Errata for Financial Mathematics: a Comprehensive Treatment
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1 Errata for Financial Mathematics: a Comprehensive Treatment G. Campolieti R. Makarov March 3, 05
2 Page 4 Line 4, 6 For: t Read: t Page 9 Lines 9,, 4, 6 For: V A Read: P A Page 37 Prop..4 (line 4 Remove the condition in brackets: Page 69 Line For: conditions (i and (ii Read: conditions (a and (b ( or C 0 > n C k k= Page 79 Exercise. (Line For: time t = T Read: time T = Page 80 Exercise.3 For: Suppose that V 0 < W 0 Read: Suppose that V 0 > W 0 Page 8 Exercise.9 For: Given the bond and stock prices in Exercise.7 Read: Given the bond and stock prices in Exercise.7 except that S (ω = S (ω 3 = 50 Page 08 Eqn. in line 3 For: V = αb + ( α Read: r V = αr + ( α N w i A i = αb + ( αv M i= } {{ } =:V M N w i r i = αr + ( αr M i= } {{ } =:r M Page 09 Line For: all portfolios of the form V = αb + ( αv M Read: all portfolios with r V = αr + ( αr M Page 0 Line For: initiated at time 0 Read: initiated at time t Page 36 Line 9 Remove the second last term: = = $ Page 40 Line For: P A (8 Read: P A (8 Page 55 Exercise 4. For: F 0 (S 0, K Read: V 0 (S 0, K Page 55 Exercise 4.4 For: F t = F t (S t, K Read: V t = V t (S t, K Page 65 Line In the calculation of the determinant: For: det(d = Read: det(d =
3 Page 79 Eqn. (5.0 For: M = u(πϕ T p = ( M = u N i= ϕ ist i p Read: M = u(πϕ T (ω p = M = u ( N i= ϕ is i T (ω Page 80 Line 9 (ust below (5.3 For: X(ω = x Read: X(ω = x Page 80 Line 0 For: the minimization problem Read: the optimization problem p Page 80 Line 6 For: f(x = 4 x x Read: f(x = 4 x x Page 8 Line (ust above (5.4 For: the following simultaneous linear equations Read: the following simultaneous equations Page 84 Line 7 (the st bullet For: Let Ψ. Read: Ψ 0. Page 84 Line 3 For: m d or m u Read: m d or m u Page 85 Line For: with the forward price Read: with the delivery (strike price Page 88 Line 6 For: Π T [ϕ d X = X d X > 0 Read: X Π T [ϕ d = X X d > 0 Page 88 Line 9 For: (π 0 (X d π 0 (X + X d X Read: (π 0 (X d π 0 (X + X X d Page 89 Example 5.3 For: strike K = $0 Read: strike K = $00 p ( + p ( + p ( 3 = Page 97 Eqn. (5.50 For: 40 p ( + 0 p ( + 80 p ( 3 = p ( + 0 p ( + 0 p ( 3 = 0 p ( + p ( + p ( 3 = Read: 40 p ( + 0 p ( + 80 p ( 3 = 00 5/6 40 p ( + 0 p ( + 0 p ( 3 = 0 5/6
4 Page 97 Eqn. (5.53 For: ϱ (g f Read: ϱ (f g Page 98 Prop. 5.5 (Line 5 For: ϱ (g f Read: ϱ (f g Page 98 Prop. 5.5 (Line 6 For: P (f Read: P (f Page 98 Prop. 5.5 (Line 7 For: ϱ (g f Read: ϱ (f g Page 98 Eqn. (5.56 For: ϱ (g f Read: ϱ (f g Page 98 Eqn. (5.57 For: ϱ (g f Read: ϱ (f g Page 98 Lines 3 to 0 In the paragraph that starts with Note that the variable replace ϱ (g f by ϱ (f g and vice versa (4 places Page 98 Line For: switching from P (f to Read: switching from P (g to Page 98 Line For: L(Ω Read: L(Ω Page 98 Line 0 For: Ẽ(f [X = Ẽ(g [ Read: Ẽ(f [X = Ẽ(g [ ϱ (g f T P (g X X ϱ (f g P (f = Ẽ(g [ϱ (f g X = Ẽ(g [ϱ (g f X [5pt Page 98 Line 8 For: p (g and p (g Read: p (g and p (f Page 99 Line For: ϱ P P Read: ϱ P P Page 0 Exercise 5.8(c For:. arbitrage-free Read: arbitrage-free Page 04 Exercise 5. For: is attainable. Read: is not attainable. Page 09 Line For: k U n Read: k U k Page 09 Line For: k U n Read: k U k Page 4 Line - For: S n,k = S k mu k l d (n m (k l Read: S n,k = S m,l u k l d (n m (k l Page 68 Line 9 Remove the last term: V = ( + r Ẽ [V = ( + r Ẽ [V Page 69 Eqn. (7.3 For: V t = Ẽt[V T Read: V t = (+r T t Ẽt[V T 3
