CHAPTER 1
0 P( R8 A& _. t, H6 G From Art to Engineering in Finance 1
/ |- Z; ?3 k, w0 d$ y Investment Management Process 2( W: u% a. n( p5 Y" G4 Q
Step 1: Setting Investment Objectives 26 |) o' G) A# |, U ]
Step 2: Establishing an Investment Policy 2Step 3: Selecting a Portfolio Strategy 6" ]; b- g9 Z# I, e; I
Step 4: Selecting the Specific Assets 7
; ?: R+ ]$ j( @ k3 N# t Step 5: Measuring and Evaluating Performance 9Financial Engineering in Historical Perspective 10The Role of Information Technology 113 u% t# b. f) {6 x2 E6 p
Industry’s Evaluation of Modeling Tools 13Integrating Qualitative and Quantitative Information 15Principles for Engineering a Suite of Models 17Summary 18
. N3 z: }9 L: ?- s4 R) ~) l) x CHAPTER 28 ^2 F1 y8 l w; j4 e1 e; c
Overview of Financial Markets, Financial Assets, and Market Participants 21Financial Assets 219 r! |8 N9 n' u) ]7 p7 o
Financial Markets 25& W; |8 ]! Y6 ^ |5 I, d0 `
Classification of Financial Markets 253 o0 G$ K/ I- u0 A8 E! d: D% T
Economic Functions of Financial Markets 26Secondary Markets 27
0 Y8 m0 q2 q) N6 y Overview of Market Participants 34
' d0 _: U, z/ V" | Role of Financial Intermediaries 35
+ c7 s* k- _+ ?& k; f( g. a0 u Institutional Investors 37
1 i7 M# z# A0 Q: N! [9 v2 `! s Insurance Companies 41" \9 |3 i7 s+ q( q& I/ m4 h4 U
Pension Funds 41! W- O% w8 f) }& ^% Z6 s
Investment Companies 42
. t8 |, A, X. ^$ Z9 L Depository Institutions 43
# M1 T5 j/ s* x2 ^' d Endowments and Foundations 45
\1 G% F9 w! z$ j7 o( b Common Stock 45
4 `! l+ l9 W8 [+ ~7 j) O& g2 i iii! v8 S/ I/ N; m+ p, y3 ^) J% ]
iv Contents
6 o% I% A* n0 | Trading Locations 45
# ?$ d0 w5 J* v3 v; q1 W6 n Stock Market Indicators 46 o% ]0 _+ |; b0 _
Trading Arrangements 48
6 O* ^1 s C$ C0 @% f* \$ A Bonds 516 e- v: w3 N2 n; ?* y8 k
Maturity 51
7 [4 g) i$ F" V0 w9 n Par Value 52! {, T! H& O3 e( D/ J
Coupon Rate 52, B! ]3 q6 F7 i3 p1 I; t
Provisions for Paying off Bonds 55 U+ u- V6 |5 C
Options Granted to Bondholders 56
" R8 g# N+ |5 ^! J6 t. e Futures and Forward Contracts 57# d6 j; h% G2 c# j# [$ |4 z8 O* ?
