Asset Pricing for Dynamic Economies
By Sumru Altug, Pamela Labadie

Publisher:   Cambridge University Press
Number Of Pages:   602
Publication Date:   2008
ISBN-13 / EAN:   9780521875851

I B A S IC C O N C E P T S 1
1 Complete contingent claims 3
1.1. A one-period model 3
1.1.1. Contingent claims equilibrium 5
1.1.2. Computing the equilibrium 6
1.1.3. Pareto optimal allocations 11
1.2. Security market equilibrium 12
1.2.1. Definition 12
1.2.2. Attaining a CCE by an SME 16
1.2.3. The Pareto optimum and the representative consumer 20
1.3. Conclusions 22
1.4. Exercises 22
2 Arbitrage and asset valuation 25
2.1. Absence of arbitrage: some definitions 25
2.1.1. The law of one price 27
2.1.2. Arbitrage opportunities 30
2.2. Existence of a state-price vector 32
2.2.1. Risk-free asset 34
2.2.2. Risk-neutral pricing 35
2.2.3. The stochastic discount factor 37
2.3. Binomial security markets 38
2.3.1. An economy with two dates 39
2.3.2. A multi-period economy 41
2.4. Conclusions 47
2.5. Exercises 47
3 Expected utility 51
3.1. Expected utility preferences 51
3.1.1. Some definitions 51
3.2. Risk aversion 54
3.3. One-period expected utility analysis 56
3.3.1. The risk premium 58
4 CAPM and APT 72
4.1. The capital asset-pricing model 72
4.1.1. The discount factor 72
4.1.2. Expected utility maximization 74
4.1.3. Alternative derivations 77
4.2. Arbitrage pricing theory 80
4.3. Conclusions 83
4.4. Exercises 83
5 Consumption and saving 86
5.1. A deterministic economy 86
5.1.1. Properties of the saving function 88
5.1.2. Optimal consumption over time 90
5.2. Portfolio choice under uncertainty 94
5.3. A more general problem 95
5.3.1. Precautionary saving 100
5.4. Conclusions 103
5.5. Exercises 104
II R E C U R S I V E M O D E L S 107
6 Dynamic programming 109
6.1. A deterministic growth problem 109
6.1.1. Guess-and-verify 111
6.1.2. Finite horizon economies 113
6.2. Mathematical preliminaries 115
6.2.1. Markov processes 116
6.2.2. Vector space methods 118
6.2.3. Contraction mapping theorem 122
6.3. A consumption-saving problem under uncertainty 126
6.4. Exercises 129
7 Intertemporal risk sharing 133
7.1. Multi-period contingent claims 133
7.1.1. Aggregate uncertainty 134
7.1.2. Central planning problem 139
7.1.3. Sequential trading 140
7.1.4. Implications for pricing assets 145
7.2. Idiosyncratic endowment risk 146
7.2.1. Notation 147
7.2.2. The economy 148
7.2.3. Complete contingent claims 149
8 Consumption and asset pricing 162
8.1. The consumption-based CAPM 162
8.1.1. Recursive competitive equilibrium 164
8.1.2. Asset-pricing functions 167
8.1.3. Risk premia 171
8.1.4. Volatility bounds for intertemporal MRSs 175
8.1.5. The “equity premium puzzle” 178
8.2. Pricing alternative assets 180
8.2.1. Discount bonds and the yield curve 180
8.2.2. Pricing derivative instruments 186
8.2.3. The Black-Scholes options pricing formula 188
8.3. A growing economy 191
8.3.1. Cointegration in asset-pricing relations 195
8.4. Conclusions 198
8.5. Exercises 199
9 Non-separable preferences 202
9.1. Non-time-additive preferences 202
9.1.1. Habit persistence and consumption durability 203
9.1.2. A more general specification 204
9.1.3. A recursive framework 206
9.1.4. Pricing durable consumption goods 209
9.1.5. Asset-pricing relations 210
9.1.6. Log-linear asset-pricing formulas 213
9.2. Non-expected utility 215
9.2.1. Recursive preferences under certainty 215
9.2.2. The role of temporal lotteries 217
9.2.3. Properties of non-expected utility preferences 220
9.2.4. Optimal consumption and portfolio choices 223
9.3. Tests of asset-pricing relations 228
9.4. A model with an external habit 231
9.5. Conclusions 235
9.6. Exercises 235
10 Economies with production 239
10.1. Recursive competitive equilibrium with production 240
10.1.1. Households own the capital stock 241
10.1.2. Households lease capital to firms 246
10.2. Extensions 248
10.2.1. Economies with distortions 248
10.2.2. The role of expectations 252
10.3. Solving models with production 255
10.3.1. A parametric model 256
10.3.2. The stationary distribution 260
10.4. Financial structure of a firm 262
11 Investment 285
11.1. The neoclassical model of investment 286
11.2. The Q theory adjustment-cost model of investment 288
11.2.1. The Q theory of investment 288
11.2.2. Adjustment costs 288
11.2.3. The social planner’s problem 289
11.2.4. The market economy 291
11.2.5. Asset-pricing relations 295
11.3. Irreversible investment 296
11.3.1. A model with partial irreversibility and expandability 297
11.3.2. A model of irreversible investment 305
11.4. An asset-pricing model with irreversible investment 307
11.4.1. The model 307
11.4.2. The social planner’s problem 308
11.4.3. The competitive equilibrium 314
11.4.4. The value of the firm and Q 319
11.4.5. The relation among stock returns, investment, and Q 321
11.5. Conclusions 323
11.6. Exercises 323
12 Business cycles 326
12.1. Business cycle facts 327
12.2. Shocks and propagation mechanisms 331
12.3. Real business cycle models 333
12.3.1. An RBC model 335
12.3.2. A model with indivisible labor supply 338
12.3.3. Other “puzzles” 342
12.4. Solving business cycle models 346
12.4.1. Quadratic approximation 346
12.5. Business cycle empirics 352
12.5.1. Dynamic factor analysis 353
12.5.2. ML and GMM estimation approaches 357
12.5.3. A New Keynesian critique 360
12.6. Conclusions 366
12.7. Exercises 367
III M O N E TA RY A N D I N T E R N AT I O N A L M O D E L S 371
13 Models with cash-in-advance constraints 373
13.1. “Evil is the root of all money” 374
13.2. The basic cash-in-advance model 376