Contents	5
	Contributors	17
	Preface	19
	Part I Finance	23
	1 Stable Distributions	25
	1.1 Introduction	25
	1.2 Definitions and Basic Characteristics	26
	1.2.1 Characteristic Function Representation	28
	1.2.2 Stable Density and Distribution Functions	30
	1.3 Simulation of stable Variables	32
	1.4 Estimation of Parameters	34
	1.4.1 Tail Exponent Estimation	35
	1.4.2 Quantile Estimation	37
	1.4.3 Characteristic Function Approaches	38
	1.4.4 Maximum Likelihood Method	39
	1.5 Financial Applications of Stable Laws	40
	2 Extreme Value Analysis and Copulas	49
	2.1 Introduction	49
	2.1.1 Analysis of Distribution of the Extremum	50
	2.1.2 Analysis of Conditional Excess Distribution	51
	2.1.3 Examples	52
	2.2 Multivariate Time Series	57
	2.2.1 Copula Approach	57
	2.2.2 Examples	60
	2.2.3 Multivariate Extreme Value Approach	61
	2.2.4 Examples	64
	2.2.5 Copula Analysis for Multivariate Time Series	65
	2.2.6 Examples	66
	3 Tail Dependence	69
	3.1 Introduction	69
	3.2 What is Tail Dependence?	70
	3.3 Calculation of the Tail-dependence Coefficient	73
	3.3.1 Archimedean Copulae	73
	3.3.2 Elliptically-contoured Distributions	74
	3.3.3 Other Copulae	78
	3.4 Estimating the Tail-dependence Coefficient	79
	3.5 Comparison of TDC Estimators	82
	3.6 Tail Dependence of Asset and FX Returns	85
	3.7 Value at Risk – a Simulation Study	88
	4 Pricing of Catastrophe Bonds	97
	4.1 Introduction	97
	4.1.1 The Emergence of CAT Bonds	98
	4.1.2 Insurance Securitization	100
	4.1.3 CAT Bond Pricing Methodology	101
	4.2 Compound Doubly Stochastic Poisson Pricing Model	103
	4.3 Calibration of the Pricing Model	104
	4.4 Dynamics of the CAT Bond Price	108
	5 Common Functional Implied Volatility Analysis	119
	5.1 Introduction	119
	5.2 Implied Volatility Surface	120
	5.3 Functional Data Analysis	122
	5.4 Functional Principal Components	125
	5.4.1 Basis Expansion	127
	5.5 Smoothed Principal Components Analysis	129
	5.5.1 Basis Expansion	130
	5.6 Common Principal Components Model	131
	6 Implied Trinomial Trees	139
	6.1 Option Pricing	140
	6.2 Trees and Implied Trees	142
	6.3 Implied Trinomial Trees	144
	6.3.1 Basic Insight	144
	6.3.2 State Space	146
	6.3.3 Transition Probabilities	148
	6.3.4 Possible Pitfalls	149
	6.4 Examples	151
	6.4.1 Pre-speci.ed Implied Volatility	151
	6.4.2 German Stock Index	156
	7 Heston’s Model and the Smile	165
	7.1 Introduction	165
	7.2 Heston’s Model	167
	7.3 Option Pricing	170
	7.3.1 Greeks	172
	7.4 Calibration	173
	7.4.1 Qualitative E.ects of Changing Parameters	175
	7.4.2 Calibration Results	177
	8 FFT-based Option Pricing	187
	8.1 Introduction	187
	8.2 Modern Pricing Models	187
	8.2.1 Merton Model	188
	8.2.2 Heston Model	189
	8.2.3 Bates Model	191
	8.3 Option Pricing with FFT	192
	8.4 Applications	196
	9 Valuation of Mortgage Backed Securities: from Optimality to Reality	205
	9.1 Introduction	205
	9.2 Optimally Prepaid Mortgage	208
	9.2.1 Financial Characteristics and Cash Flow Analysis	208
	9.2.2 Optimal Behavior and Price	208
	9.3 Valuation of Mortgage Backed Securities	216
	9.3.1 Generic Framework	217
	9.3.2 A Parametric Speci.cation of the Prepayment Rate	219
	9.3.3 Sensitivity Analysis	222
	10 Predicting Bankruptcy with Support Vector Machines	229
	10.1 Bankruptcy Analysis Methodology	230
	10.2 Importance of Risk Classification in Practice	234
	10.3 Lagrangian Formulation of the SVM	237
	10.4 Description of Data	240
	10.5 Computational Results	241
	11 Econometric and Fuzzy Modelling of Indonesian Money Demand	253
