 15.24, “forward start swaption” should be “forward start swap”.
p. 467
“discount factors greater than zero” should be “discount factors greater than one”.
p. 479
In the bullet point below Figure 16.7, “current repo rate” should read “current repo haircut”.
p. 488
Equation (17.2) should have du term at the end.
p. 488
Below Equation (17.2) discount factor should have integral inside exponential function. 
p. 500
Equation (17.7c) should have lamda_P and not lamda_C (first term after integral).
p. 500
Below Equation (17.7c) discount factor should have integral inside exponential function.
p. 501
At the top, it should read “one party’s CVA is equal and opposite to the other’s DVA”.
p. 509
Just before Section 17.4.2. Stand-alone value should be -26.3 and not 17.9 bps and lower limit should be -9.0 and not -6.2 bps. 
p. 558
Bottom of page should be 20% RSF (not ASF).

Thanks to…

  • Dipanjan Biswas
  • Mark Blok
  • David Harper
  • Koichi Ito
  • Eason Lin
  • Byron Noon
  • Kibbs Osafo
  • Brian Smith
  • Mark Tomsett
  • Dai Yamashita
  • Fangzhou Zhang

Third Edition

p. 8 It is more accurate to say that IFRS 13 replaces the fair value (and therefore CVA) aspects of IAS 39 rather than the general statement that IFRS 13 replaces IAS 39.
p. 28 Reference to Section 5.5.2 should be Section 5.4.2.
p. 89 Should be a bracket after “Mechanism” four lines from top
p. 103 Table 6.6 caption should refer to total notional as of month end and not newly executed
p. 106 In the equation for net initial margin it should be (0.4 + 0.6 * NGR) * Gross initial margin. The calculation example that follows should give 2.46 and not 2.1
p. 124 In Figures 7.14 and 7.15, the EFV is not the sum of the EE and NEE which it should be (the EE and NEE profiles are correct)
p. 127
Footnote 12 should read “Depending on the currency, either swap or physical settlement may be most common.”
p. 130 Footnote 16 should refer to Table 7.2 not 7.3.
p. 131 Just above Figure 7.22 “lower netting value” should read “lower netting factor”
p. 136 Figure 7.27 – on the right hand side of the figure funding cost and funding benefit should be reversed
p. 137 Near the top of the page “complimentary” should be “complementary”
p. 138 Footnote 21 – reference should be IFR SSA Special Report 2012
p. 154 Two lines after equation (8.7) should read “surprising” and not “surprisingly”
p. 159 Figure 8.6 caption should refer to as a function of MTM (not maturity)
p. 159 No bracket after used on forth line from bottom
p. 161 Figure 8.8 – the bottom graph is missing the multiplier of 1.4 on the SA-CCR line (i.e. this line should be 40% higher). The CEM result assumes an NGR of 1 whereas 60% might be better gives this is a netting example (the problem is that the swaps are assumed to have a MTM of zero and hence the NGR is not defined due to a divide by zero!).
p. 169 Two lines before section 8.7.2 should read “CVA capital charge”
p. 170 Equation (8.14) should have X on second line instead of X^2
p. 171 Note that approval for specific risk is under the IMA (internal model approach)
p. 183
Third line should read “third component” and not “second component”
p. 218 In Figure 10.11 The y-axis labels and caption should be switched
p. 232 Footnote 15 should read “as in Section 7.4.2”
p. 237 Section 10.7.2 second line “in order to assess…..”
p. 241 Reference to Figure 10.28 should be Figure 10.27.
p. 301 Figure 13.1 is not a five-year interest rate swap as stated but a 10-year portfolio. This doesn’t change the analysis otherwise.
p. 306 Figure 13.6 caption should be “respondents” not “respondants”.
p. 307 The repo and CSA haircuts in the multiplier in Section 13.4.4 should be exchanged.
p. 310 Note that Equation 14.1 refers to the historic treatment and the minus is not required in the formulas that follow
p. 332 Second bullet point should read “A party unwinding, novating or restructuring a transaction might claim to recognise some of the DVA benefit since this may be paid out due to a reduction in their counterparty’s CVA”.
p. 343 In equation (15.3), the survival adjustment was removed. This is for simplicity and nothing mathematical. Market practice is still divergent on this point.
p. 356 In the last line on this page “price symmetry” should read “price asymmetry”.
p. 360 Reference to Table 6.1 should be Table 6.2
p. 367 Figure 16.5 caption should be “respondents” not “respondants”.
p. 369 Figure 16.7 is incomplete. Please see here.
p. 374 Four lines after equation (16.4) “this may seen” should be “this may seem”
p. 374 In the paragraph after Equation 16.4 the last line should read “Alternatively if the EL and KVA (second term above) is charged then there will seemingly be no cash to use for CVA hedging.”
p. 382 Near the bottom the sentence should be “Overall, the wrong-way collateralised exposure is around 50% higher than the normal collateralised exposure”
p. 384 Footnote 7 should be ignored.
p. 388 3rd line in second paragraph should read “The RV is smaller for better rated Sovereigns”.
p. 390 Reference to Figure 15.22 should be to Figure 17.12.
p. 393 Reference to Figure 14.1 should be to Figure 17.15.
p. 398 Complimentary should be Complementary.
p. 402 Reference to Section 5.5.2 should be Section 5.4.2.

