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Hidden Markov Models in Finance

herausgegeben von: Rogemar S. Mamon, Robert J. Elliott

Verlag: Springer US

Buchreihe : International Series in Operations Research & Management Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

1. An Exact Solution of the Term Structure of Interest Rate Under Regime-Switching Risk

Summary

Regime-switching risk has been recently studied in an general equilibrium setting and empirically documented as an significant factor in bond premium. In this paper we apply no arbitrage approach to derive an exact solution of the term structure of interest rates in an essentially-affine-type model under regime-switching risk.

Shu Wu, Yong Zeng

2. The Term Structure of Interest Rates in a Hidden Markov Setting

Summary

We describe an interest rate model in which randomness in the short-term interest rate is partially due to a Markov chain. We model randomness through the volatility and mean-reverting level as well as through the interest rate directly. The short- term interest rate is modeled in a risk-neutral setting as a continuous process in continuous time. This allows the valuation of interest rate derivatives using the martingale approach. In particular, a solution is found for the value of a zero-coupon bond. This leads to a non-linear regression model for the yield to maturity, which is used to filter the state of the unobservable Markov chain.

Robert J. Elliott, Craig A. Wilson

3. On Fair Valuation of Participating Life Insurance Policies With Regime Switching

Summary

We consider the valuation of participating life insurance policies using a regime-switching Esscher transform developed in Elliott, Chan and Siu (2005) when the market values of the reference asset are driven by a Markov-modulated geometric Brownian motion (GBM). We employ the Markov-modulated GBM driven by a continuous-time hidden Markov chain model to describe the impact of the switching behavior of the states of economy on the price dynamics of the reference asset. We also explore the change of measures technique to reduce the dimension of the valuation problem.

Tak Kuen Siu

4. Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets

Summary

A Markov-modulated market consists of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on Markov process x. We study the pricing of options and variance swaps in such markets. Using the martingale characterization of Markov processes, we note the incompleteness of Markov-modulated markets and find the minimal martingale measure. Black-Scholes formulae for Markov-modulated markets with or without jumps are derived. Perfect hedging in a Markov-modulated Brownian and a fractional Brownian market is not possible as the market is incomplete. Following the idea proposed by Föllmer and Sondermann [13] and Föllmer and Schweizer [12]) we look for the strategy which locally minimizes the risk. The residual risk processes are determined in these situations. Variance swaps for stochastic volatility driven by Markov process are also studied.

Robert J. Elliott, Anatoliy V. Swishchuk

5. Smoothed Parameter Estimation for a Hidden Markov Model of Credit Quality

Summary

We consider a hidden Markov model of credit quality. We assume that the credit rating evolution can be described by a Markov chain but that we do not observe this Markov chain directly. Rather, it is hidden in “noisy” observations represented by the posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise. We derive smoothed estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model.

Małgorzata W. Korolkiewicz, Robert J. Elliott

6. Expected Shortfall Under a Model With Market and Credit Risks

Summary

Value-at-Risk (VaR), due to its simplicity and ease of interpretability, has become a popular risk measure in finance nowadays. However, recent research find that VaR is not a coherent risk measure and cannot incorporate the loss beyond VaR or tail risk. This chapter considers expected shortfall (ES) as an alternative risk measure. We consider a portfolio subject to both market and credit risks. We model the credit rating using a Markov chain. Thus our model can be treated as a Markovian regime-switching model. We also propose a weak Markov chain model which can take into account the dependency of the risks. Expressions for VaR, ES and numerical results are presented to illustrate the proposed ideas.

Kin Bong Siu, Hailiang Yang

7. Filtering of Hidden Weak Markov Chain -Discrete Range Observations

Summary

In this paper we consider a hidden discrete time finite state process X whose behavior at the present time t depends on its behavior at the previous k time steps, which is a generalization of the usual hidden finite state Markov chain, in which k equals to one. We consider the case when the range space of our observations is finite. We present filtering equations for certain functionals of the chain and perform related error analysis.

Shangzhen Luo, Allanus H. Tsoi

8. Filtering of a Partially Observed Inventory System

Summary

The vast majority of work done on inventory system is based on the critical assumption of fully observed inventory level dynamics and demands. Modern technology, like the internet, offers a tremendous number of opportunities to businesses to collect imperfect but useful information on potential customers which helps them planning efficiently to meet future demands. For instance visits to commercial web sites provides the management of a business of a source of partial information on future demands. On the other hand it is often the case that it is not economically viable to fully observe the dynamics of inventory levels and only partial information is accessible to the management. In this article, using hidden Markov model techniques we estimate the inventory level as well as future demands of partially observed inventory system. The parameters of the model are updated via the EM algorithm.

Lakhdar Aggoun

9. An empirical investigation of the unbiased forward exchange rate hypothesis in a regime switching market

Summary

In this article we develop a model for exchange rate dynamics in an economy that exhibits regime shifts. The switching of regimes is modulated by a Markov chain in discrete time. A description of the foreign exchange market and of its stylised features is given. Finally, unbiased forward exchange rate hypothesis (UFER) is tested in the context of the US-dollar/UK-pound spot and forward exchange rates.

Emilio Russo, Fabio Spagnolo, Rogemar Mamon

10. Early Warning Systems for Currency Crises: A Regime-Switching Approach

Summary

Previous early warning systems (EWS) for currency crises have relied on models that require a priori dating of crises. This paper proposes an alternative EWS, based on a Markov-switching model, which identifies and characterizes crisis periods endogenously; this also allows the model to utilize information contained in exchange rate dynamics. The model is estimated on data from 1972–1999 for the Asian crisis countries, taking a country-by-country approach. The model outperforms standard EWSs, both in signaling crises and reducing false alarms. Two lessons emerge. First, accounting for the dynamics of exchange rates is important. Second, different indicators matter for different countries, suggesting that the assumption of parameter constancy underlying panel estimates of EWSs may contribute to poor performance.

Abdul Abiad

Backmatter

Titel: Hidden Markov Models in Finance
herausgegeben von: Rogemar S. Mamon
Robert J. Elliott
Verlag: Springer US
Electronic ISBN: 978-0-387-71163-8
Print ISBN: 978-0-387-71081-5
DOI: https://doi.org/10.1007/0-387-71163-5

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Über dieses Buch

Inhaltsverzeichnis

Frontmatter

1. An Exact Solution of the Term Structure of Interest Rate Under Regime-Switching Risk

2. The Term Structure of Interest Rates in a Hidden Markov Setting

3. On Fair Valuation of Participating Life Insurance Policies With Regime Switching

4. Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets

5. Smoothed Parameter Estimation for a Hidden Markov Model of Credit Quality

6. Expected Shortfall Under a Model With Market and Credit Risks

7. Filtering of Hidden Weak Markov Chain -Discrete Range Observations

8. Filtering of a Partially Observed Inventory System

9. An empirical investigation of the unbiased forward exchange rate hypothesis in a regime switching market

10. Early Warning Systems for Currency Crises: A Regime-Switching Approach

Backmatter

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