	11.1 Speci.cation of Money Demand Functions	254
	11.2 The EconometricApproach to Money Demand	256
	11.2.1 Econometric Estimation of Money Demand Functions	256
	11.2.2 Modelling Indonesian Money Demand with Econometric Techniques	258
	11.3 The Fuzzy Approach to Money Demand	264
	11.3.1 Fuzzy Clustering	264
	11.3.2 The Takagi-Sugeno Approach	265
	11.3.3 Model Identi.cation	266
	11.3.4 Modelling Indonesian Money Demand with Fuzzy Techniques	267
	11.4 Conclusions	270
	12 Nonparametric Productivity Analysis	275
	12.1 The Basic Concepts	276
	12.2 Nonparametric Hull Methods	280
	12.2.1 Data Envelopment Analysis	281
	12.2.2 Free Disposal Hull	282
	12.3 DEA in Practice: Insurance Agencies	283
	12.4 FDH in Practice: Manufacturing Industry	285
	Part II	292
	13 Loss Distributions	293
	13.1 Introduction	293
	13.2 Empirical Distribution Function	294
	13.3 Analytical Methods	296
	13.3.1 Log-normal Distribution	296
	13.3.2 Exponential Distribution	297
	13.3.3 Pareto Distribution	299
	13.3.4 Burr Distribution	302
	13.3.5 Weibull Distribution	302
	13.3.6 Gamma Distribution	304
	13.3.7 Mixture of Exponential Distributions	306
	13.4 Statistical Validation Techniques	307
	13.4.1 Mean Excess Function	307
	13.4.2 Tests Based on the Empirical Distribution Function	309
	13.4.3 Limited Expected Value Function	313
	13.5 Applications	315
	14 Modeling of the Risk Process	323
	14.1 Introduction	323
	14.2 Claim Arrival Processes	325
	14.2.1 Homogeneous Poisson Process	325
	14.2.2 Non-homogeneous Poisson Process	327
	14.2.3 Mixed Poisson Process	330
	14.2.4 Cox Process	331
	14.2.5 Renewal Process	332
	14.3 Simulation of Risk Processes	333
	14.3.1 Catastrophic Losses	333
	14.3.2 Danish Fire Losses	338
	15 Ruin Probabilities in Finite and Infinite Time	345
	15.1 Introduction	345
	15.1.1 Light- and Heavy-tailed Distributions	347
	15.2 Exact Ruin Probabilities in Infinite Time	350
	15.2.1 No Initial Capital	351
	15.2.2 Exponential Claim Amounts	351
	15.2.3 Gamma Claim Amounts	351
	15.2.4 Mixture of Two Exponentials Claim Amounts	353
	15.3 Approximations of the Ruin Probability in Infinite Time	354
	15.3.1 Cram´ er–Lundberg Approximation	355
	15.3.2 Exponential Approximation	356
	15.3.3 Lundberg Approximation	356
	15.3.4 Beekman–Bowers Approximation	357
	15.3.5 Renyi Approximation	358
	15.3.6 De Vylder Approximation	359
	15.3.7 4-moment Gamma De Vylder Approximation	360
	15.3.8 Heavy Tra.c Approximation	362
	15.3.9 Light Tra.c Approximation	363
	15.3.10 Heavy-light Tra.c Approximation	364
	15.3.11 Subexponential Approximation	364
	15.3.12 Computer Approximation via the Pollaczek-Khinchin Formula	365
	15.3.13 Summary of the Approximations	366
	15.4 Numerical Comparison of the Infinite Time Approximations	367
	15.5 Exact Ruin Probabilities in Finite Time	371
	15.5.1 Exponential Claim Amounts	372
	15.6 Approximations of the Ruin Probability in Finite Time	372
	15.6.1 Monte Carlo Method	373
	15.6.2 Segerdahl Normal Approximation	373
	15.6.3 Diffusion Approximation	375
	15.6.4 Corrected Di.usion Approximation	376
	15.6.5 Finite Time De Vylder Approximation	377
	15.6.6 Summary of the Approximations	378
	15.7 Numerical Comparison of the Finite Time Approximations	378
	16 Stable Difiusion Approximation of the Risk Process	385
	16.1 Introduction	385
	16.2 Brownian Motion and the Risk Model for Small Claims	386
	16.2.1 Weak Convergence of Risk Processes to Brownian Motion	387