Futures versus Forward Contracts 58
, M7 }! [7 [/ k. Y' ]( w9 c% D* @+ P Risk and Return Characteristics of Futures Contracts 59Pricing of Futures Contracts 59) r% S8 e9 k9 J: |( A
The Role of Futures in Financial Markets 63Options 64
, s" J& }5 `3 G% S( t! T Risk-Return for Options 667 c8 H1 E) i; }
The Option Price 662 o" i* a6 O% t- D
Swaps 693 g0 Q; C- z7 p0 V2 Y
Caps and Floors 709 u+ S" x! ~4 h' j9 i
Summary 71' S- ~+ f S( l) F; g
CHAPTER 3$ X; B6 {( H/ l9 t
Milestones in Financial Modeling and Investment Management 75The Precursors: Pareto, Walras, and the Lausanne School 76Price Diffusion: Bachelier 78( {3 `& s* I8 a8 Q+ z9 d8 P/ |
The Ruin Problem in Insurance: Lundberg 80The Principles of Investment: Markowitz 81Understanding Value: Modigliani and Miller 83Modigliani-Miller Irrelevance Theorems and theAbsence of Arbitrage 842 H3 S% n9 h8 `1 H; \( G
Efficient Markets: Fama and Samuelson 85
! D9 ~# k' \9 \9 m, s5 I Capital Asset Pricing Model: Sharpe, Lintner, and Mossin 86The Multifactor CAPM: Merton 877 w. P9 z7 W: ~: R) q5 k
Arbitrage Pricing Theory: Ross 88
1 M2 ?+ T a% W% E" ^; i0 u Arbitrage, Hedging, and Option Theory:
) D' v) A% W( A! e3 t6 J Black, Scholes, and Merton 89* {# U* }) }- k6 ?% n4 t
Summary 90
+ l5 C2 f' u2 r- s3 Q+ l& r CHAPTER 4) r- j' n9 j* W" b, A
Principles of Calculus 91
# s1 {4 K1 J! y* ]: ~3 \ P Sets and Set Operations 93) o3 S/ q2 D$ E( b; y
Proper Subsets 93
- d/ E. \% h; ^1 N3 o- h$ A Empty Sets 95
# B5 ?. q9 Y l Union of Sets 95
' e. Z: c+ c$ d4 n5 { Intersection of Sets 95
6 q' P1 b- r, e# B: @ Elementary Properties of Sets 965 K: c1 ~( R) T$ }0 X
Distances and Quantities 967 W* R: S. {6 H! i! t
n-tuples 97, H0 K3 F; M& N8 I9 L7 g! N: Y
Distance 981 c# G9 U( C8 v8 t
Contents v1 k1 z/ P0 D: f; t! b' `5 ?) b
Density of Points 990 }9 {" s( s1 r$ m, t$ o
Functions 100$ _6 [# D4 r% d( t# o0 z
Variables 101
# }8 E v E' f+ ^* q+ O9 r( F Limits 102/ `* H3 [" |7 n5 T: K
Continuity 103! e( A. e L9 P& R. Z
Total Variation 105
: g8 F: _4 g! G$ Q Differentiation 106
( t0 O: f3 d! E) T. N* h0 G+ D Commonly Used Rules for Computing Derivatives 107Higher Order Derivatives 111
; @( Q% }9 h. ^( s! q Application to Bond Analysis 112
1 c* y: ?, C) t7 e0 _+ Z Taylor Series Expansion 121 ?- F: w" K2 r; p( G, i+ _ ?( P
Application to Bond Analysis 122
k: q. j9 e$ ?8 C# D& w9 B' g Integration 127- y' L+ N7 ~ U
Riemann Integrals 1278 {& N+ _7 @2 l$ U$ w
Properties of Riemann Integrals 129
: Y; P+ m0 `& J6 s Lebesque-Stieltjes Integrals 130
z- ]& _2 J$ D6 p) z Indefinite and Improper Integrals 131
/ k% i; q2 V [* l0 g! q The Fundamental Theorem of Calculus 132" f( F7 r ]7 \4 ]
Integral Transforms 134
6 u- _" R' D4 i! L% v Laplace Transform 1345 R, r) {! ^) P- U
Fourier Transforms 1370 \6 z, d- y7 [: G2 t; ~
Calculus in More than One Variable 1381 q4 A( f5 H2 U% Q3 R6 y1 r
Summary 139- ]/ P1 B# z5 G
CHAPTER 5
3 ?- f$ B0 ~' }$ y Matrix Algebra 1413 L. f" f; C; J$ p; B% j" f2 o3 L
Vectors and Matrices Defined 141
" O$ s8 o: K4 T. P Vectors 141
% E) K' ^6 u; y* o- ^) }$ m% g Matrices 144; D4 O. F4 \ y) D
Square Matrices 145, G* j/ x2 v% G; p0 C- w
Diagonals and Antidiagonals 145
4 R# O* r$ Z; i& s3 m Identity Matrix 146
. S3 s- I. D' Z6 l Diagonal Matrix 146( z, _- [- F$ ^, g7 y
Upper and Lower Triangular Matrix 148
% v/ |& W; a5 R. { Determinants 148
5 ~, d0 ^. m* | Systems of Linear Equations 149
% {1 T4 E; ? t Linear Independence and Rank 151' o" {$ [/ E9 j z& X$ `* h
Hankel Matrix 152* [5 k& R! P3 X# R; F" M
Vector and Matrix Operations 1530 L: v0 `& h0 A5 E2 G/ O {
Vector Operations 153
: f% E: G) \+ Y# E2 X7 _4 U4 A Matrix Operations 1561 J y/ R j& K! Y: z
Eigenvalues and Eigenvectors 1609 x3 k$ j0 l' c5 N! i& p: u
Diagonalization and Similarity 1610 o4 n" I% `- j
Singular Value Decomposition 162
! }+ L5 q0 j8 H& L1 t* ~$ u) e5 e Summary 163: d" {6 v$ z {2 J* i# m1 |
CHAPTER 6
7 }7 | U! ^" m0 b3 k% B4 g6 G Concepts of Probability 165
; U) \# K, l3 _ Y9 ^2 s' p Representing Uncertainty with Mathematics 165Probability in a Nutshell 167$ ^* g, ^3 F) l3 Q) ?
