Quantitative Finance (eBook)

Adil Reghai (Paris, France) is head of Quantitative Research on Equity and Commodity Derivatives and Quantitative Investments at Natixis, a leading asset management company and one of the largest in the world. A graduate from Ecole Polytechnique (X92) and Ecole des Mines (P94), Paris, Adil was formerly in charge of quantitative research at Merrill Lynch, BNP Paribas and Calyon. He has participated in numerous quantitative finance conferences including Mathfinance and IQPC events, and lectures on the Financial Mathematics MSc in Nice. Adil's main research interests are local volatility, stochastic volatility, local correlation and hybrids, numerical techniques and applied finance.

Cover 1
Half-Title 2
Title 4
Copyright 5
Dedication 6
Contents 8
List of Figures 12
List of Tables 16
Foreword I 18
Foreword II 20
Acknowledgments 23
1 FinancialModeling 25
Introduction 25
2 AboutModeling 27
A Philosophy ofmodeling 27
B An example from physics and some applications in finance 35
3 From Black & Scholes to SmileModeling
A Study of derivatives under theBlack& Scholesmodel
Methodology 53
The search for convexity 55
Vanilla European option 58
Numerical application 58
Price scenarios 59
Delta gamma scenarios: 59
European binary option 61
Price Scenario 62
Delta and gamma scenarios 62
American binary option 64
Numerical application 64
Price scenario 64
Delta and gamma scenarios 65
Barrier option 66
Price scenario 67
Delta and gamma scenarios 68
Asian option 69
Numerical application 69
Price scenario 70
Delta and gamma scenarios 70
When is it possible to useBlack& Scholes
B Study of classical Smilemodels 80
Black& Scholesmodel
Termstructure Black& Scholes
MonteCarlo simulation 85
Terminal smilemodel 85
Replicationapproach (an almostmodel-free approach) 88
MonteCarlo simulation (direct approach) 89
MonteCarlo simulation (fastmethod) 89
Classic example 91
Separable local volatility 92
Termstructure of parametric slices 93
Dupire/Derman& Kani local volatilitymodel
Stochastic volatilitymodel 102
C Models, advanced characteristics and statistical features 107
Local volatilitymodel 115
Stochastic volatilitymodel 115
4 What is the Fair Value in the Presence of the Smile? 118
A What is the value corresponding to the cost of hedge? 118
TheDelta spot ladder for two barrier options 120
The vega volatility ladder 120
The vega spot ladder 121
Conclusion 123
5 Mono Underlying Risk Exploration 125
Dividends 126
Models: discrete dividends 126
Models: cash amount dividendmodel 127
Models: proportional dividendmodel 128
Models:mixed dividendmodel 129
Models: dividend toxicity index 129
Statistical observations on dividends 130
Interest ratemodeling 133
Models:why dowe need stochastic interest rates? 133
Models: simple hybridmodel 134
Models: statistics and fair pricing 135
Forward skewmodeling 136
The local volatilitymodel is not enough 137
Local volatility calibration 139
Alpha stable process 139
Truncated alpha stable invariants 141
Local volatility truncated alpha stable process 143
6 A General Pricing Formula 146
7 Multi-Asset Case 148
A Study of derivatives under the multi-dimensional Black & Scholes
Methodology 148
PCAfor PnL explanation 151
Eigenvalue decomposition for symmetric operators 151
Stochastic application 152
Profit and loss explanation 153
The source of the parameters 155
Basket option 156
Worst of option (wo: call) 159
Best of option(Bo: put) 163
Other options (Best of call andworst of put) 165
Model calibrationusing fixed-point algorithm 169
Model estimation using an envelope approach 172
Conclusion 176
8 Discounting and General Value Adjustment Techniques 177
Full and symmetric collateral agreement 178
Perfect collateralization 180
Applications 181
Repomarket 182
Optimal posting of collateral 182
Partial collateralization 183
Asymmetric collateralization 183
9 Investment Algorithms 185
What is a good strategy? 186
Asimple strategy 191
Reverse the time 193
Avoidthis datawhen learning 194
Strategies are assets 199
Multi-asset strategy construction 200
Signal detection 200
Predictionmodel 204
Riskminimization 205
10 Building Monitoring Signals 208
A Fat-tail toxicity index 208
B Volatility signals 211
Nature of the returns 213
The dynamic of the returns 217
Signal definition. 218
Asset and strategies cartography 222
Assetmanagement 224
C Correlation signals 225
Simple basketmodel 225
Estimating correlation level 226
Implied correlation skew 230
Multi-dimensional stochastic volatility 232
Local correlationmodel 235
General Conclusion 239
Solutions 240
Bibliography 244
Index 246