NOTE: the Errata below are relevant only for the first print run of the book (which effects only a relatively small percentage of those sold).

p. 113 Figure 7.2 should have a white area below the x-axis to illustrate the exposure concept
p. 169 Instead of Appendix 8D I recommend reading Pykhtin (2012) in the bibliography
p. 172 The term PD(t_i-1,t_i) is slightly miswritten below equation 8.16 (see equation for correct notation)
p. 238 In Figure 10.24 caption it should say “Payer IRS 7Y” and not “Payer IRS 5Y”
p. 271 in equation 12.1 the s should be lower case
p. 280 In Figure 12.8 the line has printing incorrectly and should follow the best fit to the points shown
p. 300 fifth line from bottom should refer to spread (CS_X) and not (S_X) as in equation 13.1
p. 313 Number at the end of first paragraph should be -4.52 bps (per annum)
p. 359 Chapter 16 title should be “Margin and Capital Value Adjustments”
p. 364 The large S_IM should become small s_IM once in equation 16.1 and twice in the paragraph below. Note: the other S(.) should not change
p. 384 The sentence beginning “Cases of zero (top)……..” from figure 17.4 caption should not be there.

Thanks to…

  • Manuel Araos
  • Teimuraz Barbakadze
  • Andrew Cooke
  • Christian Crispoldi
  • Leonard Fichte
  • Sayoko Fujisawa
  • Naoyuki Fujita
  • Shota Fukamizu
  • Glen Gibson
  • Sergej Goriatchev
  • Kazuhisa Hirota
  • Toshiyuki Kitano
  • Alex Lee
  • Edvin Lundstrom
  • Richard Morrin
  • Kibbs Osafo
  • Yufi Pak
  • Francesco Ivan Pomarico
  • Kei Sagami
  • Andreas Schwaderlapp
  • Vera Sing
  • Salvatore Stefanelli
  • Norikazu Takei
  • Satoshi Terakado
  • Nana Yamada
  • Alex ?

Second Edition

Chapter 5

p. 62 It has been brought to my attention that in the collateral data represented in Figure 5.2 is double counted because “The collateral assets in this case are counted twice, once as received and once as delivered”. This means that the estimated collateral values needs to be halved and the ratio of 90% for year 2009 is actually around 45%.
p. 70 First paragraph, last sentence “Another reason for a collateral giver to pay a return in excess of OIS…” Should read “… a collateral receiver to pay…” as collateral receiver pays interest on received collateral.

Chapter 7

p. 112 The sentence about half-way down the page should read “For example, it is possible that an NCM may post less liquid margin to a GCM and then the GCM will in turn post the required more liquid margin to the CCP.”
p. 112 The sentence about two-thirds of the way down the page should read “However, we note that such a liquidity provision creates potentially dangerous problems because the fee for margin lending will increase as the credit quality of the borrower decreases.”

Chapter 8

p. 144 In formula (8.6) threshold_I and threshold_C should be switched.

Chapter 9

p. 155 On the fifth line “as already” should read “as will be”.
p. 194 In Figure 9.30 the secondary y-axis should read Ratio (bond divided by cash)

Chapter 10

p. 205 after equation (10.2) “where h defines the hazard rate of default, which is the conditional default probability in an infinitesimally small period.” Should read “where h defines the hazard rate of default which means that the conditional default probability in a period of length dt is given by h×dt).
p. 206 The hazard rates in the third column of Table 10.3 are obtained from the approximation in equation (10.3). The actual hazard rates that give the exact annual default probabilities in the last column of this table are 4.94%, 6.674%, 8.54%, 10.60% and 12.95%.
p. 215 (bottom of page) higher funding costs will tend to make the CDS-bond basis negative (not positive).