vi Contents* L& r" K. X5 a+ g8 {1 m0 f
Outcomes and Events 169$ x, l' E! x# m* m. l
Probability 170& V6 k0 O/ m( ]1 P9 v0 H
Measure 171# U1 t8 n' P6 I# M
Random Variables 172
A9 Z9 z" l8 r: f Integrals 1721 E) C* d- h. o! R2 B
Distributions and Distribution Functions 174Random Vectors 1759 h0 }' E& G& G$ b0 O6 U7 ^
Stochastic Processes 1787 g7 R& l' M, e
Probabilistic Representation of Financial Markets 180Information Structures 181 u) }; B8 g( p8 T( |2 P
Filtration 182
, Z# r$ S% f6 F* v) y- v2 W Conditional Probability and Conditional Expectation 184Moments and Correlation 186( o( f, D0 i' A8 _- A; g9 l# S. q! U; R
Copula Functions 1887 U+ g+ \! ~: ^' C+ F9 k+ \
Sequences of Random Variables 189. O: X* R1 e" ^$ ^! `; t9 Y
Independent and Identically Distributed Sequences 191Sum of Variables 191" z; T1 P `4 B" Z# d& Q
Gaussian Variables 194& Y0 T9 C' C& p' G5 Q6 W
The Regression Function 197
" U7 ?* \1 `/ e# C/ z( R$ @4 Q Linear Regression 1975 z( J" J. S, d( N$ R
Summary 199
2 N+ E1 u! K7 q, o/ M6 _ CHAPTER 7
! [' v6 g9 l% f4 ~ Z. q% @ Optimization 201
& G" y! h% }1 b7 c0 p0 q Maxima and Minima 202. y. w9 `; t. Z3 o2 l* p P( v; T
Lagrange Multipliers 204
) P. a! E- k; q& S, X Numerical Algorithms 206
% b+ v2 n y+ U' U+ J. S Linear Programming 206) d/ [5 J6 }3 Q+ Y- e1 T
Quadratic Programming 211
2 D# C! j h! T6 A: T: y Calculus of Variations and Optimal Control Theory 212Stochastic Programming 214
2 D. g4 ?* H. T; _! m- \( j4 ~ Summary 216
8 N1 i7 v; u5 o CHAPTER 8$ k7 q2 r, u) A$ J+ u7 P
Stochastic Integrals 217
9 [$ f) N# c- H, Z/ f# b The Intuition Behind Stochastic Integrals 219Brownian Motion Defined 2257 K2 c! k; z( k( z( C) \' d' R
Properties of Brownian Motion 230% l" c! w/ P3 E) M' u+ q
Stochastic Integrals Defined 232
; c$ D9 D! t- N3 X3 A# R0 c6 H Some Properties of It?Stochastic Integrals 236Summary 237
2 S! t1 z% v1 z. v$ _8 C CHAPTER 9- h, N, e1 _) m7 b+ n. F
Differential Equations and Difference Equations 239Differential Equations Defined 240( [& t, ^9 s0 {9 h' z* v, z7 L2 A
Ordinary Differential Equations 240* ~8 u/ V6 _* Q; d
Order and Degree of an ODE 241$ u2 O! h$ u6 D4 f: r8 L: N4 D* l
Solution to an ODE 241
8 [7 Y u' w" u" c% b1 M# o, i. o Systems of Ordinary Differential Equations 243Contents vii+ R1 x$ M7 ]- S( V- Q" A
Closed-Form Solutions of Ordinary Differential Equations 246Linear Differential Equation 2475 \/ I+ [( p5 r2 W
Numerical Solutions of Ordinary Differential Equations 249The Finite Difference Method 249
L5 b$ [ B2 _1 ]6 Q/ w( C9 } Nonlinear Dynamics and Chaos 256
) M( \& l+ U9 p- Y Fractals 258
2 W! T- w: b. Q, T: W Partial Differential Equations 259
4 x$ D$ X$ X# u; w5 @3 @2 C1 \: A Diffusion Equation 259* e! D8 b, g1 Z+ q
Solution of the Diffusion Equation 261
