Stochastic Filtering With Applications in Finance

Contents......Page 12
Preface......Page 8
1. Introduction: Stochastic Filtering in Finance......Page 16
1.2 Examples of Filtering Applications......Page 17
1.3 Linear Kalman Filter......Page 18
1.4 Extended Kalman Filter (EKF)......Page 21
1.5 Applying EKF to Interest Rate Model......Page 22
1.6 Unscented Kalman Filter (UKF) for Nonlinear Models......Page 25
1.7 Background to Particle Filter for Non Gaussian Problems......Page 28
1.8 Particle Filter Algorithm......Page 29
1.9 Unobserved Component Models......Page 31
1.10 Concluding Remarks......Page 34
2. Foreign Exchange Market – Filtering Applications......Page 35
2.1 Mean Reversion in Real Exchange Rates......Page 36
2.2 Common and Specific Components in Currency Movements......Page 40
2.3 Persistent in Real Interest Rate Differentials......Page 45
2.4 Risk Premia in Forward Exchange Rate......Page 49
2.4.1 Approach based on Market Price of Risk (BCP)......Page 51
2.4.2 Method of Wolff/Cheung......Page 55
2.4.3 Data and Empirical Results......Page 56
2.4.4 Summary of Section 2.4......Page 58
2.5 Concluding Remarks......Page 62
3. Equity Market – Filtering Applications......Page 63
3.1 Introduction to Equity Price of Risk......Page 64
3.1.1 A Model for Equity Price of Risk......Page 66
3.1.2 Data Used for Empirical Study......Page 67
3.1.3 Discussion of Empirical Results......Page 68
3.1.4 Summary of Results......Page 76
3.2 Economic Convergence in a Filtering Framework......Page 77
3.2.1 Defining Convergence......Page 79
3.2.2 Testing for Convergence......Page 80
3.2.3 Testing Convergence – Dickey-Fuller......Page 81
3.2.4 Testing Convergence – Kalman Filter......Page 82
3.3.1 Background to Ex Ante Risk Premium......Page 84
3.3.2 A Model for Ex Ante Risk Premium......Page 85
3.3.3 Filtering Ex Ante Risk Premium......Page 87
3.3.5 Summarizing Ex-Ante Risk Premium for UK......Page 88
3.4 Concluding Remarks......Page 90
4. Filtering Application — Inflation and the Macroeconomy......Page 91
4.1 Background and Macroeconomic Issues......Page 92
4.2 Inflation Targeting Countries and Data Requirement......Page 94
4.3 Model for Inflation Uncertainties......Page 95
4.4 Testing Fisher Hypothesis......Page 97
4.5 Empirical Results and Analysis......Page 98
4.6 Concluding Remarks......Page 100
5. Interest Rate Model and Non-Linear Filtering......Page 109
5.1 Background to HJM Model and the Related Literature......Page 110
5.2 The Basic HJM Structure......Page 112
5.3 Forward Rate Volatility: Deterministic Function of Time......Page 115
5.4 Forward Rate Volatility: Stochastic......Page 117
5.5 Estimation via Kalman Filtering......Page 122
5.6 Preference-Free Approach to Bond Pricing......Page 124
5.7 Concluding Remarks......Page 127
Appendix 5.1 Arbitrage-Free SDE for the Bond Price......Page 129
Appendix 5.2: Proof of Proposition 1......Page 132
Appendix 5.3: Proof of Proposition 2......Page 134
Appendix 5.4: Proof Proposition 3......Page 137
6. Filtering and Hedging using Interest Rate Futures......Page 140
6.1 Background Details......Page 141
6.2 The Futures Price Model in the HJM Framework......Page 142
6.3 Non-Linear Filter for Futures Price System......Page 146
6.4 Data Used in Empirical Study......Page 149
6.5 Empirical Results......Page 150
6.6 Concluding Remarks......Page 153
Appendix 6.1......Page 154
7. A Multifactor Model of Credit Spreads......Page 164
7.1 Background and Related Research......Page 165
7.2 Variables Influencing Changes in Credit Spreads......Page 166
7.3 Credit Spread and Default Risk......Page 168
7.4 Credit Spread and Liquidity......Page 170
7.5 Alternative Approach to Analyzing Credit Spread......Page 171
7.6 Data Used......Page 174
7.7 Multifactor Model for Credit Spread......Page 175
7.9.1 Results for Apr-96 to Mar-03......Page 177
7.9.2 Results for Apr-96 to Mar-08......Page 180
7.9.4 Discussion......Page 183
7.10 Concluding Remarks......Page 184
8. Credit Default Swaps – Filtering the Components......Page 199
8.1 Background to Credit Default Swaps......Page 200
8.2 What is in the Literature Already?......Page 203
8.3 Credit Derivatives Market and iTraxx Indices......Page 205
8.4 CDS Index Data and Preliminary Analysis......Page 207
Credit Rating:......Page 210
Short-Term Interest Rate:......Page 211
Slope of the Yield Curve:......Page 212
Equity Volatility:......Page 213
Bid-Ask Spread (Proxy for Liquidity)......Page 215
8.6.1 Latent-Component Model for iTraxx Indices......Page 216
8.6.2 State Space Model and Stochastic Filtering......Page 218
8.6.3 Linear Regression Model for the Determinants of the CDS Components......Page 219
8.7.1 Model Parameters and the Extracted Components......Page 220
8.7.2 Determinants of the Extracted Components......Page 222
8.8 Concluding Summary......Page 226
9. CDS Options, Implied Volatility and Unscented Kalman Filter......Page 244
9.1 Background to Stochastic Volatility......Page 245
9.2 Heston Model in Brief......Page 246
9.3.1 Transition Equation......Page 247
9.3.2 Measurement Equation: CDS Option Price......Page 248
9.3.3 Measurement Equation Derivation......Page 250
9.4 General State Space Model and Filter Revisited......Page 252
9.4.1 Additive Non-Linear State Space model (Recap)......Page 253
9.4.2 The Scaled Unscented Transformation (Recap)......Page 255
9.5 The Application of Unscented Kalman Filter......Page 258
9.6 Empirical Results......Page 260
9.7 Concluding Remarks......Page 264
10. Stochastic Volatility Model and Non-Linear Filtering Application......Page 272
10.1 Background to Stochastic Volatility Models......Page 273
10.2 Stochastic Volatility Models of Short-term Interest Rates......Page 274
10.2.1 SV-ARMA Specification......Page 276
10.2.2 Exogenous Variables......Page 277
10.3 Data for Analysis......Page 278
10.4 Analysis of Estimation Results......Page 279
10.5 Comparison of Volatility Estimates......Page 281
10.6 Outline of State Space Model Estimation via MCL......Page 286
10.7 Concluding Summary......Page 288
11. Applications for Filtering with Jumps......Page 299
11.1 Background to Electricity Market and Prices......Page 300
11.2 A Model for Spot Electricity Prices......Page 303
11.3 State Space Model, Kalman Filter and Poisson Jumps......Page 306
11.4 Data and Empirical Results for Electricity Market......Page 309
11.5 Summarizing Electricity Market Application......Page 311
11.6 Background to Jumps in CDS Indices......Page 312
11.7 CDS Data and Preliminary Analysis......Page 315
11.8.2 Model for Individual iTraxx Indices......Page 316
11.8.3 Multivariate Analysis of Jumps in iTraxx Index with One Latent Common Factor......Page 319
11.9 Analysis of Results from the CDS Market......Page 322
11.10 Summarizing CDS Market Application......Page 323
Bibliography......Page 335
Index......Page 352