Financial Engineering and Computation: Corrigenda

# Financial Engineering and Computation

## Cambridge University Press, 2002

Preamble | Preface | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 | Chapter 6 | Chapter 7 | Chapter 8 | Chapter 9 | Chapter 10 | Chapter 11 | Chapter 12 | Chapter 13 | Chapter 14 | Chapter 15 | Chapter 16 | Chapter 17 | Chapter 18 | Chapter 19 | Chapter 20 | Chapter 21 | Chapter 22 | Chapter 23 | Chapter 24 | Chapter 25 | Chapter 26 | Chapter 27 | Chapter 28 | Chapter 29 | Chapter 30 | Chapter 31 | Chapter 32 | Chapter 33 | Bibliography | Index | Back cover | Acknowledgments

Substantial errors are colored red below.

## Preamble

1. 1st paragraph, line -3: , in keeping with'' should be to keep up with''
2. 3rd paragraph: delete the last sentence, Each instrument is treated in a short, self-contained chapter for ready reference use''
3. 4th paragraph, 1st sentence: coded in Java'' should be coded in Java or JavaScript''

## Preface

1. p. xiv, 2nd paragraph, line 2: the more challenging'' should be some of the more challenging''
2. p. xv, line -12: time-series models'' should be time series models''
3. p. xvii: CIR Cox-Ingersoll-Ross'' should be CIR Cox-Ingersoll-Ross (model)''
4. p. xviii: HJM Heath-Jarrow-Morton'' should be HJM Heath-Jarrow-Morton (model)''
5. p. xviii: RS Ritchken-Sankarasubramanian'' should be RS Ritchken-Sankarasubramanian (model)''

## Chapter 1

1. p. 1, Section 1.1, line -2: [ahead ... years]'' should be (ahead ... years)''
2. p. 3, Figure 1.1, caption, line -1: mortgage-backed security'' should be bold-faced
3. p. 4, line 4: , and leases'' should be , leases, and even future ticket sales of movies''
4. p. 5, table in 2nd paragraph: the font for heading Attribute Null? Type'' is inconsistent with that in other tables such as Figure 23.17 on p. 343

## Chapter 2

1. p. 7, line -1: take them into account'' should be take all into account''

## Chapter 3

1. p. 12, EXAMPLE 3.1.1, line 2: 1 year'' should be one year''
2. p. 12, Exercise 3.1.3: ~300,000'' should be approximately 300,000''
3. p. 12, Exercise 3.1.3: ~500,000'' should be approximately 500,000''
4. p. 16, EXAMPLE 3.3.2, line -2: delete the extra space before Interest ...''
5. p. 21, algorithm in Figure 3.4: Add c := a;\\'' after length := b - a;''
6. p. 21, Figure 3.4, caption, line -1: add Statement'' before the sentence
7. p. 26, line -3: add 2 sentences, Bonds selling at a premium are called premium bonds. Bonds selling at a discount are called discount bonds''
8. p. 28, 1 line above Subsection 3.5.4: add sentence Other possibilities exist, however.'' after ... the above formula.''
9. p. 29, 4 lines above EXAMPLE 3.5.3: the PV'' should be PV''
10. p. 30, EXAMPLE 3.5.4, line 2: The term'' should be The maturity''
11. p. 31, EXAMPLE 3.5.5, line 6: 12.767'' should be 11.31''
12. p. 31, Exercise 3.5.9, line 1: exactly'' should be exactly the period yield''
13. p. 31, NOTE 1: ''PV'' should be present value''
14. p. 31, NOTE 3: the 1st and the 2nd comma should not be bold-faced
15. p. 31, NOTE 5: the 1st and the 2nd comma should not be bold-faced

## Chapter 4

1. p. 34, 1st paragraph, line -3: Macaulay duration'' should be MD''
2. p. 34, 2nd paragraph, line -2: Exercise 4.1.3, Part (2)'' should be Exercise 4.1.3(2)''
3. p. 34, 2nd paragraph, line -1: may decrease'' should be should decrease by definition''
4. p. 35, middle of 1st paragraph: is Eq. (4.1)'' should be was shown in Eq. (4.1)''
5. p. 36, 1 line above Exercise 4.2.1: delete [55]''
6. p. 36, Exercise 4.2.2, line -1: equals modified duration'' should be equals the modified duration''
7. p. 38, Figure 4.5, caption, line -1: the rate moves'' should be the yield moves''
8. p. 39, 3rd paragraph, line -4 and line -3: Interest rates will fluctuate during the holding period, but it was assumed that ...'' should be simplified to Recall that it was assumed that ...''
9. p. 39, 4th paragraph, line -2: certificates of deposit'' and ''CDs'' should be bold-faced
10. p. 39, Exercise 4.2.8, line -1: falls short of'' should be ''is less than''
11. p. 40, Eq. (4.12): MD'' should be ''D''
12. p. 40, 1 line below Eq. (4.12): MD denotes ...'' should be ''D denotes ...''
13. p. 41, Subsection 4.2.4, 1st paragraph: Define dollar duration'' should be Define the dollar duration''

## Chapter 5

1. p. 46, Section 5.2, 1st paragraph, line -1: exactly that'' should be exactly that, as we will see shortly''
2. p. 47, Exercise 5.2.1, line -3: rate y'' should be yield y''
3. p. 47, Exercise 5.2.1, line -1: of the cash flow.'' should be of the corresponding cash flow.''
4. p. 48, 1st paragraph after EXAMPLE 5.3.1, line 4: step 3'' should be statement 3''
5. p. 48, 1st paragraph after EXAMPLE 5.3.1, line 6: Step 1'' should be Statement 1''
6. p. 48, 2nd paragraph after EXAMPLE 5.3.1, line 1: step 1'' should be statement 1''
7. p. 48, 2nd paragraph after EXAMPLE 5.3.1, line 2: -1 and'' should be -1, and''
8. p. 48, 2nd paragraph after EXAMPLE 5.3.1, line 3: step 3'' should be statement 3''
9. p. 48, Figure 5.4, caption, line -2: longest maturity bond'' should be longest-maturity bond''
10. p. 49, 2nd line from bottom of page: 5%'' should be ''8%''
11. p. 50, Section 5.5, 1st paragraph, line 4: Exercise 5.5.1, statement (1)'' should be Exercise 5.5.1(1)''
12. p. 50, Section 5.5, 1st paragraph, line -2: Exercise 5.5.1, statement (2)'' should be Exercise 5.5.1(2)''
13. p. 50, Section 5.5, 3rd paragraph, line -5: However, when'' should be When''
14. p. 51, line 8: delete implied'' from implied forward rate''
15. p. 52, EXAMPLE 5.6.1, 3rd paragraph, line -5: 1.708'' should be 1.708 dollars''
16. p. 53, Subsection 5.6.1, 1st paragraph, line 3: m-year'' should be m-period''
17. p. 55, algorithm in Figure 5.9, line -3: Replace it with p[i] := p[i-1]+(1-p[i-1]) * f[i];
18. p. 56, Exercise 5.6.11, line 1: this spot rate curve'' should be these spot rates''
19. p. 56, Subsection 5.6.4, 1st paragraph, line -3: (i-j)'' should be (j-i)''
20. p. 58, 1 line above Exercise 5.7.3: time-independent'' should be time independent''
21. p. 59, line -5: A horizon'' should be A person with a horizon''
22. p. 60, Subsection 5.8.1, line 7: relation between duration and MD (4.4)'' should be relation (4.4) between duration and MD''
23. p. 60, Subsection 5.8.1, 1st paragraph, line -3: (5.17):'' should be (5.17), then''
24. p. 60, Subsection 5.8.1, 1st paragraph, line -1: This measure'' should be This duration measure''
25. p. 60, Subsection 5.8.1, 2nd paragraph, line 2: often'' should be sometimes''
26. p. 60, line -3: delete Ho's''
27. p. 60, line -2: durations have'' should be duration has''
28. p. 61, Exercise 5.8.2: duration (5.17)'' should be duration formula (5.17)''
29. p. 61, 1 line below 5.8.2 Immunization'': The Case of NO Rate Changes'' should be The Case of No Rate Changes''
30. p. 61, 1st paragraph below The Case of NO Rate Changes, line 1: Recall that in ...'' should be In ...''
31. p. 61, line -3: 2nd summand should be braced with {...}
32. p. 61, line -2: 2nd summand should be braced with {...}
33. p. 62, line 8: We are'' should be We will be''
34. p. 63, Additional Reading, line 2: spread.'' should be spreads.''