Chapter 12

p. 245 Appendix 12C just below the heading for section 12.1.3 should be Appendix 12B.
p. 245 Last paragraph, first sentence “The approximate formula in equation (12.2) is often not used for actual calculation…”. According to the context of the paragraph, the correct reference should be (12.3).
p. 246 In footnote 10, the reference to Equation (12.2) should be Equation (12.3)
p. 253 Equation 12.7 should have EE(tj) not EE(tj-1, tj)
p. 256 The more accurate spread referred to below equation (12.8) should be 2.61 bps (slightly higher than the approximation in the above equation)
p. 277 Should read “since the global financial crisis” at the start of the last paragraph.

Chapter 15

p. 323 Near the top of the page the sentence “In doing so, we assume a payer swap is a wrong-way (right-way) risk product for negative (positive) correlation…” This should be the opposite way around. A payer swap is a wrong-way product for positive correlation.  
p. 335
Appendix 15E is mentioned which does not exist. However, there is a paper that covers this in more detail which I’ll happily send on request.

Chapter 17

p. 381 Text near the bottom should read “can be replaced by the effective EPE without a collateral agreement in case this amount is lower”.
p. 389 On the third line Equation (7.4) should be Equation (17.4).
p. 396 Reference to Pykhtin(2011) should be as follows Pykhtin, M., 2011, “Counterparty risk capital and CVA” Risk, August.

Thanks to…

  • Vladimir Cheremisin
  • Daniel Dickler
  • Julia Fernald
  • Piero Foscari
  • Dimitrios Giannoulis
  • David Martinez
  • Henry Kwon
  • Kale Kakhiani
  • Ivan Pomarico
  • Erik van Raaij
  • Masum Shaikh
  • Richard Stratford
  • Todd Tauzer
  • Nick Vause
  • Shannon York

First Edition

Please also see here that some additional examples have been added in the spreadsheets.

Chapter 1

p. 5 Section 1.2.2 The reasons….arises should read “arise”, should have ever be applied – “be” should read “been”, to quantity such risks – should read “quantify”
p. 6 Section 1.3.1 “One of more underlying assets” – should read “one or more”, “a” is missing from “There is natural limitation”
p. 8 Section 1.4.2 “a relatively large number of dominant counterparties” if they are dominant can there be a large number of them?

Chapter 2

p. 15 Section 2.1.4 “With foreign exhange and credit default swaps….” this sentence should be part of the previous one.
p. 16 Section 2.1.5 “Only saving by last-ditch rescue” should read “saved”
p. 35 Section 2.5 “Unlike tradition single-horizon” should read “traditional”.
p. 36 Section 2.5.3 “What is the worse exposure” should read “worst”.
p. 37 Should read 95% not 99% in the example.
p. 38 The y-axis of Figure 2.9 should be labelled “PFE” and not “Expected exposure”.
p. 40 Under point (3) should read V(t) = mu.t +….

Chapter 3

p. 61 Section 3.6.2 should be “mortgagor” and not “mortgagee”.
p. 66 Section 3.7.2 “Whist” should read “Whilst”. Table 3.6 BBB-/Ba1 should read BB+/Ba1
p. 67 Table 3.7 BB+/Baa3 should read BB+/Ba1
p. 68 Table 3.8 BBB+/Ba3 should read BB-/Ba3
p. 70 In the example at the top of the page it should read 5% of $105,263 and not 5% of $105,000.
p. 71 Section 3.7.9 the full stop after “for example.to meet” should be removed
p. 93 Footnote 7 should read “divided by the variance of the index returns”.

Chapter 4

p. 87 It has been noted that in Figure 4.6 the y-axis should not be labelled PFE as this cannot be negative. Maybe it is best for the reader to simply ignore the one negative value in this figure.
p. 95 Alpha should be a on the third line after equation (4.8)
p. 98 Equation 4.10 should have n replaced by m.
p. 99 Equation 4.11 the numerator and denominator should be swapped.

