Market Consistency: Model Calibration in Imperfect Markets (The Wiley Finance Series)

Market Consistency......Page 3
Contents......Page 7
Preface......Page 15
Acknowledgements......Page 19
Abbreviations......Page 21
Notation......Page 25
1.1 Market consistency......Page 29
1.2 The primacy of the ‘market’......Page 30
1.4 Structure of the book......Page 31
1.5 Terminology......Page 33
2.2.1 The concept of ‘value’......Page 37
2.2.2 The time value of money......Page 38
2.2.3 Axioms of additivity, scalability and uniqueness......Page 39
2.2.4 Market consistent valuations......Page 41
2.2.5 Should financial practitioners always use market consistent valuations?......Page 42
2.2.6 Equity between parties......Page 43
2.2.7 Embedded values and franchise values......Page 44
2.2.8 Solvency calculations......Page 45
2.2.10 Bid–offer spreads......Page 47
2.3 Regulatory drivers favouring market consistent valuations......Page 48
2.4 Underlying theoretical attractions of market consistent valuations......Page 50
2.5 Reasons why some people reject market consistency......Page 51
2.6 Market making versus position taking......Page 52
2.8 Valuation and regulation......Page 53
2.9 Marking-to-market versus marking-to-model......Page 56
2.10 Rational behaviour?......Page 58
3.3 The importance of the ‘marginal’ trade......Page 61
3.4.2 US accounting – FAS 157......Page 63
3.4.3 Guidance on how to interpret FAS, IAS, IFRS, etc.......Page 64
3.4.4 EU insurance regulation – ‘Solvency II’......Page 65
3.4.6 UK pension fund accounting and solvency computation......Page 70
3.5.2 Contrasting ‘market consistent’ values with ‘real world’ values......Page 71
3.5.3 Stressing the aim of avoiding subjectivity where possible......Page 74
3.5.5 Application only if obvious market observables exist......Page 75
3.5.6 Hedgeable liabilities......Page 76
3.5.7 Fair valuation in an asset management context......Page 77
4.1 Introduction......Page 79
4.2.1 No arbitrage......Page 80
4.2.2 Valuation of symmetric derivatives......Page 84
4.2.3 Valuation of asymmetric derivatives......Page 89
4.2.4 Valuation of path dependent derivatives......Page 91
4.3.1 Lattice valuation approaches......Page 92
4.3.2 Stochastic (Ito) calculus......Page 98
4.3.3 The martingale formulation......Page 103
4.3.4 Hedging......Page 104
4.3.5 Path dependent derivatives......Page 108
4.4.1 Market conventions versus underlying market beliefs......Page 109
4.4.2 Why calculate market implied parameters such as implied volatility?......Page 111
4.4.3 The volatility smile or skew......Page 112
4.5.1 Mileage options......Page 113
4.5.2 Jump processes......Page 114
4.5.3 Stochastic volatility......Page 116
4.5.4 Non-zero dealing costs......Page 117
4.5.5 Interpretation in the context of Modern Portfolio Theory......Page 118
4.6 Equity, commodity and currency derivatives......Page 119
4.7 Interest rate derivatives......Page 120
4.8 Credit derivatives......Page 121
4.9 Volatility derivatives......Page 123
4.10 Hybrid instruments......Page 124
4.11 Monte Carlo techniques......Page 125
4.12.1 Weighted Monte Carlo......Page 126
4.12.2 Analytical weighted Monte Carlo......Page 127
4.13 Further comments on calibration......Page 129
5.2 What do we mean by ‘risk-free’?......Page 131
5.3.2 Choice between different reference rates......Page 143
5.3.3 How risk-free is government debt?......Page 148
5.3.4 Impact of choice of reference rate......Page 152
6.2 Market experience......Page 155
6.3.1 Consideration of ‘extreme’ events......Page 158
6.3.2 Or maybe not such extreme events?......Page 159
6.3.3 Contagion......Page 160
6.4 General principles......Page 161
6.5.1 Different points of view......Page 162
6.5.2 Funding versus market liquidity......Page 164
6.5.3 The impact of these different points of view......Page 165
6.5.4 Modelling liquidity premia on different instruments......Page 166
6.6 Liquidity of pooled funds......Page 167
6.7 Losing control......Page 169
7.2 Instrument-specific risk measures......Page 173
7.3.1 Introduction......Page 176
7.3.2 Ex-post (i.e. historic, backward-looking, retrospective) risk measures......Page 178
7.3.3 Ex-ante (i.e. forward-looking, prospective) risk measures......Page 181
7.4.2 Mathematical characterisation of different types of risk model......Page 185
7.4.3 Intrinsic ways of estimating risk models from past data......Page 186
7.4.4 Matrix analysis......Page 187
7.4.6 Choice of underlying distributional form......Page 189
7.5.1 The sparsity of the data available......Page 192