## Chapter 6

1. p. 64, line -1: unbiased one'' should be the standard deviation''
2. p. 65, 1st paragraph, line -1: delete the extra Sj
3. p. 65, lines 5--6: Call X and Y uncorrelated random variables'' should be Call random variables X and Y uncorrelated''
4. p. 65, line -4: transpose'' should be bold-faced
5. p. 66, Subsection 6.1.2, line 1: have normal distribution'' should be have a normal distribution''
6. p. 66, Subsection 6.1.2, 2nd paragraph, line -2: Replace the sentence Then ... is normally distributed with mean ... and variance ... [343].'' with this sentence, Suppose furthermore that every linear combination Si=1 ti Xi is normally distributed with mean Si=1 ti mi and variance Si Sj ti tj Cov[Xi,Xj] [764].
7. p. 67, line 6: delete the'' from the X's''
8. p. 67, line -3: uniformly distributed'' should be bold-faced
9. p. 71, line 3: definedas'' should be defined as''
10. p. 72, Subsection 6.4.1, 1st paragraph, line -2: of (6.13)'' should be of expression (6.13)''
11. p. 73, Subsection 6.4.2, 1st paragraph, line -4: delete product'' from function product''
12. p. 73, Subsection 6.4.2, 1st paragraph, line -3: add , '' between xi'' and when''
13. p. 73, Subsection 6.4.2, 1st paragraph, line -2: qm'' should be qn''
14. p. 73, EXAMPLE 6.4.2, line -2: (yi - m)'' should be (xi - m)2''
15. p. 74, Subsection 6.4.3, 1st paragraph, line -1: where the moments'' should be where the population moments''
16. p. 74, Subsection 6.4.3, 2nd paragraph, line 1: delete name'' from the name''

## Chapter 7

1. p. 75, Section 7.1, 1st paragraph, line 5: by paying a'' should be for a''
2. p. 76, 2nd paragraph: merge the paragraph It is easier ...'' with the previous paragraph
3. p. 76, 2nd paragraph, last sentence: move the sentence For derivatives ... [60].'' to the end of p. 78's last paragraph before Section 7.4
4. p. 77, Figure 7.2, caption: Payoff'' should be Payoffs''
5. p. 77, 1st paragraph, line 6: S>X'' should be S< X''
6. p. 77, 1st paragraph, lines -4 and -3: Move the sentence Surprisingly, ... [340].'' to NOTES
7. p. 77, 1st paragraph, line -1: before expiration.'' should be before expiration as functions of the stock price.''
8. p. 78, 3rd paragraph, line -4: delete only'' from is only m/n''
9. p. 81, Subsection 7.4.2, 2nd paragraph, line 3: CH - CL.'' should be CL - CH.''
10. p. 83, Figure 7.11, caption, line -3: is set up'' should be is initially set up''

## Chapter 8

1. p. 84, Section 8.1, 2nd paragraph, line 2: PV'' should be value''
2. p. 85, Figure 8.1, caption, line 1: Price of fixed cash flow'' should be Price of a fixed cash flow''
3. p. 85, LEMMA 8.2.1, Proof, line 2: a net cash flow'' should be a positive net cash flow''
4. p. 86, LEMMA 8.2.4, Proof, last sentence: add the sentence Review Exercise 7.4.2.''
5. p. 86, Exercise 8.2.1, line 3: present value'' should be PV''
6. p. 87, 3rd line below LEMMA 8.3.1: delete comma from , as follows''
7. p. 88, Section 8.4, 1st paragraph, line -4: stock price once'' should be stock price declines once''
8. p. 89, 2nd paragraph, line 2: delete , S = 0''
9. p. 89, 2nd paragraph, line 3: a put ... tendered'' should be a put and a share of stock ... tendered for the stock''
10. p. 91, 2 lines below THEOREM 8.6.1, equation: >='' should be <=''

## Chapter 9

1. p. 94, 2nd paragraph, line -2: Again,'' should be So again,''
2. p. 94, Subsection 9.2.2, line 3: risk preferences'' should not be bold-faced
3. p. 95, 2nd paragraph, line -3: delete the FV''
4. p. 97, line 1: >'' should be >=''
5. p. 97, line 2: >'' should be >=''
6. p. 100, 1 line above Subsection 9.2.4: 12'' should be 1.2''
7. p. 99, 1st paragraph below A Numerical Example'', line -3: the PV of the expected'' should be the discounted expected''
8. p. 99, 2nd paragraph below A Numerical Example'', line 3: by delta'' should be by the delta''
9. p. 100, line -6: Step 1'' should be statement 1''
10. p. 100, line -2: step 1'' should be statement 1''
11. p. 101, algorithm in Figure 9.6, line -3: 2.1.'' should be 2.''
12. p. 101, line 1: Step 2.1'' should be statement 2''
13. p. 101, Figure 9.7, caption, line -4: step 1'' should be statement 1''
14. p. 103, algorithm in Figure 9.9, line 8: add {n choose a}'' between b:='' and pa''
15. p. 104, 1st paragraph, line -2: If'' should be Because''
16. p. 105, line 3: the period continuously'' should be the per-period continuously''
17. p. 105, 2nd paragraph, line 2: stock's true'' should be stock's empirical''
18. p. 105, 2nd paragraph, line -7: Eqs. (9.15),'' should be Eqs. (9.15), indeed,''
19. p. 105, 2nd paragraph, line -1: problems disappear'' should be problem disappears''
20. p. 105, equation on line -1: n'' should be sqrt(n)''
21. p. 106, line 2, equation: n'' should be within the square root
22. p. 106, 2nd paragraph, line 1: of a stock price'' should be of the stock price''
23. p. 106, Comment 9.3.2, line 1: between Eq. (9.13) and convergence (9.16)'' should be between limits (9.13) and (9.16)''
24. p. 107, 1st paragraph, equation on line -2: n'' should be sqrt(n)''
25. p. 107, THEOREM 9.3.4, line 1: delete The'' from The Black-Scholes Formula''
26. p. 108, 3 lines above Exercise 9.3.3: as a function'' should be as functions''
27. p. 108, Exercise 9.3.4: convergence (9.17)'' should be limit (9.17)''
28. p. 111, Subsection 9.4.1, line 5: exp[...]'' should be exp(...)''
29. p. 111, line -1: m'' should be m (t/n)''
30. p. 111, line -1: s2'' should be s2(t/n)''
31. p. 114, Section 9.6, section title: that'' should be capitalized
32. p. 114, Subsection 9.6.1, subsection title: that'' should be capitalized
33. p. 114, Figure 9.15: 30'' should be 15.052''
34. p. 115, Subsection 9.6.2, subsection title: that'' should be capitalized
35. p. 115, Subsection 9.6.2, 1st paragraph, line 4: Then'' should be Then in the single-period case''
36. p. 116, Subsection 9.6.3, subsection title: that'' should be capitalized
37. p. 116, Subsection 9.6.3, 1st paragraph, line -1: delete and memory''
38. p. 117, 1st paragraph, line 2: present value'' should be PV''
39. p. 117, 1st paragraph, line 5: during the life of the option'' should be before the option expires''
40. p. 117, 1st paragraph, line 6: equal'' should be set''
41. p. 117, 1st paragraph, line 7: equal'' should be set''
42. p. 117, 1st paragraph, lines -4 and -3: can be used'' should be gives the correct answer''
43. p. 117, 2nd paragraph, line 4: European'' should be American''
44. p. 117, 2nd paragraph, lines -2 and -1: As for American options, ... need to'' should be Needless to say, the algorithm should''
45. p. 117, Subsection 9.6.4, subsection title: that'' should be capitalized
46. p. 118, line 3: dividends Other'' should be dividends. Other''
47. p. 118, Exercise 9.6.7, line -1: algorithm'' should be setup''
48. p. 119, Figure 9.21, caption, line -3: indicated'' should be indicated as such''
49. p. 119, Figure 9.21, caption, line - 2: the parentheses in (optimal)'' should not be bold-faced
50. p. 119, Figure 9.21, caption, line - 1: append the sentence It is not required that ud = 1.''
51. p. 120, 1st paragraph, line 6: This idea'' should be The whole idea''
52. p. 121, Additional Reading, 1st paragraph, line 6: options formulas'' should be option formulas''
53. p. 121, Additional Reading, 1st paragraph, line -7:  "smile" '' should be smile''
54. p. 121, Additional Reading, 1st paragraph, lines -3 and -2: delete sentence "Implied binomial ... [770].''
55. p. 122, NOTES 3, line 2: his reasoning'' should be the rationale''

## Chapter 10

1. p. 123, quote: delete (1623--1662)''
2. p. 123, Subsection 10.1.1, 1st paragraph, line -2: delete an'' from for an illustration''
3. p. 124, line -1: delete an'' from for an illustration''
4. p. 125, Subsection 10.1.3, line -1: delete an'' from for an illustration''
5. p. 126, 1st paragraph, line -1: delete an'' from for an illustration''
6. p. 126, Subsection 10.1.5, line 4: delete an'' from for an illustration''
7. p. 127, Section 10.2, 1st paragraph, line -2: numerical differentiation'' should be numerical-differentiation''
8. p. 128, 1 line above Subsection 10.2.1: delete L and''
9. p. 128, Subsection 10.2.1, subsection title: Why Numerical Differentiation Fails'' should be Why Numerical Differentiation Fails for the Numerical Gamma''
10. p. 129, 1st paragraph, line 1: gamma computed'' should be the gamma computed''
11. p. 129, 1st paragraph, line 6: 10.2.1'' should be 10.7''
12. p. 129, Exercise 10.2.1, line 1: definition (10.2)'' should be formula (10.2)''