5 Page 79 Eqn. (7.4 For: St S t Read: S T St Page 79 Line - For: m T t (K, S t, u, d, T t Read: m T t (S t Page 80 Eqn. (7.43 For: P(H T t m T t Read: P ( H T t m T t (S S=St Page 8 Eqn. (7.5 In the st line of the equation: For: G t = ((S 0 S t S t t+ ((Gt t S t t+ Read: G t = ((S 0 S t S t t+ = ((Gt t S t t+ Page 86 Line -6 For: pricing formula (7.6 Read: pricing formula (7.59 Page 87 Line For: the following the Read: the following Page 90 Line 3 For: =.5 Read: 6 4 = Page 90 Line For: The last case is when S 3 =. Read: The last case is when S =. Page 98 Eqn. (7.8 For: V t (S t,n Λ t (S t,n Read: V t (S t,n = Λ t (S t,n Page 99 Eqn. (7.83 For: C A t (S t,n (S t,n K + Read: C A t (S t,n = (S t,n K + Page 99 Eqn. (7.84 For: P A t (S t,n (K S t,n + Read: P A t (S t,n = (K S t,n + Page 303 Exercise 7.7 For: (G 3 K + Read: (G T K + Page 305 Exercise 7.5 For: B(m; p, n Read: B(m; n, p Page 306 Exercise 7.0 For: t S t n=0 Read: t S n n=0 Page 40 Eqn. (0.74 In the st line of the equation: For: f M(t,W (t (m, y Read: f M(t,W (t (w, y Page 43 Line 0 For: 0 t < 4 Read: 0 t 4 For: t [0, 4 Read: t [0, 4 Page 457 Line 4 For: E[ ϱ = E[ϱ = Read: E[ ϱ = E[ϱ = Page 509 Line For: strictly decreasing Read: strictly increasing The changes on pages are made to ensure greater consistency of notation used in Chapters 6, 8, and 3. 4
6 ( Page 535 Eqn. (.7 For: SN (d SB +, ( Read: e q SN (d SB +, Page 536 Line For: b σ ln K S Read: b σ ln B S Page 539 Line -4 For: max{m, S e σw } S e σw } Read: max{m, S e σw } S e σx (( Page 545 Line 3 For: N ( M+ν/ (σ+ν (σ + ν (( Read: N ( M+ν/ (σ+ν (σ + ν [ Page 545 Eqn. (.57 For: + (r q [ ( σ S N (d +, M [ Read: (r q [ ( σ e (r q S N (d +, M Page 545 Eqn. (.59 The following expression should be added to the existing r.h.s. expression: + σ [ ( ( e r S d S +, ( N d S M +, ( + n (d SM M +, Page 545 Eqn. (.59 Insert the following line after the equation: where d ± (x, := ln x± σ σ. Page 546 Eqn. (.6 For: e r S [ N ( σ ( N σ ( N σ + e r S[σ n(σ / + (σ /N (σ / Read: e r S [ N ( σ For: e r S [ N ( σ Read: e r S [ N ( σ + e r S[σ n(σ / + (σ /N (σ / Page 547 Exercise.4(b For: {S(T >K} Read: I {S(T >K} Page 55 Exercise.4 (iii For: P LF P (t, S, M; K Read: P LF P (t, S, m; K Page 55 Exercise.5 For: G k = [ k = S(t Read: G k = [ k /k = S(t Page 55 Exercise.5 (a For: show that G n is a normal random variable Read: show that G n is a log-normal random variable 5
7 Page 558 Defn. 3. For: every F T -measurable Read: every F T -measurable Page 559 Eqn. (3. For: e t 0 r(u du Read: e T t r(u du Page 57 Line 4 For: V max Read: v max Page 57 Eqn. (3.70 For: V min (S, S, Read: v min (, S, S Page 574 Line 6 For: (r q S f x f x ( Read: (r q S f x f x Page 597 Line 7 For: calender Read: calendar Page 60 Line 5 For: p(t t; S, S Read: p(t t; S, S Page 604 Line 3 For: σ λ (λ + (r qλ r = 0 Read: σ λ(λ + (r qλ r = 0 Page 6 In Eqs. (4.48 and (4.49: For: variable S Read: S ( Page 65 Lines 5, 8 For: calender Read: calendar Page 65 Exercise 5.7 (b For: α(t, T Read: α(t, T Page 653 Line 5 For: calender Read: calendar Page 686 Line 3 For: f ( x c big Read: f ( x c Page 734 Exercise 7.8 (d For: if x Read: if x Page 735 Exercise 7. (line 5 For: 0 t < t < t Read: 0 t < t < t Page 736 Exercise 7.9 (b (iv For: the increase of n Read: the increase of m Page 736 Exercise 7.9 (c For: Suppose Z = V Read: Suppose Z = U Page 736 Exercise 7.9 (d For: method of (b Read: method of (c 6
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