. d: t- d" L' A! h. @+ |% h4 J Numerical Solution of PDEs 263
" y3 s* d! K# Z2 Q Summary 265 R- ^7 \- Q" W' M
CHAPTER 10
# w) j* i0 q! [, a+ P9 X Stochastic Differential Equations 267
+ O- M. m9 l7 H The Intuition Behind Stochastic Differential Equations 268It?Processes 2717 L4 S5 D2 K& D- [* s
The 1-Dimensional It?Formula 272
4 |3 Q% ]: g6 R, p* c# X5 e( ?7 i Stochastic Differential Equations 2740 i1 r b' R) H
Generalization to Several Dimensions 2761 A% U) L7 w$ a( r$ i7 R1 u! u
Solution of Stochastic Differential Equations 278The Arithmetic Brownian Motion 280
9 {: `* s1 m9 ~2 D. s9 \5 a3 y The Ornstein-Uhlenbeck Process 2806 C* E9 k2 i1 P9 W' Y
The Geometric Brownian Motion 281
6 y, t# z3 V# p; y0 F8 B Summary 2822 ^# x6 x7 D8 k$ T& ~& a3 g; l
CHAPTER 11
* R7 X1 m: M. L. g0 v Financial Econometrics: Time Series Concepts, Representations, and Models 283Concepts of Time Series 284- O6 @! o2 C. I- c
Stylized Facts of Financial Time Series 286Infinite Moving-Average and AutoregressiveRepresentation of Time Series 288. a2 U) Q- H; R1 Q7 z3 W" u8 Q
Univariate Stationary Series 288
: j% D3 ^2 h0 y8 R! ] The Lag Operator L 289
. h) R( ~* ~# p1 k Stationary Univariate Moving Average 292 o7 d( D% T! Y1 l$ K
Multivariate Stationary Series 293) C5 o# k% M7 K; e
Nonstationary Series 295
; j. A* T# U/ u ARMA Representations 297- _9 `& {6 ]/ C( q( _, n
Stationary Univariate ARMA Models 2970 m; b3 G. o! V% k8 ^
Nonstationary Univariate ARMA Models 300( P1 T# q/ j3 s0 L+ ^
Stationary Multivariate ARMA Models 301" m" T& C7 M1 b; o! d
Nonstationary Multivariate ARMA Models 304Markov Coefficients and ARMA Models 304
' M' f$ B4 G1 }9 t Hankel Matrices and ARMA Models 305- w: h) x! E* V- _. I
State-Space Representation 305
/ ^2 g& b7 o* ^; d- n Equivalence of State-Space and ARMA Representations 308Integrated Series and Trends 309
7 g/ j, N- }+ u2 } T Summary 313 Z$ ]& S* ]: X; h& b9 W
viii Contents
: j, O- _* \6 E/ J7 G/ e CHAPTER 12
5 X$ g+ o- i' X, t Financial Econometrics: Model Selection, Estimation, and Testing 315Model Selection 315
. k' {9 Z( {* ] L9 \, {, t" j" f) } Learning and Model Complexity 317! c( [; q, Q- \! G
Maximum Likelihood Estimate 319
! `9 r; t& W' g3 \2 F: R: a Linear Models of Financial Time Series 324Random Walk Models 3248 _/ u3 j/ w1 Y7 }; y3 f
Correlation 327% _7 @9 K0 p1 y$ W! e2 ]' L% \
Random Matrices 329: `5 U! J3 i* z+ m2 d$ y, W
Multifactor Models 332
' B2 Z( B& t$ K* t CAPM 3347 i- Q$ ~( G$ S; W7 F/ x7 k
Asset Pricing Theory (APT) Models 3356 ?4 B' z+ v6 r9 k) a( q
PCA and Factor Models 335" p2 J7 ~' C8 t8 g4 L! d
Vector Autoregressive Models 3388 }2 f# f7 K: u- k: m- m }
Cointegration 339, E* |' t. q; Z: ~, A
State-Space Modeling and Cointegration 342Empirical Evidence of Cointegration in Equity Prices 343Nonstationary Models of Financial Time Series 345The ARCH/GARCH Family of Models 346( W4 |& }7 U6 K7 X9 l2 Q# A: f" Z# x