## Chapter 11

1. p. 131, 1st paragraph, line 2: nontrivial'' should be complex''
2. p. 131, Section 11.1, 1st paragraph, line 1: interpretated'' should be interpreted''
3. p. 132, 1st paragraph, lines -2 and -1: expected PV'' should be discounted expected value''
4. p. 132, lines -4: are equivalent'' should be are also equivalent''
5. p. 134, 1st paragraph, line -2: watch their value'' should be see their bond value''
6. p. 134, 2nd paragraph, line 1: Bondholders'' should be The bondholders''
7. p. 134, line -2: from the corporation'' should be from a corporation''
8. p. 135, Subsection 11.1.4, 1st paragraph, line 1: the parentheses in (CB)'' should not be bold-faced
9. p. 136, line 4: stockholders'' should be the stockholders''
10. p. 137, Section 11.2, 1st paragraph, line 5: X'' should be S''
11. p. 137, Section 11.2, 1st paragraph, line 6: X'' should be S''
12. p. 137, Section 11.2, 1st paragraph, line 8: X'' should be S''
13. p. 137, Section 11.2, 1st paragraph, line -2: X'' should be S''
14. p. 137, Equation (11.4): S >= H'' should be X >= H''
15. p. 138, line 3: S <= H'' should be X <= H''
16. p. 138, line 3: call'' should be put''
17. p. 138, line 4: Exercise 11.2.1, part(2)'' should be Exercise 11.2.1(2)''
18. p. 138, lines 4-5: See [660] or Exercise 17.1.6 for proofs'' should be See Exercise 17.1.6 for a proof''
19. p. 138, Exercise 11.2.2: American-style options'' should be American barrier options''
20. p. 138, algorithm in Figure 11.4, line 2: delete (H < X, H < S)''
21. p. 139, Figure 11.5: a clearer plot
22. p. 139, Subsection 11.2.1, line -1: delete a'' from with a strike price''
23. p. 140, Subsection 11.2.3, line 4: for a particular'' should be for at least a particular''
24. p. 140, Exercise 11.2.6, line -2: knocks out'' should be is knocked out''
25. p. 141, 3rd paragraph, line 2: notional principal'' should be bold-faced
26. p. 142, Figure 11.7, caption, lines 1 and 2: evident if we compare'' should be evident by comparing''
27. p. 142, 1st paragraph, line -1: Fig. 11.7.'' should be Fig. 11.7 for a sampling.''
28. p. 145, 2nd paragraph, line 3: identical:'' should be identical in the following sense:''
29. p. 146, Exercise 11.5.1, equation: add ,'' after 0'', S - XH'', and S - XL''
30. p. 146, Exercise 11.5.2, equation: add ,'' after S - X - p'' and - p''
31. p. 146, Exercise 11.5.3, equation: add ,'' after S - X'' and alpha (S - X)''
32. p. 146, Subsection 11.5.1, 1st paragraph, lines 3 and 4: the owner of foreign currencies'' should be its owner''
33. p. 146, Subsection 11.5.1, 1st paragraph, line 4: delete the'' from r in the foreign currency''
34. p. 147, Exercise 11.5.7: (Put-Call Parity)'' should be (Put-Call Parity).'' with .'' bold-faced
35. p. 148, Exercise 11.6.3, line 3: Describe the binomial tree algorithm for this option.'' should be Describe a binomial tree algorithm for pricing this option.''
36. p. 152, Figure 11.14, caption, line 2: reduce computation time'' should be reduce the computation time for European arithmetic average-rate options''
37. p. 152, Figure 11.14, caption, line 3: add the sentence This algorithm overestimates the option value [250].'' after ... [555].''
38. p. 152, Exercise 11.7.5, line 2: the average-rate'' should be the European average-rate''
39. p. 152, line -4: S0, S1, ..., Sk'' should be parenthesized: (S0, S1, ..., Sk)''
40. p. 152, Exercise 11.7.5, line -3: the average-rate'' should be the European average-rate''
41. p. 153, Additional Reading, lines 3 and 4: An O(...)-time approximation algorithm'' should be Other O(...)-time approximation algorithms''

## Chapter 12

1. p. 155, Section 12.1, 2nd paragraph, line 4: financial instrument'' should be financial instruments''
2. p. 156, line -2: default on'' should be defaulted on''
3. p. 157, line -2: result from'' should be be secured by''
4. p. 157, line -1: result from'' should be be secured by''
5. p. 158, line 2: check that'' should be check that the parity becomes''
6. p. 158, Exercise 12.2.3, line 4: , where'' should be by setting''
7. p. 158, line -6: delete [510]''
8. p. 160, 4 lines and 3 lines above The Underlying Asset Pays a Continuous Dividend Yield: a sufficient fund'' should be sufficient funds''
9. p. 160, line -5: There is a sufficient fund'' should be There are sufficient funds''
10. p. 161, Section 12.3, 1st paragraph, line -3: gain or loss'' should be gains or losses''
11. p. 162, 3rd paragraph, lines 4 and 5: options on stock index'' should be stock index options''
12. p. 163, line -1: how'' should be how the amount''
13. p. 164, Subsection 12.3.2, 2nd paragraph, line -2: end of day zero'' should be beginning of day one''
14. p. 166, lines -6 and -5: cash flows generated by the asset D'' should be the cash flow D generated by the asset''
15. p. 169, EXAMPLE 12.4.3, line 1: with strike'' should be with strike price''
16. p. 169, EXAMPLE 12.4.3, line -2: September'' should be December''
17. p. 170, 1 line above (12.14): delete when they are exercised''
18. p. 170, Equation (12.14): add ,'' at the end
19. p. 170, Equation (12.15): add .'' at the end
20. p. 170, Subsection 12.4.1, 2nd paragraph, line 3: futures/forward prices'' should be futures or forward price''
21. p. 171, line 2: PV'' should be discounted value''
22. p. 171, line 2: max(F - X, 0)'' should be (F - X)''
23. p. 171, Subsection 12.4.2, lines 1 and 4: move [81]'' to follow 1976''
24. p. 171, Subsection 12.4.2, line 6: Formulas (12.16)'' should be the above formulas''
25. p. 171, Subsection 12.4.2, 2nd paragraph, line 3: add )'' after or T.''
26. p. 171, Subsection 12.4.2, 2nd paragraph, line 3: delete then''
27. p. 171, Subsection 12.4.2, 2nd paragraph, line 4: The delta for the call'' should be The deltas''
28. p. 171, Subsection 12.4.2, 2nd paragraph, line 5: spot price:'' should be spot price; for example:''
29. p. 172, Subsection 12.4.3, 1st paragraph, line -3: (12.15)'' should be formula (12.15)''
30. p. 172, Subsection 12.4.3, 3rd paragraph, line 3: To set up an'' should be An''
31. p. 172, Subsection 12.4.3, 3rd paragraph, line 5: , we set up'' should be satisfies''
32. p. 173, Section 12.5, 1st paragraph, line -1: forward-rate agreement'' should be forward rate agreement''
33. p. 175, Subsection 12.5.2, 1st paragraph, line 1: of currency'' should be of a currency''
34. p. 175, EXAMPLE 12.5.2, line 1: 2-year'' should be 3-year''

## Chapter 13

1. p. 179, Section 13.2, 1st paragraph, line 5: says'' should be says that''
2. p. 180, Exercise 13.2.2, line 3: 6.4.3, part (2)'' should be 6.4.3(2)''
3. p. 181, Exercise 13.2.8, line 5: 11.5.4, part (1)'' should be 11.5.4(1)''
4. p. 182, Subsection 13.2.2, 1st paragraph, line 1: Futures prices form'' should be The futures price is''
5. p. 182, Subsection 13.2.3, 1st paragraph, line 4: times,'' should be times and does not pay dividends,''
6. p. 182, Subsection 13.2.3, 1st paragraph, line 4: says'' should be says that''
7. p. 182, Subsection 13.2.3, 1st paragraph, line -2: add in other words, '' after ;''
8. p. 183, Exercise 13.2.12, line 3: the binomial option pricing model'' should be the BOPM''
9. p. 183, Exercise 13.2.13, line 1: delete risk-neutral''
10. p. 185, Exercise 13.3.4, line 4: delete ,'' from , and''
11. p. 185, Subsection 13.3.1, line -9: (...)/2'' should be [ ... ]/2''
12. p. 185, Subsection 13.3.1, line -7: (...)/2'' should be [ ... ]/2''
13. p. 186, Exercise 13.3.7, line 1: add ,'' after "}"
14. p. 188, Section 13.4, line 1: process'' in Brownian bridge process'' should be bold-faced
15. p. 188, Section 13.4, line 1: Brownian motion'' in tied-down Brownian motion'' should be bold-faced
16. p. 188, Additional Reading, line 2: Add  (1910--2004)'' after Doob''

## Chapter 14

1. p. 191, 2nd paragraph, lines -6 and -5: , written as'' should be :''
2. p. 191, 2nd paragraph, line -2: says'' should be says that''
3. p. 191, 2nd paragraph, line -1: , and a'' should be . One''
4. p. 192, Exercise 14.1.2, line -1: (...)/2'' should be [ ... ]/2''
5. p. 192, Comment 14.1.2, line 3: point ... point'' should be points ... points''
6. p. 193, Section 14.2, 1st paragraph, line 6: Langevin's work'' should be Langevin''
7. p. 193, Section 14.2, 1st paragraph, line 9: delete an'' from an instantaneous''
8. p. 193, Section 14.2, 1st paragraph, line 10: delete of'' from drift of''
9. p. 193, Section 14.2, 1st paragraph, line 10: delete an'' from an instantaneous''
10. p. 193, Section 14.2, 1st paragraph, line 10: delete of'' from variance of''
11. p. 193, Section 14.2, 1st paragraph, line 12: mean zero and variance dt'' should be zero mean and a variance of dt''
12. p. 193, line -1: delete an'' from an illustration''
13. p. 194, 2nd paragraph, line 5: The'' should be A''
14. p. 194, Equation (14.7): a[...] ... b[...]'' should be a(...) ... b(...)''
15. p. 194, Subsection 14.2.2, 1st paragraph, line 1: Consider an'' should be Consider the''
16. p. 196, THEOREM 14.2.2: (Higher-Dimensional Ito's Lemma)'' should be (Higher-Dimensional Ito's Lemma).'' with .'' bold-faced
17. p. 198, Exercise 14.3.6: there should be an extra +g2dt'' term
18. p. 199, Figure 14.4, caption, line 3: add extra space after 0.3''
19. p. 199, 2nd paragraph, line 1: property'' in mean-reversion property'' should be bold-faced
20. p. 199, line -2: structure'' should be structures''
21. p. 199, line -1: volatility'' should be volatilities''
22. p. 199, line -1: return'' should be returns''
23. p. 200, Exercise 14.3.10, line -2: price'' should be prices''
24. p. 200, Subsection 14.3.2, line -1: for an illustration'' should be for illustration''
25. p. 200, Subsection 14.4.1, line -2: add an'' before European''
26. p. 202, 4 lines above Exercise 14.4.2: with longer'' should be with a longer''
27. p. 202, line -3: delete be''
28. p. 203, 3 lines above Exercise 14.4.2: interest'' should be short''
29. p. 203, Exercise 14.4.2, line 2: interest'' should be short''
30. p. 204, 1 line above Exercise 14.4.5: delete ('' and )''
31. p. 204, Exercise 14.4.8, line 4: delete the extra space between sigma^2'' and T'' in 2 places
32. p. 204, line -8: add ,'' after u''
33. p. 204, line -7: add ,'' after d''
34. p. 205, NOTE: delete all''

