Hidden Markov Models in Finance
by Mamon, Rogemar S.; Elliott, Robert J.Format: Hardcover
Pub. Date: 2007-04-27
Publisher(s): Springer Nature
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Summary
A number of methodologies have been employed to provide decision making solutions to a whole assortment of financial problems in today's globalized markets. Hidden Markov Models in Finance by Mamon and Elliott will be the first systematic application of these methods to some special kinds of financial problems; namely, pricing options and variance swaps, valuation of life insurance policies, interest rate theory, credit risk modeling, risk management, analysis of future demand and inventory level, testing foreign exchange rate hypothesis, and early warning systems for currency crises. This book provides researchers and practitioners with analyses that allow them to sort through the random "noise" of financial markets (i.e., turbulence, volatility, emotion, chaotic events, etc.) and analyze the fundamental components of economic markets. Hence, Hidden Markov Models in Finance provides decision makers with a clear, accurate picture of core financial components by filtering out the random noise in financial markets.
Table of Contents
| An Exact Solution of the Term Structure of Interest Rate under Regime-Switching Risk | p. 1 |
| Introduction | p. 1 |
| A new representation for modeling regime shift | p. 3 |
| The model | p. 5 |
| Two state variables | p. 5 |
| Pricing kernel | p. 5 |
| The risk-neutral probability measure | p. 5 |
| The term structure of interest rates | p. 8 |
| A tractable specification with exact solution | p. 9 |
| Affine regime-switching models | p. 9 |
| Conclusions | p. 13 |
| References | p. 13 |
| The Term Structure of Interest Rates in a Hidden Markov Setting | p. 15 |
| Introduction | p. 15 |
| The Model | p. 17 |
| The Markov chain | p. 17 |
| The short-term interest rate | p. 20 |
| The zero-coupon bond value | p. 21 |
| Implementation | p. 22 |
| Results | p. 25 |
| Conclusion | p. 30 |
| References | p. 30 |
| On Fair Valuation of Participating Life Insurance Policies With Regime Switching | p. 31 |
| Introduction | p. 31 |
| The model dynamics | p. 33 |
| Dimension reduction to regime-switching PDE | p. 38 |
| Further investigation | p. 42 |
| References | p. 42 |
| Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets | p. 45 |
| Introduction | p. 45 |
| Literature review | p. 47 |
| Martingale characterization of Markov processes | p. 48 |
| Pricing options for Markov-modulated security markets | p. 51 |
| Incompleteness of Markov-modulated Brownian security markets | p. 51 |
| The Black-Scholes formula for pricing options in a Markov-modulated Brownian market | p. 53 |
| Pricing options for Markov-modulated Brownian markets with jumps | p. 58 |
| Incompleteness of Markov-modulated Brownian (B, S)-security markets with jumps | p. 58 |
| Black-Scholes formula for pricing options in Markov-modulated Brownian (B, S)-security market with jumps | p. 60 |
| Pricing of Variancev swaps for stochastic volatility driven by Markov process | p. 62 |
| Stochastic volatility driven by Markov process | p. 62 |
| Pricing of variance swaps for stochastic volatility driven by Markov process | p. 63 |
| Example of variance swap for stochastic volatility driven by two-state continuous Markov chain | p. 64 |
| Some auxiliary results | p. 64 |
| A Feynmann-Kac formula for the Markov-modulated process (ys(t),xs(t))t ≥ s | p. 64 |
| 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) | p. 66 |
| References | p. 67 |
| Smoothed Parameter Estimation for a Hidden Markov Model of Credit Quality | p. 69 |
| Introduction | p. 69 |
| Dynamics of the Markov chain and observations | p. 70 |
| Reference probability | p. 71 |
| Recursive filter | p. 71 |
| Parameter estimates | p. 72 |
| Smoothed estimates | p. 75 |
| Appendix | p. 80 |
| References | p. 90 |
| Expected Shortfall Under a Model With Market and Credit Risks | p. 91 |
| Introduction | p. 91 |
| Markov regime-switching model | p. 94 |
| Weak Markov-regime switching model | p. 98 |
| Concluding remarks | p. 99 |
| References | p. 99 |
| Filtering of Hidden Weak Markov Chain -Discrete Range Observations | p. 101 |
| Introduction | p. 101 |
| Basic Settings | p. 103 |
| Change of Measure | p. 105 |
| A general unnormalized recursive filter | p. 107 |
| Estimation of states, transitions and occupation times | p. 109 |
| State estimation | p. 109 |
| Estimators for the number of jumps | p. 109 |
| Estimators for 1-state occupation times | p. 110 |
| Estimators for 2-state occupation times | p. 111 |
| Estimators for state to observation transitions | p. 111 |
| Parameter re-estimations | p. 112 |
| Error analysis | p. 116 |
| Conclusion | p. 117 |
| References | p. 118 |
| Filtering of a Partially Observed Inventory System | p. 121 |
| Introduction | p. 121 |
| Model description | p. 123 |
| Reference probability | p. 124 |
| Filtering | p. 125 |
| Filters for <$>G_n^{m \ell i}<$>, and <$>S_n^{\ell i} | p. 128 |
| Parameter re-estimation | p. 131 |
| References | p. 131 |
| An empirical investigation of the unbiased forward exchange rate hypothesis in a regime switching market | p. 133 |
| Introduction | p. 134 |
| Stylised features and statistical properties of foreign exchange rates | p. 135 |
| Stationary and nonstationary time series | p. 139 |
| Cointegration and the unbiased forward exchange rate (UFER) hypothesis | p. 142 |
| Evidence from exchange rate market via a Markov regime-switching model | p. 146 |
| Concluding remarks | p. 151 |
| References | p. 151 |
| Early Warning Systems for Currency Crises: A Regime-Switching Approach | p. 155 |
| Introduction | p. 155 |
| A Markov-switching approach to early warning systems | p. 159 |
| Data description and transformation | p. 162 |
| Estimation results | p. 168 |
| Indonesia | p. 168 |
| Korea | p. 170 |
| Malaysia | p. 170 |
| The Philippines | p. 171 |
| Thailand | p. 175 |
| Forecast assessment | p. 176 |
| Conclusions | p. 180 |
| References | p. 182 |
| Table of Contents provided by Publisher. All Rights Reserved. |
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