Markov Switching Models 3470 o6 B' k9 W4 Y9 `
Summary 349
. G! E! ~- v- B5 j$ O$ b0 L% u6 j1 s CHAPTER 13' l5 \# c; T4 N8 _5 m. s/ u
Fat Tails, Scaling, and Stable Laws 351
. x6 d4 {( \7 ?& B6 D6 p Z" Z Scaling, Stable Laws, and Fat Tails 352
' G" A: } z: ]1 n& T Fat Tails 352
" d& P, ~1 P- r, a( o The Class L of Fat-Tailed Distributions 353The Law of Large Numbers and the Central Limit Theorem 358Stable Distributions 360
* b- x; \, K, E" O5 r5 v. n Extreme Value Theory for IID Processes 362Maxima 362 e# j" T, b! i8 }9 U; @
Max-Stable Distributions 368
! U: f7 m. Z$ e) |' d" M& L Generalized Extreme Value Distributions 368Order Statistics 369
/ D1 R& a/ w# I% R `( G0 [ Point Process of Exceedances or Peaks over Threshold 371Estimation 373
0 C' B4 M7 k: y+ } v Eliminating the Assumption of IID Sequences 378Heavy-Tailed ARMA Processes 3812 z: u+ w+ q; @3 t- u$ e2 r
ARCH/GARCH Processes 382
0 l8 q7 d1 v# o* D9 s Subordinated Processes 383
; k2 n8 ~: w- ~% S& Q) E; B Markov Switching Models 384
* F8 l: P7 ]4 D' C* D: I Estimation 384
+ g8 N8 l& N: J4 k e, o5 q8 i9 X" ~ Scaling and Self-Similarity 3851 M5 ?2 j0 Y+ |1 N
Evidence of Fat Tails in Financial Variables 388On the Applicability of Extreme Value Theory in Finance 391Summary 392
: g2 y7 q; J' }9 a Contents ix) ?! b1 X+ K( B" }; B2 g
CHAPTER 14
3 n1 O& `4 w) G% M Arbitrage Pricing: Finite-State Models 393The Arbitrage Principle 393
# K$ D0 [( R+ V5 w+ H) {/ C) H Arbitrage Pricing in a One-Period Setting 395State Prices 397
$ A! M5 ^! a( \ Z Risk-Neutral Probabilities 398
" w5 A# [- @" A Complete Markets 3996 [/ {3 W ~$ a3 g- Z
Arbitrage Pricing in a Multiperiod Finite-State Setting 402Propagation of Information 402; V3 w* [8 f' W" Y7 x
Trading Strategies 4030 \; C/ P2 S% X) M* l5 ]
State-Price Deflator 404" n" H6 \4 |: V' H
Pricing Relationships 405
& d |- ]( f, P0 E0 a( t$ A Equivalent Martingale Measures 414
- A0 \( n1 V' W' e Risk-Neutral Probabilities 416
, A4 c* C0 Q4 F% {1 G7 Z+ h Path Dependence and Markov Models 423& V4 s) C& {3 U* A1 A2 d
The Binomial Model 423
& U9 i5 W0 U( b7 O1 ~2 Y; X3 g Risk-Neutral Probabilities for the Binomial Model 426Valuation of European Simple Derivatives 427Valuation of American Options 429; ~3 W* Z5 j4 s' L9 K2 y% K
Arbitrage Pricing in a Discrete-Time, Continuous-State Setting 430APT Models 435+ [' R! P; n* j3 m `4 V$ A5 c
Testing APT 4363 k R2 ^1 g% k; L
Summary 439
J- H _& Z5 F: q* M8 ?. I. a CHAPTER 15
& |. ~/ ]9 _- A; [& ?, p Arbitrage Pricing: Continuous-State, Continuous-Time Models 441The Arbitrage Principle in Continuous Time 441Trading Strategies and Trading Gains 443