## Chapter 15

1. p. 206, 1st paragraph, line 3: to derivatives'' should be to many derivatives''
2. p. 207, 1st paragraph, line 3: the parentheses in (heat)'' should not be bold-faced
3. p.207, 1st paragraph, line -3: to generalized forms'' should be to a generalized form''
4. p. 207, Section 15.2, 1st paragraph, line -2: and forces'' should be , forcing''
5. p. 207, Section 15.2, 2nd paragraph, line 2: motion'' should be motion process''
6. p. 207, Section 15.2, 2nd paragraph, lines -2 and -1: delete (in years)''
7. p. 211, Subsection 15.2.3, 1st paragraph, line -4: The accuracy is even better if'' should be For numerical reasons,''
8. p. 211, Subsection 15.2.3, 1st paragraph, line -3: is'' should be may be''
9. p. 211, Subsection 15.2.3, equations, line 1: add ,'' after X - S''
10. p. 211, Subsection 15.2.3, equations, line 2: add ,'' after X - S''
11. p. 211, Subsection 15.2.3, equations, line 3: add ,'' after X - S''
12. p. 211, Subsection 15.2.3, equations, line 4: add ,'' after 0''
13. p. 212, 2nd paragraph, equations, line 1: add ,'' after S - X''
14. p. 212, 2nd paragraph, equations, line 2: add ,'' after S - X''
15. p. 212, 2nd paragraph, equations, line 3: add ,'' after S - X''
16. p. 212, 2nd paragraph, equations, line 4: add ,'' after 0''
17. p. 215, 1st paragraph, equations: move label (15.7)'' to line 1 of equation
18. p. 215, Exercise 15.3.6: (Euler's Theorem).'' should be (Euler's Theorem).'' with .'' bold-faced
19. p. 215, Exercise 15.3.9: (Put-Call Parity).'' should be (Put-Call Parity).'' with .'' bold-faced
20. p. 215, Subsection 15.3.6, 2nd paragraph, line 2: that foreign currency'' should be that a foreign currency''
21. p. 217, 1st paragraph below Cross-Currency Options, line -1: add from the earlier ones'' after different''
22. p. 217, 3 lines above Exercise 15.3.14: there should be an extra +s 2Cdt'' term
23. p. 218, line -4: delete the extra space before In fact''
24. p. 219, line -16: delete and'' from and relation''
25. p. 219, line -13: add if'' before 1000 x''
26. p. 219, line -12: add if'' before V(T)<=''

## Chapter 16

1. p. 225, Subsection 16.2.2, 1st paragraph, line 6: delete cash market''
2. p. 225, Subsection 16.2.2, 1st paragraph, line -2: delete cash''
3. p. 226, Subsection 16.2.3, 1st paragraph, line -2: if'' should be when''
4. p. 229, 3 lines above (16.3): delete net'' from dollars net''
5. p. 229, line -11: ~68%'' should be approximately 68%''
6. p. 229, line -9: delete to'' from decrease to''
7. p. 229, line -1: delete with zero value''
8. p. 231, Subsection 16.3.2, line 3: is like'' should be is like a''
9. p. 232, 1st paragraph, line 4: delete with zero value''
10. p. 232, line -4: look back'' should be lookback''

## Chapter 17

1. p. 234, Section 17.1, 1st paragraph, line 1: add process'' after motion''
2. p. 234, Section 17.1, 1st paragraph, line -5: works'' should be meets the requirements''
3. p. 234, Section 17.1, 1st paragraph, line -1: convergence'' should be limit''
4. p. 235, Equation (17.2): (...) for even ... b'' should be (...), for even ... b,''
5. p. 235, Figure 17.1, caption: delete sentence Two paths ...).''
6. p. 236, 3rd paragraph, line 3: S line'' should be H line''
7. p. 237, Figure 17.3, algorithm, line -5: swap p'' and (1-p)''
8. p. 237, Figure 17.3, algorithm, line -4: swap u'' and d''
9. p. 237, 1st paragraph, line 6: :'' should be because''
10. p. 238, Programming Assignment 17.1.10, line 2: 11.7.11, part (1)'' should be 11.7.11(1)''
11. p. 238, line -2: *'' should be 1''
12. p. 239, Figure 17.4, caption, line 1: calls. A'' should be calls: a''
13. p. 239, Equation (17.7): add where'' before l \equiv''
14. p. 241, 1st paragraph, line -3: H u2 should be X but paying zero unless S(t)>H
15. p. 241, 1st paragraph, line -2: is'' should be is again''
16. p. 241, Exercise 17.1.16, lines 2 and 3: add ,'' before for'' (4 places)
17. p. 242, Section 17.2, 1st paragraph, line 1: add process'' after motion''
18. p. 242, Section 17.2, 1st paragraph, line -4: We need'' should be We also need''
19. p. 243, line 2: which resulting'' should be which the resulting''
20. p. 243, Subsection 17.2.1, line 9: min'' should be max''
21. p. 244, Figure 17.8, line 2: delete H < X,''
22. p. 244, 1st paragraph, line 1: like'' should be Like''
23. p. 248, Exercise 17.3.5: (Optimal Hedge Ratio)'' should be (Optimal Hedge Ratio).'' with .'' bold-faced

## Chapter 18

1. p. 249, Section 18.1, 2nd paragraph, lines 1 and 2: By replacing'' should be We replace''
2. p. 249, Section 18.1, 2nd paragraph, line 4: axis, the ... is'' should be axis. The ... becomes''
3. p. 255, 1st paragraph, line 9: add a period
4. p. 255, 1st paragraph, line -3: add once and for all'' after tridiagonal matrix''
5. p. 255, line -3: have a joint distribution'' should be are random variables''
6. p. 258, Exercise 18.2.4, liine 2: add process'' after motion''
7. p. 258, Exercise 18.2.4, liine 4: add the'' before normal''
8. p. 259, 2nd line below subsubsection Antithetic Variates: delete independent''
9. p. 259, 6th line below subsubsection Antithetic Variates: add thus'' before smaller''
10. p. 259, 8th line below subsubsection Antithetic Variates: technique'' should be bold-faced
11. p. 260, EXAMPLE 18.2.2, line -1: add using this idea'' before the period
12. p. 260, Figure 18.7, caption, line 2: m is the number replications'' should be 2m is the number sample paths''
13. p. 261, 1st paragraph, line 1: There'' should be Suppose there''
14. p. 261, 1st paragraph, line 6: delete we obtain by''
15. p. 266, EXAMPLE 18.3.2, line 7: add component'' after c2''
16. p. 266, Additional Reading, 2nd paragraph, line 4: component'' after c2''
17. p. 267, NOTES, line -1: add a period after 11010''

## Chapter 19

1. p. 268, line -5: add a period
2. p. 269, Figure 19.1, caption, line 2: (left to right)'' should be (from left to right)''
3. p. 271, line 2: delete furthermore''
4. p. 272, subsubsection Generation of the Multivariate Normal Distribution, 1st paragraph, line 2: distribution'' should be covariance structure''
5. p. 272, THEOREM 19.1.1: (SVD)'' should be (SVD).'' with .'' bold-faced
6. p. 275, THEOREM 19.2.10: (Underdetermined Linear Equations)'' should be (Underdetermined Linear Equations).'' with .'' bold-faced
7. p. 276, Exercise 19.2.13: (Lawson-Hanson Algorithm)'' should be (Lawson-Hanson Algorithm).'' with .'' bold-faced
8. p. 280, EXAMPLE 19.3.1, line 2: add ,'' before y4=4.''
9. p. 281, Figure 19.7, caption, line 2: just a data point'' should be just one data point''
10. p. 282, Subsection 19.3.3, 1st paragraph, line 1: Bi'' should be Bi(x)''

