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Papers by Christina Erlwein

International Series in Operations Research & Management Science, 2014

ABSTRACT In this paper, we establish a robustification of Elliott's on-line EM algorithm ... more ABSTRACT In this paper, we establish a robustification of Elliott's on-line EM algorithm for modelling asset prices within a hidden Markov model (HMM). In this HMM framework, parameters of the model are guided by a Markov chain in discrete time, parameters of the asset returns are therefore able to switch between different regimes. The parameters are estimated through an on-line algorithm, which utilizes incoming information from the market and leads to adaptive optimal estimates. We robustify this algorithm step by step against additive outliers appearing in the observed asset prices with the rationale to better handle possible peaks or missings in asset returns.

This paper is concerned with some properties of the generalized GARCH models, obtained by extendi... more This paper is concerned with some properties of the generalized GARCH models, obtained by extending GARCH models with exogenous variables, the so-called GARCH extended (GARCHX) models. For these, we establish sufficient conditions for some properties such as stationarity, existence of moments, ergodicity, geometric ergodicity, consistence and asymptotic normality of likelihood estimators of the model parameters. For some of these properties we show that the conditions that we propose are also necessary. We further provide examples and applications to illustrate and highlight the importance of our findings.

This paper considers the implementation of a mean-reverting interest rate model with Markov-modul... more This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott [8] and Elliott et al. [9] are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial data set of 30-day T-bill yields. We found that within the data set and period studied, a model with three regimes is sufficient to describe the interest rate dynamics on the basis of very small predictions errors.

... of Risk and Optimisation Modelling Applications CTR/26/03 May 2004 Treasury Management Model ... more ... of Risk and Optimisation Modelling Applications CTR/26/03 May 2004 Treasury Management Model with Foreign Exchange Exposure Konstantin Volosov, Gautam Mitra, Fabio ... Sharda and Musser (1986) used a multi-objective goal programming model for bond portfolios. ...

Statistical Methods and Applications, 2009

This paper considers the implementation of a mean-reverting interest rate model with Markov-modul... more This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are

North American Actuarial Journal, 2008

We consider the valuation of credit default swaps (CDSs) under an extended version of Merton's st... more We consider the valuation of credit default swaps (CDSs) under an extended version of Merton's structural model for a firm's corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm's value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm's value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation.

Information Sciences, 2008

ABSTRACT In this paper we illustrate the optimal filtering of log returns of commodity prices in ... more ABSTRACT In this paper we illustrate the optimal filtering of log returns of commodity prices in which both the mean and volatility are modulated by a hidden Markov chain with finite state space. The optimal estimate of the Markov chain and the parameters of the price model are given in terms of discrete-time recursive filters. We provide an application on a set of high frequency gold price data for the period 1973–2006 and analyse the h-step ahead price predictions against the Diebold–Kilian metric. Within the modelling framework where the mean and volatility are switching regimes, our findings suggest that a two-state hidden Markov model is sufficient to describe the dynamics of the data and the gold price is predictable up to a certain extent in the short term but almost impossible to predict in the long term. The proposed model is also benchmarked with ARCH and GARCH models with respect to price predictability and forecasting errors.

Applied Stochastic Models in Business and Industry, 2011

We develop and analyse investment strategies relying on hidden Markov model approaches. In partic... more We develop and analyse investment strategies relying on hidden Markov model approaches. In particular, we use filtering techniques to aid an investor in his decision to allocate all of his investment fund to either growth or value stocks at a given time. As this allows the investor to switch between growth and value stocks, we call this first strategy a switching investment strategy. This switching strategy is compared with the strategies of purely investing in growth or value stocks by tracking the quarterly terminal wealth of a hypothetical portfolio for each strategy. Using the data sets on Russell 3000 growth index and Russell 3000 value index compiled by Russell Investment Services for the period 1995-2008, we find that the overall risk-adjusted performance of the switching strategy is better than that of solely investing in either one of the indices. We also consider a second strategy referred to as a mixed investment strategy which enables the investor to allocate an optimal proportion of his investment between growth and value stocks given a level of risk aversion. Numerical demonstrations are provided using the same data sets on Russell 3000 growth and value indices. The switching investment strategy yields the best or second best Sharpe ratio as compared with those obtained from the pure index strategies and mixed strategy in 14 intervals. The performance of the mixed investment strategy under the HMM setting is also compared with that of the classical mean-variance approach. To make the comparison valid, we choose the same level of risk aversion for each set-up. Our findings show that the mixed investment strategy within the HMM framework gives higher Sharpe ratios in 5 intervals of the time series than that given by the standard mean-variance approach. The calculated weights through time from the strategy incorporating the HMM set-up are more stable. A simulation analysis further shows a higher performance stability of the HMM strategies compared with the pure strategies and the mean-variance strategy.

Annals of Operations Research, 2012

The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An ... more The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of

Energy Economics, 2010

In this paper we develop a model for electricity spot price dynamics. The spot price is assumed t... more In this paper we develop a model for electricity spot price dynamics. The spot price is assumed to follow an exponential Ornstein-Uhlenbeck (OU) process with an added compound Poisson process. In this way, the model allows for mean-reversion and possible jumps. All parameters are modulated by a hidden Markov chain in discrete time. They are able to switch between different economic regimes representing the interaction of various factors. Through the application of reference probability technique, adaptive filters are derived, which in turn, provide optimal estimates for the state of the Markov chain and related quantities of the observation process. The EM algorithm is applied to find optimal estimates of the model parameters in terms of the recursive filters. We implement this self-calibrating model on a deseasonalised series of daily spot electricity prices from the Nordic exchange Nord Pool. On the basis of one-step ahead forecasts, we found that the model is able to capture the empirical characteristics of Nord Pool spot prices.