: u2 I3 s( _: C) [ Arbitrage Pricing in Continuous-State, Continuous-Time 445Option Pricing 447& h' J9 w, c9 _9 X
Stock Price Processes 447* v0 q! q3 c* X! X
Hedging 448
" V9 d# n2 }! O$ K The Black-Scholes Option Pricing Formula 449Generalizing the Pricing of European Options 452State-Price Deflators 454
3 Y* ^) n, v0 F4 h Equivalent Martingale Measures 457
( C$ ~8 C# v5 }3 O6 b( I$ R, ^# { Equivalent Martingale Measures and Girsanov’s Theorem 459The Diffusion Invariance Principle 461( o/ t, x+ V7 p b0 F
Application of Girsanov’s Theorem to Black-ScholesOption Pricing Formula 462
8 f+ J! q( x& b2 u* E Equivalent Martingale Measures and Complete Markets 463Equivalent Martingale Measures and State Prices 464Arbitrage Pricing with a Payoff Rate 466
( O* j: w- X- O% p" E- ~ Implications of the Absence of Arbitrage 467Working with Equivalent Martingale Measures 468Summary 468. V7 G0 g0 x) h3 B, D2 B
x Contents# [: T: w$ \2 H. d
CHAPTER 16
" D2 K8 X) ^0 x @ e* d# Y# X$ D Portfolio Selection Using Mean-Variance Analysis 471Diversification as a Central Theme in Finance 472Markowitz’s Mean-Variance Analysis 474( Y2 I+ k, q, Z% j
Capital Market Line 477
M) r$ v2 G4 b) C+ J Deriving the Capital Market Line 478
8 k3 p8 C4 Z* b6 C5 f3 X What is Portfolio M? 481
: B# R* G2 k2 Q" O& B Risk Premium in the CML 482
7 \' @: c: g* I2 Q The CML and the Optimal Portfolio 482
O* ? n* Q; `: @* s7 i Utility Functions and Indifference Curves 482Selection of the Optimal Portfolio 484, a6 g, Y% f' h8 r) E% {
Extension of the Markowitz Mean-Variance Model toInequality Constraints 4851 U/ q+ G/ M/ b3 ^: X0 a8 H
A Second Look at Portfolio Choice 4875 @- B( L9 o4 g) @& v$ C& {( T
The Return Forecast 487: I2 r% h& _- p+ }
The Utility Function 488
9 S& a! t2 Z( c e Optimizers 490( K6 y4 s5 b0 Z) E1 C% a
A Global Probabilistic Framework for Portfolio Selection 490Relaxing the Assumption of Normality 491! [2 M. f) Y0 c4 l
Multiperiod Stochastic Optimization 492
5 H5 F: g3 y6 D6 I Application to the Asset Allocation Decision 494The Inputs 495: f( x' V, _3 U$ V- F z B
Portfolio Selection: An Example 500* F2 n$ H3 `: e% S! X; R
Inclusion of More Asset Classes 503
+ k; z# ]# C+ _7 [) Q/ g' [& g Extensions of the Basic Asset Allocation Model 507Summary 509
4 d8 X2 ? R F d CHAPTER 17
$ e$ j7 U( V' j- V2 H$ a Capital Asset Pricing Model 511
: U3 e1 y! a0 j6 A: G CAPM Assumptions 512- ?( F; \8 s9 L7 g: r! O
Systematic and Nonsystematic Risk 513
7 [0 M [& e* I" j/ J$ d) a' C7 d Security Market Line 5161 B. h! u' E5 L1 H9 z5 X
Estimating the Characteristic Line 518+ ?5 a2 N. N4 d
Testing The CAPM 518" M/ L& j; |* d# B% i9 w$ H
Deriving the Empirical Analogue of the CML 518Empricial Implications 5199 x& d- `" a* y
General Findings of Empirical Tests of the CAPM 520A Critique of Tests of the CAPM 520, ~) E; C4 d! y' p+ N* ?