## Chapter 20

1. p. 287, Exercise 20.1.3: add of the Ogden model'' before the period
2. p. 287, Subsection 20.1.1: move the 1st sentence of the first paragraph to head the second paragraph
3. p. 288, Subsection 20.1.2, 1st paragraph: form'' in semistrong form'' should be bold-faced
4. p. 288, Subsection 20.1.2, 1st paragraph: form'' in strong form'' should be bold-faced
5. p. 289, line 14: effect'' should be effects''
6. p. 289, line 18: ; thus'' should be :''
7. p. 290, line -5: white noise'' should be white noise process''
8. p. 293, line 12: Exercise 20.2.3, part (1)'' should be Exercise 20.2.3(1)''
9. p. 293, line 15: Exercise 20.2.3, part (2)'' should be Exercise 20.2.3(2)''
10. p. 293, Additional Reading, line 1: time-series'' should be time series''
11. p. 293, Additional Reading, line -5: sampled; the'' should be sampled. The''

## Chapter 21

1. p. 298, line -9: add ,'' after therefore''
2. p. 298, line -7: delete the'' from the 6-month''
3. p. 300, 2nd paragraph, line 2: now that June 1995'' should be that now (June 1995)''
4. p. 301, Subsection 21.1.4, 2nd paragraph, line -5: 8%'' should be 6%''
5. p. 301, Subsection 21.1.4, 3rd paragraph, line -5: 8%'' should be 6%''
6. p. 301, Subsection 21.1.4, 3rd paragraph, line -1: replace 1.04'' with 1.03'' (4 places)
7. p. 302, 2nd paragraph, line 4: 8%'' should be 6%''
8. p. 302, 2nd paragraph, line 6: Replace 1.04'' with 1.03'' (2 places)
9. p. 302, 2nd paragraph, line 6: 148.42'' should be 178.72''
10. p. 302, 2nd paragraph, line 7: 1.4842'' should be 1.7872''
11. p. 302, 2nd paragraph, line -2: Replace 1.04'' with 1.03'' (2 places)
12. p. 302, 2nd paragraph, line -2: 148.66'' should be 179.26''
13. p. 302, 2nd paragraph, line -1: 1.4866'' should be 1.7926''
14. p. 303, Exercise 21.1.3, line 1: 8%'' should be 6%''
15. p. 303, EXAMPLE 21.1.6, line 2: 1.0982'' should be 1.3374''
16. p. 303, EXAMPLE 21.1.6, line -3: 8%'' should be 6%''
17. p. 303, EXAMPLE 21.1.6, line -3: 1.0982'' should be 1.3374''
18. p. 303, EXAMPLE 21.1.6, line -2: 1.0982'' should be 1.3374''
19. p. 303, EXAMPLE 21.1.6, line -2: 97.997'' should be 80.470''
20. p. 304, Subsection 21.1.5, 1st paragraph, line 3: 8%'' should be 6%''
21. p. 305, line 16: add both 3-'' should be both the 3-''
22. p. 309, Figure 21.6, caption, line 1: delete the'' from the LIBOR''
23. p. 309, subsection 21.2.4, 2nd paragraph, line 1: Replace caps'' with caplets'' (2 occurrences)
24. p. 309, subsection 21.2.4, 2nd paragraph, line 1: Replace floors'' with floorlets''
25. p. 309, subsection 21.2.4, 2nd paragraph, line 3: Replace cap's'' with caplet's''
26. p. 312, Figure 21.8, caption, line 2: (93-futures price)'' should be max(93-futures price,0)''
27. p. 313, line 7: delete the'' from over the LIBOR''
28. p. 313, 5 lines above EXAMPLE 21.4.1: delete the'' from the LIBOR''
29. p. 313, 2 lines above EXAMPLE 21.4.1: delete the'' from the LIBOR''
30. p. 313, line -7: delete the'' from the LIBOR''
31. p. 313, line -1: delete the'' from the LIBOR''
32. p. 314, line 3: delete the'' from the LIBOR''
33. p. 314, line 6: delete the'' from the LIBOR''
34. p. 314, lines 7-8: delete the'' from the LIBOR''
35. p. 314, line -4: delete the'' from the 6-month LIBOR''
36. p. 315, line 6: delete a'' from a 6-month''
37. p. 315, line 11: delete the'' from the 6-month LIBOR''
38. p. 316, line 1: delete the'' from the LIBOR''
39. p. 316, EXAMPLE 21.4.2, line 1: delete the'' from the 6-month LIBOR''
40. p. 316, Exercise 21.4.2, line 2: delete the'' from the 6-month LIBOR''
41. p. 316, subsubsection Valuation of Swaps as a Package of Forward Rate Agreements: Forward Rate Agreements'' should be FRAs''
42. p. 317, EXAMPLE 21.4.3, line 2: delete the'' from the 6-month LIBOR''
43. p. 319, displayed equation for at: add ,'' after 0,'' b0,'' b1,'' b2,'' b3,'' b4,'' and 1''

## Chapter 22

1. p. 321, Section 22.1, 2nd paragraph, line 1: A functional'' should be In term structure fitting, usually a functional''

## Chapter 23

1. p. 328, Section 23.1, 1st paragraph, line 3: delete the quotes around the word consistent''
2. p. 328, Section 23.1, 1st paragraph, line -2: consistent'' should be compatible''
3. p. 329, 2 lines above (23.1): Exercise 23.2.3, part (1)'' should be Exercise 23.2.3(1)''
4. p. 329, line -1: Exercise 23.2.3, part (2)'' should be Exercise 23.2.3(2)''
5. p. 333, lines 2-3 below An Approximation Calibration Scheme: delete . This certainly works in a deterministic economy''
6. p. 334, line 9: Exercise 23.2.5, part (1)'' should be Exercise 23.2.5(1)''
7. p. 334, Subsection 23.2.2, 1st paragraph, line 7: delete and r1, r2, ... , rm-1''
8. p. 334, Subsection 23.2.2, 1st paragraph, line 8: delete , thus hopelessly slow [508]''
9. p. 334, Subsection 23.2.2, 2nd paragraph, line 3: add , we recall, '' after ''This number''
10. p. 334, Subsection 23.2.2, 2nd paragraph, line 3: state price'' should not be bold-faced
11. p. 334, Subsection 23.2.2, 3rd paragraph, line 3: delete comma from , corresponding''
12. p. 335, Figure 23.8, caption, line 2: add derived'' before from''
13. p. 336, algorithm in Figure 23.9, line -4: delete the enclosing parentheses ( ... )'' below P[ j ]
14. p. 336, line 5: delete , each consuming O(n) work''
15. p. 339, line 6: wide'' should be many''
16. p. 339, lines 9-10: step 1 ... step 2 ... step 3'' should be statement 1 ... statement 2 ... statement 3''
17. p. 340, Figure 23.14, caption, line -2: model'' should be market''
18. p. 341, Figure 23.15, caption, line 3: rate'' should be rates''
19. p. 341, Subsection 23.3.3, line 6: 2 years'' should be two years''
20. p. 342, Programming Assignment 23.3.7, line 1: delete European''
21. p. 343, line 1: delete [84]''
22. p. 344, 2nd paragraph, line -1: is covered'' should be will be covered''

## Chapter 24

1. p. 346, Section 24.2, line 2, equations, line 1: add ,'' after (T-t)''
2. p. 346, Section 24.2, line 2, equations, line 2: add ,'' after (T-t)''
3. p. 346, Section 24.2, line 5, equations, line 1: add ,'' after t+1)''
4. p. 346, Section 24.2, line 5, equations, line 2: add ,'' after t)''
5. p. 346, Section 24.2, line 10: Exercise 24.2.1, part (1)'' should be Exercise 24.2.1(1)''
6. p. 348, Exercise 24.2.10, line 4: add extra space between ]'' and sigma(t)^2''
7. p. 348, Section 24.3, line 3: t+1 < T'' should be t < T''
8. p. 349, 3rd paragraph, line 2: at times'' should be at future times''
9. p. 349, line -5: delete the multiplication operator x''
10. p. 350, Exercise 24.3.2, line 5: Exercise 5.7.3, part (2)'' should be Exercise 5.7.3(2)''
11. p. 351, Equation (24.10): replace equivalence sign with =''
12. p. 351, line -6: delete [76]''
13. p. 353, Section 24.5: Forward-Rate Process'' should be Forward Rate Process''
14. p. 353, Section 24.5, line 5: forward-rate process'' should be forward rate process''
15. p. 353, Exercise 24.5.1: delete directly''
16. p. 355, Subsection 24.6.1, table on line 3: the font for heading Year 1 2'' and table contents is inconsistent with that in earlier tables such as Figure 23.17 on p. 343
17. p. 355, Subsection 24.6.1, 2nd paragraph, line -3: an up'' should be a down''
18. p. 356, Exercise 24.6.8: (Dynamic Immunization)'' should be (Dynamic Immunization).'' with .'' bold-faced
19. p. 358, line 1: 10% - one-year rate'' should be (10% - one-year rate)''

## Chapter 25

1. p. 361, Section 25.1, line 1: the model'' should be a model''
2. p. 362, Exercise 25.1.3, line 1: Show'' should be Prove''
3. p. 362, Exercise 25.1.5, displayed equation: add extra space between ]'' and dt''
4. p. 363, Exercise 25.1.6, line 1: sv2'' should be v(t,T)2B(t,T)2''
5. p. 363, line -1: add further'' after explored''
6. p. 365, Exercise 25.2.2: Show'' should be Prove''
7. p. 365, Exercise 25.2.4: (Affine Models)'' should be (Affine Models).'' with .'' bold-faced
8. p. 365, Exercise 25.2.4, line 1: add (1)'' before For any ...''
9. p. 366, Subsection 25.2.1, line 4: Exercise 25.2.14, part (1)'' should be Exercise 25.2.14(1)''
10. p. 368, line 7: PA (...)'' should be PA [ ... ]''
11. p. 369, table on line 3: the font for heading Discount factor Year (Now) (Time Delta t; up state)'' and table contents is inconsistent with that in earlier tables such as Figure 23.17 on p. 343
12. p. 369, 3 lines above Subsection 25.2.2: ... pricing. We ...'' should be ... pricing: We ...''
13. p. 369, Subsection 25.2.2, 1st paragraph, equation, line 5: replace the yu'' in the numerator with yd''
14. p. 369, Subsection 25.2.2, 1st paragraph, line 6: delete +'' from yu+''
15. p. 370, Exercise 25.2.14, line 1: Show ... untransformed ...'' should be Confirm ... original, untransformed ...''
16. p. 371, Section 25.4, line 2: approach'' in time-series approach'' should be bold-faced
17. p. 371, Section 25.4, line -3: approach'' in cross-sectional approach'' should be bold-faced
18. p. 372, 2nd paragraph, line 5: delete [234]''
19. p. 372, 3rd paragraph, line 5: delete [42,149]''
20. p. 373, 4 lines above Exercise 25.5.1: replace Si X'' with Si ci Xi''
21. p. 374, line 5: fit'' should be fits''
22. p. 374, 2nd paragraph, line -1: emerges.'' should be emerges here.''

