Option Pricing, Interest Rates and Risk Management

Cover......Page 1
About......Page 2
Option Pricing, Interest Rates and Risk Management......Page 4
9780521792370......Page 5
Contents......Page 6
Contributors......Page 8
Introduction......Page 10
Option Pricing: Theory and Practice......Page 18
1 Introduction......Page 20
2 Discrete-time models......Page 24
3 Multi-step models......Page 26
4 No-arbitrage criteria in continuous time......Page 34
5 Large financial markets......Page 41
Appendix: Facts from convex analysis......Page 53
References......Page 56
1 Introduction......Page 60
2 The Fundamental Theorem of Asset Pricing......Page 62
3 Arbitrage intervals and superreplication cost......Page 67
4 Models with fixed transaction costs......Page 71
Appendix A......Page 76
Appendix B......Page 81
References......Page 82
1 Introduction......Page 84
2 Put–call symmetry in the standard model......Page 87
3 Put–call symmetry with Ito price processes......Page 90
4 Options with random expiration dates......Page 97
5 Multiasset derivatives......Page 101
6 Occupation time derivatives......Page 106
7 Symmetry property without homogeneity of degree one......Page 110
8 Changes of numeraire and representation of prices......Page 115
9 Conclusion......Page 119
References......Page 120
1 Introduction......Page 122
2 Properties of the price process......Page 127
3 The implications of economic theory......Page 133
4 Economic models of finite variation for asset price processes......Page 138
5 Prices as Levy processes......Page 141
6 The variance gamma model......Page 146
7 Asset allocation in Levy systems......Page 154
8 Spot slide calibration and position measures......Page 161
9 Conclusion......Page 167
References......Page 169
1 Introduction......Page 171
2 Stochastic discount factors and conditioning information......Page 172
3 Conditioning the discounted payoffs on state variables......Page 174
4 Affine regression of payoffs on factors with conditioning on state variables......Page 177
5 A dynamic asset pricing model with latent variables......Page 187
References......Page 199
1 Introduction......Page 202
2 Variance reduction techniques......Page 204
3 Low-discrepancy sequences......Page 224
4 Estimating price sensitivities......Page 235
5 Pricing American options by simulation......Page 242
6 Further topics......Page 248
Appendix: Moment controls beat moment matching asymptotically......Page 249
References......Page 250
Interest Rate Modeling......Page 256
1 Introduction......Page 258
2 Linear realization theory......Page 260
3 Invariant manifolds......Page 271
4 Existence of nonlinear realizations......Page 281
References......Page 293
1 Introduction......Page 295
2 Model preliminaries......Page 297
3 Swap rate dynamics in the Libor model......Page 301
4 Greeks in the Libor model......Page 304
5 Numerical testing and results......Page 311
6 Conclusions......Page 320
Appendix B. Rank one and separable volatility......Page 322
Appendix C. Yield curve and volatility structures......Page 327
References......Page 329
1 Introduction......Page 331
2 The BGM Model......Page 339
3 Kolmogorov equations......Page 342
References......Page 352
1 Introduction......Page 353
2 Modelling of forward Libor rates......Page 355
3 Modelling of forward swap rates......Page 384
4 Markov-functional models......Page 402
References......Page 410
Risk Management and Hedging......Page 414
1 Introduction......Page 416
2 Credit derivatives......Page 417
3 Valuation of defaultable claims......Page 421
4 Alternative recovery schemes......Page 429
5 Credit-ratings-based Markov model......Page 437
6 Modelling with state variables......Page 440
7 Credit-spreads-based HJM type model......Page 445
References......Page 471
1 Introduction......Page 475
2 Trading realized volatility via static positions in options......Page 477
3 Trading realized volatility by delta-hedging options......Page 480
4 Trading realized volatility by using volatility contracts......Page 482
5 Connection to recent work on stochastic volatility......Page 489
Appendix 1: Spanning with bonds and options......Page 490
Appendix 2: Derivation of futures position when synthesizing contract paying future variance along a strike......Page 491
References......Page 492
1 Introduction......Page 494
2 A model of exposure and hedging......Page 497
3 Spot risk and running risk......Page 502
4 Without mean reversion......Page 504
5 With mean reversion......Page 507
6 Most likely paths......Page 511
7 Assessing the approximations......Page 515
Appendix A: Futures and forwards......Page 519
Appendix B: The rolling stack and conditional expectations......Page 522
Appendix C: Derivation of optimal paths......Page 523
References......Page 524
1 Introduction......Page 526
2 A Markovian stochastic volatility framework......Page 527
3 Local risk-minimisation......Page 528
4 Mean-variance hedging......Page 531
5 Some specific models......Page 535
6 Computation of expected squared costs, prices and hedge ratios......Page 539
7 Distributions of squared costs......Page 546
8 Other numerical results......Page 550
9 Conclusion......Page 553
References......Page 554
0 Introduction......Page 555
1 Notations and preliminaries......Page 558
2 The martingale case......Page 560
3 Local risk-minimization......Page 565
4 Mean-variance hedging......Page 577
References......Page 588
Utility Maximization......Page 592
1 Introduction......Page 594
2 The complete market model......Page 597
3 Pricing in the complete market......Page 599
4 Portfolio constraints......Page 602
5 Superreplication under portfolio constraints......Page 604
6 The case of concave drift......Page 614
7 Utility functions......Page 618
8 Portfolio optimization under constraints......Page 620
9 Examples......Page 624
10 Utility based pricing......Page 627
11 The transaction costs model......Page 629
12 State-price densities......Page 630
13 The minimal superreplication price......Page 632
14 Utility maximization under transaction costs......Page 638
References......Page 645
1 Introduction......Page 649
2 Formulation and financial interpretation......Page 650
3 Filtering and martingale methods......Page 654
4 Dynamic programming......Page 660
5 The cost of uncertainty......Page 667
6 The constrained optimization problems......Page 671
7 Auxiliary markets and optimality conditions......Page 673
8 Appendix: proofs of selected results......Page 680
References......Page 684