Merton and Black Modifications of the CAPM 521CAPM and Random Matrices 5226 K! a' @7 D) h& i# n; m
The Conditional CAPM 523
* L8 \( Y8 U) @) G: Y2 ? f Beta, Beta Everywhere 524" L& [! l p* Y7 q6 h, w
The Role of the CAPM in Investment Management Applications 525Summary 5262 o2 @5 P" H7 _- F
CHAPTER 18
5 o+ Y# x" T+ r j$ D- O Multifactor Models and Common Trends for Common Stocks 529Multifactor Models 530
# }! V8 I! p, U$ r0 @$ g Determination of Factors 532
5 h4 K! J) A# `1 z3 G4 @) _ Contents xi$ `5 p; ]. [& K6 s$ E' T* s
Dynamic Market Models of Returns 537& v$ H& A5 r i" }+ ^* j3 A
Estimation of State-Space Models 538" }9 Z I) y; c$ W
Dynamic Models for Prices 538
) C7 D$ ?. y* X) F$ g7 @ Estimation and Testing of Cointegrated Systems 543Cointegration and Financial Time Series 544Nonlinear Dynamic Models for Prices and Returns 546Summary 549
# e" f) U6 j$ T8 v4 h( D' m; x' e CHAPTER 19' O1 x: W* A/ A0 A' _9 b
Equity Portfolio Management 551
! T. f, w+ b: }* Q Integrating the Equity Portfolio Management Process 551Active versus Passive Portfolio Management 552Tracking Error 553' L) M; n8 k, }$ h
Backward-Looking versus Forward-Looking Tracking Error 555The Impact of Portfolio Size, Benchmark Volatility, andPortfolio Beta on Tracking Error 556
1 `8 n+ i" Y" w; D Equity Style Management 560
7 w+ [9 L: a. p$ P* B+ A \ Types of Equity Styles 5606 F Z8 M: v( K$ C9 K$ Z1 j
Style Classification Systems 562" M6 }6 D& K: t1 V3 Q9 o. T
Passive Strategies 564$ f% X; T# J. E& Y Q
Constructing an Indexed Portfolio 5649 t( ]# s) K7 C" b, R9 B
Index Tracking and Cointegration 565- x# \4 R! P+ f5 U$ H9 n
Active Investing 566
* f) h- T; G) D) J2 G% g Top-Down Approaches to Active Investing 566Bottom-Up Approaches to Active Investing 567Fundamental Law of Active Management 568
: j: f7 _' ?8 f3 r; ~& m3 e& Z Strategies Based on Technical Analysis 571Nonlinear Dynamic Models and Chaos 573% a* q# F, `; u6 _: B
Technical Analysis and Statistical NonlinearPattern Recognition 574
0 q6 _2 g% M, m0 B! m Market-Neutral Strategies and Statistical Arbitrage 575Application of Multifactor Risk Models 577Risk Decomposition 577! C' A5 l" f9 u Z& x; u- f
Portfolio Construction and Risk Control 582Assessing the Exposure of a Portfolio 583Risk Control Against a Stock Market Index 587Tilting a Portfolio 587
5 [& E) [ `3 G0 n) B- n2 n7 m Summary 589' ^. { J: A( m( c3 N7 x' S
CHAPTER 206 n, V9 _ A/ f) @. `- {) E
Term Structure Modeling and Valuation of Bonds and Bond Options 593Basic Principles of Valuation of Debt Instruments 594Yield-to-Maturity Measure 596, S& y" l- z' g2 I
Premium Par Yield 598
* W* o4 o% x5 V8 z( x6 y Reinvestment of Cash Flow and Yield 598
* ?. s- }1 c: W: P t$ z8 S8 ]6 a The Term Structure of the Interest Rates and the Yield Curve 599Limitations of Using the Yield to Value a Bond 602Valuing a Bond as a Package of Cash Flows 603Obtaining Spot Rates from the Treasury Yield Curve 603Using Spot Rates to the Arbitrage-Free Value of a Bond 606xii Contents8 u9 o" y: d, y1 P1 A- z" W
The Discount Function 606" _1 I- a* K3 o4 z. g' m
Forward Rates 607
: X4 V2 S; x! @2 a! f2 G6 r Swap Curve 608
: v- U' @0 t# @5 @6 ] Classical Economic Theories About the Determinants of theShape of the Term Structure 612( D. D6 }$ I0 M q6 V2 s
Expectations Theories 613) H8 x* q7 |# C. N
Market Segmentation Theory 618
* y( Q( ^5 A' a ^& H) c& T% ? Bond Valuation Formulas in Continuous Time 618The Term Structure of Interest Rates in Continuous Time 623Spot Rates: Continuous Case 624
- T, |+ v) U) v6 A) I: l: S Forward Rates: Continuous Case 625
$ U. j% x. i9 M) ^% h0 H! t Relationships for Bond and Option Valuation 626The Feynman-Kac Formula 627
+ q: Z1 b) s0 x5 A ~ Multifactor Term Structure Model 632
- q8 Q0 y' R3 r; z Arbitrage-Free Models versus Equilibrium Models 634Examples of One-Factor Term Structure Models 635Two-Factor Models 638
: R! y" g4 w# F$ B" Q& K8 g Pricing of Interest-Rate Derivatives 638" b5 Q" m2 |- A/ _& F: ?