## Chapter 26

1. p. 375, Section 26.1, 2nd paragraph, line 2: delete citation [477,482]''
2. p. 376, line 5: delete it is not hard to see that,''
3. p. 376, line 7: add comma after (Exercise 26.2.1)''
4. p. 377, Subsection 26.2.1, 1st paragraph, line 7: delete reference 504'' from [304,504]''
5. p. 377, Subsection 26.2.1, 2nd paragraph, line 1: delete all''
6. p. 377, Subsection 26.2.1, 3rd paragraph, line 4: delete citation [359]''
7. p. 379, Exercise 26.2.9, line 4: add The'' before T''
8. p. 380, Problems with no-arbitrage models in general: Make it a subsection instead of subsubsection
9. p. 380, Section 26.3, 1st paragraph, line 6: comparison'' should be contrast''
10. p. 381, line 1: these'' should be the following''
11. p. 381, Subsection 26.3.1, 3rd paragraph, line 1: delete let''
12. p. 381, Subsection 26.3.1, 3rd paragraph, line 2: delete let''
13. p. 382, algorithm in Figure 26.3, line 13: delete the enclosing parentheses ( ... )'' below P[ j ]
14. p. 382, algorithm in Figure 26.3, line 14: delete the enclosing parentheses ( ... )'' below Pu[ j ]
15. p. 382, algorithm in Figure 26.3, line 14: delete the enclosing parentheses ( ... )'' below Pd[ j ]
16. p. 382, Figure 26.3, caption, line 4: Eqs'' should Eq''
17. p. 382, line 3: delete reference 149'' from 149,508]''
18. p. 383, line -4: longterm'' should be long-term''
19. p. 384, line 2: has to be carried out for'' should be is tailored to''
20. p. 384, Section 26.4, 1st paragraph, line 5: theta(.)'' should be theta(t)''
21. p. 384, Section 26.4, 1st paragraph, line -3: theta(.), a(.), and sigma(.)'' should be theta(t), a(t), and sigma(t)''
22. p. 384, Section 26.4, 2nd paragraph, line 1: delete the'' from the Ho-Lee''
23. p. 384, Subsection 26.4.1, 1st paragraph, line 3: is'' should be are''
24. p. 385, line 2: period [ ... ]'' should be period [ ... )''
25. p. 386, 2nd paragraph, line 2: Q(i,k) ... for all k ... Q(i,k)'' should be Q(i,j) ... for all j ... Q(i,j)''
26. p. 386, 2nd paragraph, line 3: (i,k)'' should be (i,j)''
27. p. 388, Section 26.5, 2nd paragraph, line -1: delete reference [515]''
28. p. 390, 1st paragraph, line -6: the third'' should be third''
29. p. 392, line 7: [ ... ] dt'' should be { ... } dt''
30. p. 394, line -1: x[ ... ]'' should be x( ... )''
31. p. 398, line 4: to pricing'' should be to price''

## Chapter 27

1. p. 400, line 4: view'' should be snapshot''
2. p. 400, 3rd paragraph, line -4: the GSEs'' should be GSEs''
3. p. 400, 4th paragraph, line 1: issuedby state'' should be issued by states''
4. p. 402, line 3: at a bank'' should be from a bank''
5. p. 403, line 2: called'' should be called then''
6. p. 403, Subsection 27.3.2, 1st paragraph, line 4: trustee'' should be trustee,''
7. p. 404, line 7: delete reference [328]''
8. p. 404, 2nd paragraph, line 2: immediately'' should be immediately:''
9. p. 405, algorithm in Figure 27.6, line 8: delete the second =''
10. p. 406, Exercise 27.3.6, line 2: Exercise 11.1.10, part (2)'' should be Exercise 11.1.10(2)''
11. p. 407, Subsection 27.4.2, 1st paragraph, line 2: the option feature ... without the option.'' should be the option ... without it.''
12. p. 407, Subsection 27.4.2, 2nd paragraph, line -1: delete reference 330'' from [325,330]''
13. p. 408, Subsection 27.4.3, 1st paragraph, line 5: Chap. 23 is ... ideas.'' should be Chap. 23 will be ... ideas here.''
14. p. 410, Figure 27.8, caption, line 6: add make the following changes:'' after putable bonds,''
15. p. 410, Figure 27.8, caption, line 6: capitalize the two occurrences of replace''
16. p. 410, Figure 27.8, caption, line 7: capitalize make''
17. p. 411, 1st paragraph below Option-Adjusted Spread Duration and Convexity, line 2: delete ''plus''
18. p. 411, 1st paragraph below Option-Adjusted Spread Duration and Convexity, line 6: add as'' after ''effective duration''
19. p. 411, 1st paragraph below Option-Adjusted Spread Duration and Convexity, line 7: Eqs'' should be Eq''
20. p. 411, 1st paragraph below Option-Adjusted Spread Duration and Convexity, line 7: delete reference 848'' from [325,848]''
21. p. 411, 1st paragraph below Option-Adjusted Spread Duration and Convexity, line 7: delete reference 330'' from [55,330]''
22. p. 411, line -3: delete reference 429'' from [36,329,429]''
23. p. 411, line -2: add as done above'' after model''
24. p. 411, line -1: delete reference [731]''
25. p. 412, 1 line above Exercise 27.4.12: better'' should be more comprehensive''
26. p. 412, line -7: The price'' should be Each price''

## Chapter 28

1. p. 417, 2nd paragraph, line -4: delete the'' from , and the''
2. p. 421, line -2: 0.05/0.09'' should be 0.05/0.95''
3. p. 422, line -1: delete like Fannie Mae''
4. p. 423, Subsection 28.5.3, 1st paragraph, line 2: 575'' should be 800''
5. p. 423, Subsection 28.5.3, 1st paragraph, line 3: 1999'' should be 2001''
6. p. 423, Section 28.6, 1st paragraph, line -1: remain prepaid'' should be are prepaid''
7. p. 424, Subsection 28.6.1, line 5: add that'' after meaning''

## Chapter 29

1. p. 427, 1st paragraph, line 1: delete the'' from the MBS''
2. p. 427, 1st paragraph, line 2: use normal font instead of small cap for PRINCIPAL AND INTEREST''
3. p. 427, Section 29.1, 1st paragraph, line 3: 100,000. Figure'' should be 100,000, and Figure''
4. p. 428, 1st paragraph, 1 line below Eq. (29.2): Bal0'' should be the same equation with k=0.''
5. p. 432, subsection 29.1.2, 1st paragraph, line -2: exceeds'' should be is exceeded by ''
6. p. 432, line -3: delete must''
7. p. 433, line -3: ~6%'' should be approximately 6%''
8. p. 434, Exercise 29.1.6, table: the font for headings Month'' and PSA'' and table contents is inconsistent with that in earlier tables such as Figure 23.17 on p. 343
9. p. 437, Figure 29.10, caption, line -1: Exercise 29.1.9, part (1)'' should be Exercise 29.1.9(1)''
10. p. 438, Subsection 29.1.4, 2nd paragraph, line 2: add over successive months'' after SMMs''
11. p. 438, Subsection 29.1.4, 3rd paragraph, line 1: We can compute the pool's cash flow'' should be The pool's cash flow can be computed''
12. p. 440, Section 29.2, 1st paragraph, line 2: The MBS'' should be An MBS''
13. p. 441, 1st paragraph, line -1: delete [4]''
14. p. 441, 2nd paragraph, line -3: delete the'' from the house''
15. p. 441, Figure 29.14, caption, line -2: Zs'' should be Z's''
16. p. 445, line 1: delete an'' from for an illustration''
17. p. 446, Exercise 29.3.2, line 2: effective'' should be the effective''
18. p. 448, 1st paragraph, line 2, equation (29.13): Add Sn'' right before Cn*/()()...()
19. p. 448, 1st paragraph, line 3: for which'' should be in which''
20. p. 448, 2nd paragraph, line 5, equation: Add Sn'' right before Cn*/()()...()
21. p. 448, 4th paragraph, line 5: Therefore an'' should be An''
22. p. 449, 1st paragraph, line 2: delete [323,325]''
23. p. 449, Holding Period Returns, equation: delete the'' from the MBS''
24. p. 450, NOTES 2, line -1: delete 54'' from [54,330]''