	16.2.2 Ruin Probability for the Limit Process	387
	16.2.3 Examples	388
	16.3 Stable Levy Motion and the Risk Model for Large Claims	390
	16.3.1 Weak Convergence of Risk Processes to a-stable Levy Motion	391
	16.3.2 Ruin Probability in the Limit Risk Model for Large Claims	392
	16.3.3 Examples	394
	17 Risk Model of Good and Bad	399
	17.1 Introduction	399
	17.2 Fractional Brownian Motion and the Risk Model of Good and Bad Periods	400
	17.3 Ruin Probability in the Limit Risk Model of Good and Bad Periods	403
	17.4 Examples	406
	18 Premiums in the Individual and Collective Risk Models	411
	18.1 Premium Calculation Principles	412
	18.2 Individual Risk Model	414
	18.2.1 General Premium Formulae	415
	18.2.2 Premiums in the Case of the Normal Approximation	416
	18.2.3 Examples	417
	18.3 Collective Risk Model	420
	18.3.1 General Premium Formulae	421
	18.3.2 Premiums in the Case of the Normal and Translated Gamma Approximations	422
	18.3.3 Compound Poisson Distribution	424
	18.3.4 Compound Negative Binomial Distribution	425
	18.3.5 Examples	427
	19 Pure Risk Premiums under Deductibles	431
	19.1 Introduction	431
	19.2 General Formulae for Premiums Under Deductibles	432
	19.2.1 Franchise Deductible	433
	19.2.2 Fixed Amount Deductible	435
	19.2.3 Proportional Deductible	436
	19.2.4 Limited Proportional Deductible	436
	19.2.5 Disappearing Deductible	438
	19.3 Premiums Under Deductibles for Given Loss Distributions	440
	19.3.1 Log-normal Loss Distribution	441
	19.3.2 Pareto Loss Distribution	442
	19.3.3 Burr Loss Distribution	445
	19.3.4 Weibull Loss Distribution	449
	19.3.5 Gamma Loss Distribution	451
	19.3.6 Mixture of Two Exponentials Loss Distribution	453
	19.4 Final Remarks	454
	20 Premiums, Investments, and Reinsurance	457
	20.1 Introduction	457
	20.2 Single-period Criterion and the Rate of Return on Capital	460
	20.2.1 Risk Based Capital Concept	460
	20.2.2 How to Choose Parameter Values?	461
	20.3 The Top-down Approach to Individual Risks Pricing	463
	20.3.1 Approximations of Quantiles	463
	20.3.2 Marginal Cost Basis for Individual Risk Pricing	464
	20.3.3 Balancing Problem	465
	20.3.4 A Solution for the Balancing Problem	466
	20.3.5 Applications	466
	20.4 Rate of Return and Reinsurance Under the Short Term Criterion	467
	20.4.1 General Considerations	468
	20.4.2 Illustrative Example	469
	20.4.3 Interpretation of Numerical Calculations in Example 2	471
	20.5 Ruin Probability Criterion when the Initial Capital is Given	473
	20.5.1 Approximation Based on Lundberg Inequality	473
	20.5.2 Zero” Approximation	475
	20.5.3 Cram´ er–Lundberg Approximation	475
	20.5.4 Beekman–Bowers Approximation	476
	20.5.5 Di.usion Approximation	477
	20.5.6 De Vylder Approximation	478
	20.5.7 Subexponential Approximation	479
	20.5.8 Panjer Approximation	479
	20.6 Ruin Probability Criterion and the Rate of Return	481
	20.6.1 Fixed Dividends	481
	20.6.2 Flexible Dividends	483
	20.7 Ruin Probability, Rate of Return and Reinsurance	485
	20.7.1 Fixed Dividends	485
	20.7.2 Interpretation of Solutions Obtained in Example 5	486
	20.7.3 Flexible Dividends	488
	20.7.4 Interpretation of Solutions Obtained in Example 6	489
	20.8 Final Remarks	491
	Part III	494
	21 Working with the XQC	495
	21.1 Introduction	495
	21.2 The XploRe Quantlet Client	496
	21.2.1 Con.guration	496
	21.2.2 Getting Connected	497
	21.3 Desktop	498
	21.3.1 XploRe Quantlet Editor	499
	21.3.2 Data Editor	500
	21.3.3 Method Tree	505
	21.3.4 Graphical Output	507
	Index	511