The Heath-Jarrow-Morton Model of the Term Structure 640The Brace-Gatarek-Musiela Model 643
. F. C" X' w6 F Discretization of It?Processes 644, e! e4 m) Q9 f7 Z2 T+ q
Summary 646
) C; {2 t% e- z; s: |" k CHAPTER 21
, s+ T( U) B1 k$ z+ | Bond Portfolio Management 6498 @4 J, E, C" D# O! Y
Management versus a Bond Market Index 649Tracking Error and Bond Portfolio Strategies 651Risk Factors and Portfolio Management Strategies 652Determinants of Tracking Error 654
9 q; ]# l" b L d" C Illustration of the Multifactor Risk Model 654Liability-Funding Strategies 661
' o* { B7 G' z Cash Flow Matching 664
! m e* Z" Q0 l# u* ]( P Portfolio Immunization 667
* B/ h& j' O7 u8 c5 B, R3 C Scenario Optimization 672
9 `" E5 }- v8 {# H Stochastic Programming 673
& w; G5 R; s7 z" e Summary 677( J, R* H8 }( w# f) C; ^
CHAPTER 22 l7 J* _9 k5 e6 u6 ~
Credit Risk Modeling and Credit Default Swaps 679Credit Default Swaps 679+ s3 G d" }4 g* @0 b7 w
Single-Name Credit Default Swaps 680
1 s. ~8 S, v0 ~* _9 q X$ W9 ^ Basket Default Swaps 681% @# J9 F" U& t, k8 @
Legal Documentation 683) L) w* z+ w% F# Y
Credit Risk Modeling: Structural Models 683The Black-Scholes-Merton Model 685
* x1 P6 q- s7 D Geske Compound Option Model 690
8 }) H. b: E5 j7 S( Z7 { Barrier Structural Models 694
/ y1 o% Z0 k) p- p# B( y Advantages and Drawbacks of Structural Models 696Credit Risk Modeling: Reduced Form Models 696Contents xiii
" Y3 \# o+ c+ D0 K1 {' [1 L The Poisson Process 6978 G5 X* X( L% z* f/ x
The Jarrow-Turnbull Model 698
# Y8 }- ^; l+ T; E7 G Transition Matrix 7036 O% C8 N4 o# g
The Duffie-Singleton Model 706/ R& Q: ^! y& S, E" `- R, P% V; J
General Observations on Reduced Form Models 710Pricing Single-Name Credit Default Swaps 710General Framework 711
0 E* R' D0 B% q& { Survival Probability and Forward Default Probability:
# X4 T t+ a' \7 X: f& ? A Recap 712
0 q, Z9 V1 @7 _ Credit Default Swap Value 713
3 P \4 z" F% V0 O& D# Z/ x+ R- F No Need For Stochastic Hazard Rate or Interest Rate 716Delivery Option in Default Swaps 716
$ o7 E- F* t2 k$ F5 J; a+ i Default Swaps with Counterparty Risk 717
, a5 v9 J5 T X2 b6 [ Valuing Basket Default Swaps 718" k, y5 c* z9 n$ K' }* z
The Pricing Model 718
2 M' a8 b2 K# I( B5 G6 v! A How to Model Correlated Default Processes 722Summary 734+ ? E0 _, L, Y5 f$ V! U0 t
CHAPTER 23
Q" |0 i: p$ `. E Risk Management 737+ n4 N) m) h" L) ^% _* i6 R
Market Completeness 738$ \5 Y3 f- y; l# j, X( [7 ^1 x+ h
The Mathematics of Market Completeness 739The Economics of Market Completeness 742/ ^5 j, i# l9 n/ B9 M5 f/ c
Why Manage Risk? 744
! Z# e z5 Z6 c3 e Risk Models 745+ I7 ]: F, d( y; V
Market Risk 745; E+ O% K6 p9 I- \6 o6 V; S; b
Credit Risk 746
& s* a# J9 f. i5 `7 L, }- C. e) F- v Operational Risk 7468 P$ z9 S) x6 l/ X
Risk Measures 747; Q( c7 S P, u/ d+ t
Risk Management in Asset and Portfolio Management 751Factors Driving Risk Management 752- P1 c5 |, w: _4 n) w8 Z2 \/ x
Risk Measurement in Practice 752
2 M4 D' \: m! k! S Getting Down to the Lowest Level 7532 f7 p4 J6 {- U2 Z5 w- L$ i a; A3 V
Regulatory Implications of Risk Measurement 754Summary 755
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