## Chapter 30

1. p. 451, 1st paragraph, line 3: delete [660]''
2. p. 451, Section 30.1, 1st paragraph, line 3: would be'' should be is''
3. p. 452, Example 30.2.1, line 4: add a period after LIBOR''
4. p. 453, line 4: in comparison'' should be in contrast''
5. p. 453, 2nd paragraph, equation: add extra space between LIBOR'' and )''
6. p. 453, both tables in 2nd paragraph: heading LIBOR Change (Basis Points)'' should be LIBOR change (basis points)''
7. p. 453, Exercise 30.2.1, equation: add extra space between LIBOR'' and )''
8. p. 453, Section 30.3, 1st paragraph, line 1: They'' should be Their cash flows''
9. p. 453, Section 30.3, 1st paragraph, line 2: by calculation of the cash flows from'' should be from the cash flows of''
10. p. 454, 3rd paragraph, line 4: delete an'' from for an illustration''
11. p. 456, 1st paragraph, line 3: delete an'' from for an illustration''

## Chapter 31

1. p. 458, quote: add (1912--2006)'' after Friedman''
2. p. 459, 2nd paragraph, line -3: then is'' should be now becomes''
3. p. 460, Figure 31.1, caption, line 2: delete the enclosing parentheses of that are above the MVP''
4. p. 461, 2nd paragraph, line 2: delete (1)''
5. p. 461, 2nd paragraph, line 3: delete (2)''
6. p. 461, 2nd paragraph, line 6: also represents'' should be is''
7. p. 464, Subsection 31.1.2, 1st paragraph, line 5: amounts'' should be funds''
8. p. 466, 1st paragraph, line -2: shows'' should be lists''
9. p. 467, 2 lines above Exercise 31.2.3: This demonstrates'' should be So''
10. p. 467, Exercise 31.2.4, line -1: riskiness'' should be risk''
11. p. 468, Subsection 31.2.2, 1st paragraph, line 4: static'' should not be italicized
12. p. 470, 2nd paragraph, line 4: delete [799]''
13. p. 470, line -5: results'' should be identities''
14. p. 471, lines 2--3: delete sentence The single-factor ... [795].''
15. p. 473, 3rd paragraph, line 4: delete the ,'' after on the other hand''
16. p. 474, Section 31.4, quote, line 3, The Economist'': italicize
17. p. 474, Section 31.4, 1st paragraph, line -2: has become'' should be is''
18. p. 474, Section 31.4, 2nd paragraph, line -2: VaR, and we'' should be VaR. We''
19. p. 474, Section 31.4, 3rd paragraph, line 2: We assume that the'' should be The''
20. p. 476, Subsection 31.4.1, 1st paragraph, line 6: As always, actual'' should be Actual''
21. p. 477, algorithm in Figure 31.7, line -7: delete sqrt(C[j][j]) X'' in front of dW[j]''
22. p. 477, line 2: Exercise 31.4.3, part (3)'' should be Exercise 31.4.3(3)''
23. p. 478, 3rd paragraph, line -2: delete [571]''
24. p. 478, Subsection 31.4.3, 3rd paragraph, line 1: delete the'' from the VaR''
25. p. 479, NOTES 1: we use variance of return'' should be variance of return is used''
26. p. 479, NOTES 2, line 2: add here'' after involved''
27. p. 479, NOTES 8: See'' should be Recall''
28. p. 479, NOTES 9: Exercise 13.3.10, part (2)'' should be Exercise 13.3.10(2)''

## Chapter 32

1. p. 481, line 7: )," and so on'' should be )"; and so on''
2. p. 483, Section 32.3, 1st paragraph, line -1: worthwhile to parallelize'' should be worth the effort to parallelize''

## Chapter 33

1. p. 484, Exercise 3.3.1, line -1, 2 places: value" should be PV''
2. p. 485, Exercise 3.3.2, line -1: Consult" should be See''
3. p. 485, Exercise 3.5.2, line -2: 10,..." should be 10,11,...''
4. p. 487, Exercise 4.2.3: delete the last paragraph (4 lines)
5. p. 495, Exercise 8.1.2, line -3: delete called the''
6. p. 495, Exercise 8.1.2, line -2: add that'' after means''
7. p. 495, Exercise 8.2.1, line -2: add the second equation from the first equation'' after subtract''
8. p. 495, Exercise 8.2.2, line 2: noone'' should be no one''
9. p. 497, Exercise 9.2.2, line 3: delete equal to''
10. p. 497, Exercise 9.3.1, line -2: add numerically'' after limit''
11. p. 499, Exercise 9.6.1, line -2, equation: add ,0'' after X'' (2 places)
12. p. 500, Exercise 9.6.7, line 1: It retains the binomial tree's'' should be The''
13. p. 500, Exercise 9.6.7, line 2: add is retained'' after structure''
14. p. 500, Exercise 9.6.7, line 3: add that'' after pretending''
15. p. 500, Exercise 9.6.8, line 2: delete has zero value at present as it''
16. p. 500, Exercise 9.6.8, line 3: add a'' before positive''
17. p. 501, Exercise 10.1.5, line 4: add identity'' after of''
18. p. 501, Exercise 10.1.7: delete [894, p. 78]''
19. p. 501, Exercise 11.1.3: Leibnitz's rule'' should be bold-faced
20. p. 502, Programming Assignment 11.2.5, line 2: , noting'' should be . Note''
21. p. 502, Programming Assignment 11.2.5, line -3: add the pre-zeroed'' before out-value''
22. p. 503, Figure 33.2, algorithm, line 3: delete (H < X, H < S)''
23. p. 503, Figure 33.2, algorithm, line 7: delete H := Suh;''
24. p. 503, Figure 33.2, algorithm, line 13: delete 0 <=''
25. p. 503, Exercise 11.5.4, line 1: add in'' after $h'' 26. p. 503, Exercise 11.5.4, line 2: add in'' after $B''
27. p. 504, line 3: add desired'' before result''
28. p. 504, Exercise 11.7.5, equation, line 1: add ,'' after the formula before if''
29. p. 504, Exercise 11.7.5, equation, line 1: add ,'' after S0''
30. p. 505, Programming Assignment 11.7.11, 2nd paragraph, line -12: were'' should be can be''
31. p. 506, Exercise 12.2.5, line 3: add years'' before from now''
32. p. 506, Exercise 12.3.6, line 3: a T-bill'' should be T-bills''
33. p. 507, Exercise 12.4.4, line 1: into'' should be in''
34. p. 508, line 1: proof for'' should be case of''
35. p. 508, Exercise 13.1.3, line 4, equation, line 1: add ,'' after 1''
36. p. 508, Exercise 13.1.3, line 4, equation, line 2: add ,'' after 0''
37. p. 508, Exercise 13.1.4, equation, line 1: add ,'' after 1''
38. p. 508, Exercise 13.1.4, equation, line 2: add ,'' after -1''
39. p. 508, Exercise 13.1.5, line 3, equation, line 1: add ,'' after +1)''
40. p. 508, Exercise 13.1.5, line 3, equation, line 2: add ,'' after -1)''
41. p. 508, Exercise 13.1.5, line 3, equation, line 3: add ,'' after +1)''
42. p. 508, Exercise 13.1.5, line 3, equation, line 4: add ,'' after -1)''
43. p. 508, Exercise 13.2.2: delete ,'' after (2)''
44. p. 511, Exercise 14.1.1, line 6: can show'' should be shows''
45. p. 514, 1 line above LEMMA: delete then''
46. p. 514, line -4: get'' should be obtain''
47. p. 515, Exercise 14.4.5: direct'' should be directly''
48. p. 515, Exercise 14.4.5: delete , it is SeuT''
49. p. 515, Exercise 14.4.8, line 5: preceding'' should be the above''
50. p. 516, Exercise 15.2.3, line 3: expansion'' should be expansions''
51. p. 516, Exercise 15.2.10: is due to'' should be can be proved by recalling''
52. p. 519, Exercise 16.2.2: Because the'' should be The''
53. p. 519, Exercise 17.1.1: Because the'' should be The''
54. p. 519, Exercise 17.1.4, line -7: add that'' after probability''
55. p. 519, Exercise 17.1.4, line -7: delete that'' before reaches''
56. p. 522, Figure 33.4, caption, line -2: delete further''
57. p. 524, Exercise 18.2.7, line 2: mean zero'' should be zero mean''
58. p. 524, Exercise 18.2.11: >'' should be =''
59. p. 525, Exercise 18.2.13, line 4: add well-known'' before relation''
60. p. 526, Exercise 19.2.12, line 6: step'' should be statement''
61. p. 526, Exercise 19.2.12, line -3: step'' should be statement''
62. p. 526, Exercise 19.2.12, line -3: Step'' should be Statement''
63. p. 526, Exercise 19.2.12, line -2: step'' should be statement''
64. p. 528, Exercise 20.1.4, line 7: We differentiate'' should be Differentiate''
65. p. 528, Exercise 20.1.5, line -2: delete ,'' after theta
66. p. 528, Exercise 20.1.8, line 1: Exercise 6.4.3, (2)'' should be Exercise 6.4.3(2)''
67. p. 528, Exercise 20.1.9, line 4: Exercise 6.4.1, (1)'' should be Exercise 6.4.1(1)''
68. p. 528, Exercise 20.1.12, line 1: delete a'' from Take a positive''
69. p. 530, Exercise 21.1.4, line 4: 1.04'' should be 1.03'' (2 places)
70. p. 530, Exercise 21.1.4, line 4: 149.19'' should be 180.35''
71. p. 530, Exercise 21.1.4, line -1: 1.4919'' should be 1.8035''
72. p. 531, Exercise 21.4.3, line -1: add dollars'' after million''
73. p. 531, Exercise 22.2.1, lines 1--2: can be simplified to'' should be implies''
74. p. 532, Exercise 23.2.1, line 2: term ln rk is'' should be terms ln rk are''
75. p. 532, Exercise 23.2.1, line 2: it is'' should be they are''
76. p. 534, Exercise 23.2.9, line 3: delete ,'' before corresponding''
77. p. 534, Exercise 23.3.4, line -1: predicts'' should be predicted''
78. p. 535, Exercise 24.2.4, line 4, equation: add .'' at end
79. p. 535, Exercise 24.2.4, line -1: delete above''
80. p. 536, Exercise 24.3.2, line 2, equation: move .'' to end of equation
81. p. 536, Exercise 24.3.8, 2nd paragraph, line 4: delete t1'' after contingent''
82. p. 536, Exercise 24.3.8, 2nd paragraph, line -4: can be easily proved to be'' should be is''
83. p. 536, Exercise 24.3.8, 2nd paragraph, line -2: date'' should be time''
84. p. 538, Exercise 24.6.2, line -1: S3.3'' should be Section 3.3''
85. p. 538, Exercise 24.6.5: add work'' after manipulations''
86. p. 539, Exercise 25.1.5, line -3: by using'' should be with''
87. p. 539, Exercise 25.1.5, line -3: add obtain'' after to''
88. p. 539, Exercise 25.1.6, line -1: The final term is missing the multiplicative factor B(t,T)2''
89. p. 540, Exercise 25.2.14, line -3: ,'' should be .''
90. p. 543, Exercise 27.3.2, line 1: were'' should be is''
91. p. 543, Exercise 27.3.3, line 1: add the'' before bondholder''
92. p. 543, Exercise 27.3.3, line 3: However, we'' should be Of course,''
93. p. 544, Exercise 27.4.2, line 2: add the'' after The fall in''
94. p. 544, Exercise 27.4.2, line 3: add the'' after the fall in''
95. p. 544, Exercise 27.4.3, line -4: thus is'' should be is thus''
96. p. 545, Exercise 27.4.11, line 1: (1)'' should be first''
97. p. 545, Exercise 27.4.11, line 2: (2)'' should be then''
98. p. 545, Exercise 28.6.4, line 3: add later'' after (29.4)''
99. p. 546, Exercise 29.1.2, line -2: r/m'' should be (r/m)''
100. p. 546, Exercise 29.1.5: Exercise'' should be Programming assignment''
101. p. 546, Exercise 29.1.5, line 1: add the longer'' after with''
102. p. 546, Exercise 29.1.6, line 1: add The desired IRRs are tabulated below:''
103. p. 547, Exercise 29.1.9, line 1: add .'' after Bi''
104. p. 549, Exercise 31.1.7, line 2: add ,'' after variables''
105. p. 550, Exercise 31.2.11, line 1: continuous'' should be continuously''