International Series in Operations Research & Management Science, 2014

ABSTRACT In this paper, we establish a robustification of Elliott's on-line EM algorithm ... more ABSTRACT In this paper, we establish a robustification of Elliott's on-line EM algorithm for modelling asset prices within a hidden Markov model (HMM). In this HMM framework, parameters of the model are guided by a Markov chain in discrete time, parameters of the asset returns are therefore able to switch between different regimes. The parameters are estimated through an on-line algorithm, which utilizes incoming information from the market and leads to adaptive optimal estimates. We robustify this algorithm step by step against additive outliers appearing in the observed asset prices with the rationale to better handle possible peaks or missings in asset returns.

This paper is concerned with some properties of the generalized GARCH models, obtained by extendi... more This paper is concerned with some properties of the generalized GARCH models, obtained by extending GARCH models with exogenous variables, the so-called GARCH extended (GARCHX) models. For these, we establish sufficient conditions for some properties such as stationarity, existence of moments, ergodicity, geometric ergodicity, consistence and asymptotic normality of likelihood estimators of the model parameters. For some of these properties we show that the conditions that we propose are also necessary. We further provide examples and applications to illustrate and highlight the importance of our findings.

This paper considers the implementation of a mean-reverting interest rate model with Markov-modul... more This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott [8] and Elliott et al. [9] are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial data set of 30-day T-bill yields. We found that within the data set and period studied, a model with three regimes is sufficient to describe the interest rate dynamics on the basis of very small predictions errors.

... of Risk and Optimisation Modelling Applications CTR/26/03 May 2004 Treasury Management Model ... more ... of Risk and Optimisation Modelling Applications CTR/26/03 May 2004 Treasury Management Model with Foreign Exchange Exposure Konstantin Volosov, Gautam Mitra, Fabio ... Sharda and Musser (1986) used a multi-objective goal programming model for bond portfolios. ...

Statistical Methods and Applications, 2009

This paper considers the implementation of a mean-reverting interest rate model with Markov-modul... more This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are

North American Actuarial Journal, 2008

We consider the valuation of credit default swaps (CDSs) under an extended version of Merton's st... more We consider the valuation of credit default swaps (CDSs) under an extended version of Merton's structural model for a firm's corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm's value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm's value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation.

Information Sciences, 2008

ABSTRACT In this paper we illustrate the optimal filtering of log returns of commodity prices in ... more ABSTRACT In this paper we illustrate the optimal filtering of log returns of commodity prices in which both the mean and volatility are modulated by a hidden Markov chain with finite state space. The optimal estimate of the Markov chain and the parameters of the price model are given in terms of discrete-time recursive filters. We provide an application on a set of high frequency gold price data for the period 1973–2006 and analyse the h-step ahead price predictions against the Diebold–Kilian metric. Within the modelling framework where the mean and volatility are switching regimes, our findings suggest that a two-state hidden Markov model is sufficient to describe the dynamics of the data and the gold price is predictable up to a certain extent in the short term but almost impossible to predict in the long term. The proposed model is also benchmarked with ARCH and GARCH models with respect to price predictability and forecasting errors.

Applied Stochastic Models in Business and Industry, 2011

We develop and analyse investment strategies relying on hidden Markov model approaches. In partic... more We develop and analyse investment strategies relying on hidden Markov model approaches. In particular, we use filtering techniques to aid an investor in his decision to allocate all of his investment fund to either growth or value stocks at a given time. As this allows the investor to switch between growth and value stocks, we call this first strategy a switching investment strategy. This switching strategy is compared with the strategies of purely investing in growth or value stocks by tracking the quarterly terminal wealth of a hypothetical portfolio for each strategy. Using the data sets on Russell 3000 growth index and Russell 3000 value index compiled by Russell Investment Services for the period 1995-2008, we find that the overall risk-adjusted performance of the switching strategy is better than that of solely investing in either one of the indices. We also consider a second strategy referred to as a mixed investment strategy which enables the investor to allocate an optimal proportion of his investment between growth and value stocks given a level of risk aversion. Numerical demonstrations are provided using the same data sets on Russell 3000 growth and value indices. The switching investment strategy yields the best or second best Sharpe ratio as compared with those obtained from the pure index strategies and mixed strategy in 14 intervals. The performance of the mixed investment strategy under the HMM setting is also compared with that of the classical mean-variance approach. To make the comparison valid, we choose the same level of risk aversion for each set-up. Our findings show that the mixed investment strategy within the HMM framework gives higher Sharpe ratios in 5 intervals of the time series than that given by the standard mean-variance approach. The calculated weights through time from the strategy incorporating the HMM set-up are more stable. A simulation analysis further shows a higher performance stability of the HMM strategies compared with the pure strategies and the mean-variance strategy.

Annals of Operations Research, 2012

The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An ... more The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of

Energy Economics, 2010

In this paper we develop a model for electricity spot price dynamics. The spot price is assumed t... more In this paper we develop a model for electricity spot price dynamics. The spot price is assumed to follow an exponential Ornstein-Uhlenbeck (OU) process with an added compound Poisson process. In this way, the model allows for mean-reversion and possible jumps. All parameters are modulated by a hidden Markov chain in discrete time. They are able to switch between different economic regimes representing the interaction of various factors. Through the application of reference probability technique, adaptive filters are derived, which in turn, provide optimal estimates for the state of the Markov chain and related quantities of the observation process. The EM algorithm is applied to find optimal estimates of the model parameters in terms of the recursive filters. We implement this self-calibrating model on a deseasonalised series of daily spot electricity prices from the Nordic exchange Nord Pool. On the basis of one-step ahead forecasts, we found that the model is able to capture the empirical characteristics of Nord Pool spot prices.