7.5.2 Idiosyncratic risk......Page 194
7.6.1 Introduction......Page 195
7.6.2 Credit ratings......Page 196
7.6.4 Collateralised debt obligations (CDOs)......Page 198
7.6.5 An accident waiting to happen?......Page 203
7.7.1 Intrinsic rationale......Page 204
7.7.2 Traditional (covariance-based) risk attribution......Page 205
7.7.4 ‘Stand-alone’ risk statistics......Page 206
7.8.1 Introduction......Page 207
7.8.2 Different interpretations......Page 208
7.8.3 Further comments......Page 211
8.1 Introduction......Page 213
8.2 Financial stability......Page 214
8.3.1 The Basel Accords......Page 217
8.3.2 Market risk......Page 218
8.3.3 Credit risk......Page 220
8.3.4 Operational risk......Page 221
8.4.1 Solvency II......Page 222
8.4.3 Best estimate calculations......Page 223
8.4.4 Surrender rates......Page 225
8.4.5 UK regulatory capital computations for insurers......Page 226
8.5 Pension funds......Page 228
8.6 Different types of capital......Page 230
9.1 Introduction......Page 233
9.2 Referring to market values......Page 235
9.3.1 Introduction......Page 237
9.3.2 In-sample versus out-of-sample backtesting......Page 238
9.3.3 Testing backtest quality statistically......Page 239
9.4 Fitting observed distributional forms......Page 241
9.5.2 Fat tails......Page 243
9.5.3 Skew, kurtosis and the (fourth-moment) Cornish-Fisher approach......Page 248
9.5.4 Weaknesses of the Cornish-Fisher approach......Page 249
9.5.5 Improving on the Cornish-Fisher approach......Page 251
9.5.6 Time-varying volatility......Page 252
9.5.7 Crowded trades......Page 254
9.6.1 Introduction......Page 255
9.6.2 Visualising fat tails in multiple return series......Page 256
9.6.3 Copulas, Sklar’s theorem and quantiles......Page 258
9.6.4 Fractile–fractile (i.e. quantile–quantile box) plots......Page 261
9.6.5 Time-varying volatility......Page 264
9.6.6 Differentiating between return series......Page 266
10.2.1 Refining the granularity-based approach to risk modelling......Page 269
10.2.2 Time horizons......Page 271
10.2.3 Additivity, scalability and coherence......Page 273
10.3.1 Comparison with current risk management practices......Page 274
10.3.2 The CDO analogy......Page 275
11.2 The 2007–09 credit crisis......Page 279
11.3 Underwriting of failures......Page 283
11.4 Possible pro-cyclicality in regulatory frameworks......Page 284
11.5 Re-expressing capital adequacy in a market consistent framework......Page 287
11.6 Discount rates......Page 288
11.7 Pro-cyclicality in Solvency II......Page 289
11.8 Incentive arrangements......Page 291
11.10 Sovereign default risk......Page 292
12.2.1 Introduction......Page 295
12.2.3 Mean–variance optimisation......Page 296
12.2.5 Alpha–beta separation......Page 298
12.3 Other portfolio construction styles......Page 299
12.4.1 Introduction......Page 300
12.4.2 Information ratios......Page 301
12.4.3 Sensitivity to the input assumptions......Page 303
12.5.1 Implied alphas......Page 304
12.6 Calibrating portfolio construction techniques to the market......Page 305
12.7.1 Re-normalising historic return distributions......Page 306
12.7.2 Using co-skew, co-kurtosis and other co-moments......Page 307
12.8.1 Black-Litterman......Page 308
12.9 Taking due account of other investors’ risk preferences......Page 309
13.2.1 The price formation process......Page 311
13.2.2 Price discovery......Page 313
13.3.2 Relatively simple assets independent of the firm......Page 315
13.3.3 More complex assets independent of the firm......Page 317
13.3.5 Further comments......Page 319
13.4.2 Sure promises from infinitely well-capitalised entities......Page 324
13.4.3 Uncertain promises from finitely capitalised entities......Page 326
13.4.5 Bid and offer prices......Page 327
13.4.6 Annuities......Page 328
13.4.7 Unit-linked life insurance......Page 329
13.4.8 With-profits (i.e. participating) business......Page 330
13.4.9 Other non-profit non-linked life insurance......Page 331
13.4.10 Non-life (i.e. property/casualty) insurance......Page 332
13.5 Market consistent embedded values......Page 333
13.6.2 Current methodologies......Page 335
13.6.4 Correlations......Page 336
13.6.6 Credit risk......Page 337
13.6.8 Bid–offer spreads......Page 338
13.6.12 Operational risk......Page 339
13.6.13 Non-life (i.e. property/casualty) insurance risk......Page 340
13.7.2 Solvency valuations......Page 341
13.7.3 Ongoing valuations......Page 342
13.7.4 Transfer values......Page 343
13.8 Unit pricing......Page 344
14.2 Market consistent principles......Page 345
Bibliography......Page 353
Index......Page 359