Chapter 5

p. 110 s(D) should be replaced by s(E).
p. 112 near the bottom of the page, X should be replaced by E.
p. 117 The 0.225% value comes from assuming 0.5% normal interest rate volatility and scaling for a 10 day period SQRT(10/250) and assuming a swap duration of 4.5 years and finally dividing by 2 to approximate the time decay as linear.
p. 118 Figure 5.5 caption. “With” and “Without” should be swapped.
p. 127 An alternative way to consider the collateral formula is Max(Vs – K, 0) – MAX(-Vs – K, 0) – Collateral held and then to consider MTA and rounding of this amount.

Chapter 6

p. 138 First line of second paragraph “CDS” should read “CCDS”
p. 154 Equation 6.6 should not be a minus sign of the right.
p. 156 Section 6.5.1 could replace “unwinded positions” with “unwound”.
p. 161 Section 6.5.5 “Suitable high” should be replaced with “Suitably high”.

Chapter 7

p. 170 Last line the expression q(tj-1, tj) gives the marginal default probability in the interval between date t j-1 not tj+1as shown in the book.
p. 171 Line 20: The last column is a multiplication of the three (not four) numbers as the LGD is not included.
p. 182 Third line from bottom “insitution” and “counterparty” should be swapped. Also q(ti,ti-1) should be q(ti-1, ti)
p. 185 In the example, the BCVA should be 9 bps and not 11 bps
p. 186 footnote 13 “Boldholders” should read “Bondholders”
p. 195 EE is the top equation should rather be V
p. 195 CDS default payment leg is negative by convention so their should be a minus sign in the 4th, 5th and 6th equations.
p. 196 Under “payer swaption” it should read “Receiver swaption”
p. 199 In the second and fifth equations it should be BCVA and not CVA.

Chapter 8

p. 204 Section 8.2 “rather suprisingly” should be replaced by “rather surprising”.
p. 211 Section 8.3.3 μ=2% should be μ=-2%. Under Figure 8.4 the drift to mu=2%”, should be mu=-2%.
p. 216 Figure 8.8 in the title ‘put options’ should be replaced with ‘call options’
p. 239 Second to last equation should be just s with no superscript.
p. 239 last equation should have t replaced by s
p. 220 240 and 120 should be swapped.
p. 240 Last sentence before Appendix 8C should have normal distribution pdf around the two terms for A_+1 and A_+2
p. 241 2nd to last paragraph where Y=rho * Z +sqrt(1-rho^2) * Z it should be Y=rho * Z +sqrt(1-rho^2) * epsilon
p. 242 Equation at top of the page is missing a minus superscript on the second VCDS term
p. 242 Last equation first subscript on RHS should be A, A+a not A+a, B

Chapter 9

p. 270 Figure 9.11.1 potential problems ’causes’ should read ’caused’
p. 276 Figure 9.11.5 non-collateral should be non-collateralised

Chapter 10

p. 281 Figure 10.1 ‘an’ should be before ‘unexpected loss’ not ‘a’

Chapter 12

p. 334 Figure 12.2 “variability of possibility losses” – possibility should be replaced by possible
p. 337 Figure 12.2.6 “tranaction(s)” is spelt wrong – should be “transaction(s)”
p. 338 Figure 12.2.7 “related sophisticated” should read “relatively sophisticated”
p. 345 Figure 12.4.4 (for example under FAS 157. is missing a closing bracket
p. 345 Figure 12.4.5 “institution executes” should read “institution which executes”
p. 348 Sequence 3 numbers should read 1.54, -1.51, 2.35, 1.41

Chapter 13

p. 351 In opening paragraph “Achilles Heal” should read “Achilles Heel”
p. 364 Figure 13.2.7 “risk than is present” should read “risk that is present”/ “operate in a manner which” should read “operate in a manner to which”/ “compliment” should read “complement”

Chapter 14

p. 376 Figure 14.1.8 “resonable low” should read “reasonably low”/ “default on a single member” should read “default of a single member”

Chapter 15

p. 390 Figure 15.3 “Reporting tools and the ability…is important” should read “are important”
p. 391 Figure 15.4 “it not based” should read “is not based”


p. 398 “default a some” should read “default at some”

Thanks to…

  • Ronnie Barnes
  • Raymond Cheng
  • Michael Clayton
  • Wei-Ming Feng
  • Teddy Fredaigues
  • David Mengle
  • Hans-Werner Pfaff
  • Neil Schofield
  • Florent Serre
  • Ana Sousa
  • Carlos Sterling
  • Hidetoshi Tanimura
  • Frederic Vrins
  • Valter Yoshida
  • Guilherme Sanches
  • Arthur Guerin
  • Manuel Ballester