Hidden Markov models in finance

HIDDEN MARKOV MODELS IN FINANCE......Page 1
Springerlink......Page 0
Recent titles in the International Series in Operations Research and Management Science......Page 3
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
List of Contributors......Page 10
Biographical Notes......Page 12
Preface......Page 16
1.1 Introduction......Page 21
1.2 A new representation for modeling regime shift......Page 23
1.3.3 The risk-neutral probability measure......Page 25
1.3.4 The term structure of interest rates......Page 28
1.4.1 Affine regime-switching models......Page 29
References......Page 33
2.1 Introduction......Page 35
2.2.1 The Markov chain......Page 37
2.2.2 The short-term interest rate......Page 40
2.2.3 The zero-coupon bond value......Page 41
2.3 Implementation......Page 42
2.4 Results......Page 45
References......Page 50
3.1 Introduction......Page 51
3.2 The model dynamics......Page 53
3.3 Dimension reduction to regime-switching PDE......Page 58
References......Page 62
4.1 Introduction......Page 65
4.2 Literature review......Page 67
4.3 Martingale characterization of Markov processes......Page 68
4.4.1 Incompleteness of Markov-modulated Brownian security markets......Page 71
4.4.2 The Black-Scholes formula for pricing options in a Markov-modulated Brownian market......Page 73
4.5.1 Incompleteness of Markov-modulated Brownian (B, S)-security markets with jumps......Page 78
4.5.2 Black-Scholes formula for pricing options in Markov-modulated Brownian (B, S)-security market with jumps......Page 80
4.6.1 Stochastic volatility driven by Markov process......Page 82
4.6.2 Pricing of variance swaps for stochastic volatility driven by Markov process......Page 83
A.1 A Feynmann-Kac formula for the Markov-modulated process (ys(t),xs(t))t ≥ s......Page 84
A.2 Formula for the option price fT(ST) for the market combined Markov-modulated (B, S)-security market and compound geometric Poisson process (see Section 4.4.2)......Page 86
References......Page 87
5.1 Introduction......Page 89
5.2 Dynamics of the Markov chain and observations......Page 90
5.4 Recursive filter......Page 91
5.5 Parameter estimates......Page 92
5.6 Smoothed estimates......Page 95
Proof of Lemma 1......Page 100
Proof of Lemma 2......Page 101
Proof of Remark 5.2.......Page 103
Proof of Lemma 3......Page 104
Proof of Theorem 1......Page 106
Proof of Theorem 2......Page 107
Proof of Theorem 3......Page 108
Proof of Lemma 7......Page 109
References......Page 110
6.1 Introduction......Page 111
6.2 Markov regime-switching model......Page 114
6.3 Weak Markov-regime switching model......Page 118
References......Page 119
7.1 Introduction......Page 121
7.2 Basic Settings......Page 123
7.3 Change of Measure......Page 125
7.4 A general unnormalized recursive filter......Page 127
7.5.2 Estimators for the number of jumps......Page 129
7.5.3 Estimators for 1-state occupation times......Page 130
7.5.5 Estimators for state to observation transitions......Page 131
7.6 Parameter re-estimations......Page 132
7.7 Error analysis......Page 136
7.8 Conclusion......Page 137
References......Page 138
8.1 Introduction......Page 141
8.2 Model description......Page 143
8.3 Reference probability......Page 144
8.4 Filtering......Page 145
8.5 Filters for G mli n , and S li n......Page 148
References......Page 151
Emilio Russo, Fabio Spagnolo and Rogemar Mamon......Page 153
9.1 Introduction......Page 154
9.2 Stylised features and statistical properties of foreign exchange rates......Page 155
9.3 Stationary and nonstationary time series......Page 159
9.4 Cointegration and the unbiased forward exchange rate (UFER) hypothesis......Page 162
9.5 Evidence from exchange rate market via a Markov regime-switching model......Page 166
References......Page 171
10.1 Introduction......Page 175
10.2 A Markov-switching approach to early warning systems......Page 179
10.3 Data description and transformation......Page 182
10.4.1 Indonesia......Page 188
10.4.3 Malaysia......Page 190
10.4.4 The Philippines......Page 191
10.4.5 Thailand......Page 195
10.5 Forecast assessment......Page 196
10.6 Conclusions......Page 200
References......Page 202
Early Titles in the International Series in Operations Research and Management Science......Page 205