## Bibliography

1. p. 553, [7]: K. ... D. ...'' should be Kenneth ... Donald ...''
2. p. 555, [70]: Avi.'' should be Avi''
3. p. 555, [74]: Petter.'' should be Petter''
4. p. 556, [90]: delete Manuscript, November 1996.''
5. p. 556, [94]: Stephen, and'' should be Stephen and''
6. p. 556, [108]: Broadie and Paul'' should be Broadie, and Paul''
7. p. 557, [116]: Gatarek and Marek'' should be Gatarek, and Marek''
8. p. 558, [139]: Walter and Thomas'' should be Walter, and Thomas''
9. p. 558, [147]: Lo and A.'' should be Lo, and A.''
10. p. 558, [156]: Morgan Stanley.'' should be Morgan Stanley,''
11. p. 559, [171]: Carleton and Donald'' should be Carleton, and Donald''
12. p. 559, [173]: Longstaff and Anthony'' should be Longstaff, and Anthony''
13. p. 559, [177]: Chang and Kian-Guan'' should be Chang, and Kian-Guan''
14. p. 559, [181]: In ... Computing.'' should be SIAM Journal on Computing, 31, No. 2 (2001), 447--459.''
15. p. 559, [182]: Seltzer and Michael'' should be Seltzer, and Michael''
16. p. 560, [199]: Choi and Elena'' should be Choi, and Elena''
17. p. 560, [205]: Robbins and David'' should be Robbins, and David''
18. p. 560, [206]: Fabozzi and Anthony'' should be Fabozzi, and Anthony''
19. p. 561, [227]: Leiserson and Ronald'' should be Leiserson, and Ronald''
20. p. 561, [233]: Jr. and'' should be Jr., and''
21. p. 562, [246]: Meeraus and Stavros'' should be Meeraus, and Stavros''
22. p. 562, [254] and [255]: swap them to preserve the alphabetic order
23. p. 562, [263]: DBMS, March 1995, pp. A--X'' should be DBMS (March 1995), A--X''
24. p. 562, [269] and [270]: swap them to preserve the alphabetic order
25. p. 563, [281]: Samuelson and Robert'' should be Samuelson, and Robert''
26. p. 563, [288]: Gauthier and Jean-Guy'' should be Gauthier, and Jean-Guy''
27. p. 563, [301]: Jr. and'' should be Jr., and''
28. p. 564, [314]: Perraudin and Peter'' should be Perraudin, and Peter''
29. p. 565, [365]: Scharfstein and J.C.'' should be Scharfstein, and J.C.''
30. p. 566, [385]: Christian, and'' should be Christian and''
31. p. 567, [402]: Mark, and'' should be Mark and''
32. p. 568, [430]: Chaudhary and Robert'' should be Chaudhary, and Robert''
33. p. 568, [431]: Lauterbach and Cyrus'' should be Lauterbach, and Cyrus''
34. p. 568, [449]: Keenan and Walter'' should be Keenan, and Walter''
35. p. 569, [467]: California'' should be CA''
36. p. 570, [487]: Kai.'' should be Kai''
37. p. 571, [516]: Tuckman. (Ed.)'' should be Tuckman, ed.''
38. p. 572, [547]: S.G.'' should be Stephen G.''
39. p. 572, [555]: Manuscript ... Finance.'' should be The Journal of Computational Finance, 4, No. 3 (2001), 89--124.''
40. p. 573, [600]: Ritchken and L.'' should be Ritchken, and L.''
41. p. 577, [697]: move it below reference [701]
42. p. 578, [730]: B., and Michael'' should be B. and Michael''
43. p. 578, [732]: 18'' should be 78'' and 315'' should be 340''
44. p. 578, [748]: Sankarasubramanian and Anand'' should be Sankarasubramanian, and Anand''
45. p. 578, [751]: Runkle and Charles'' should be Runkle, and Charles''
46. p. 579, [767]: Westerfield and Jeffrey'' should be Westerfield, and Jeffrey''
47. p. 579, [784]: M.'' should be Manfred.''
48. p. 580, [799]: Alexander and Jeffrey'' should be Alexander, and Jeffrey''
49. p. 580, [814]: Shreve and J.'' should be Shreve, and J.''
50. p. 582, [879]: Howison and Jeff'' should be Howison, and Jeff''
51. p. 583, [897]: Vetzal and Peter'' should be Vetzal, and Peter''

## Index

1. p. 588, right column, Mathematical Theory of Speculation'' under Bachelier, Louis'': italicize
2. p. 592, right column, Capitals software'': italicize Capitals''
3. p. 603, left column, government-sponsored enterprise'': delete the page xiv entry
4. p. 619, right column, Investments'' under Sharpe, William F.'': italicize
5. p. 622, right column, swaption:valuation'': delete

## Back cover

1. 1st paragraph, line -2: , in keeping with'' should be to keep up with''
2. line -15: delete the sentence, Each instrument is treated in a short, self-contained chapter for ready reference use''
3. 4th paragraph, 1st sentence: coded in Java'' should be coded in Java or JavaScript''
4. 4th paragraph: http://www.csie.ntu.edu.tw/ffilyuu/Capitals/capitals.htm'' should be http://www.csie.ntu.edu.tw/~lyuu/Capitals/capitals.htm''
5. line -4: add a period

## Acknowledgments

The following students at National Taiwan University helped improve the quality of the book: Chih-Chung Chang, Ronald Yan-Cheng Chang, Kun-Yuan Chao, Chun-Ying Chen, Kuan-Wen Chen, Wei-Jui Chen, Yuan-Wang Chen, An-Hsun Cheng, Hsin-Huan Chien, Chih-Hung Chou, Jing-Hong Chou, Tian-Shyr Dai, Chi-Shang Draw (aka Chi-Shiang Cho), Hau-Ren Fang, Yuh-Yuan Fang, Jia-Hau Guo, Yon-Yi Hsiao, William Wei-Yuan Hsu, Guan-Shieng Huang, How-Ming Hwang, Chih-Hao Kao, Yan-Fu Liou, Heng-Yi Liu, Yu-Hong Liu, Kou-Yeh Shen, Min-Cheng Sun, Ruo-Ming Sung, Huei-Wen Teng. Chen-Leh Wang, Jere Chuan-Ju Wang, Huang-Wen Wang, Hsing-Kuo Wong, Chao-Sheng Wu, Cheng-Wei Wu, and Chi-Ning Wu.