HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.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 the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Applications of hidden Markov models in financial modelling

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.Brunel Research Initiative and Enterprise Fund (BRIEF) and European Union (Marie Curie Fellowship

Applications of hidden Markov models in financial modelling

Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.EThOS - Electronic Theses Online ServiceBrunel Research Initiative and Enterprise Fund (BRIEF) : European Union (Marie Curie Fellowship)GBUnited Kingdo

Some contributions to filtering theory with applications in financial modelling

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Two main groups of filtering algorithms are characterised and developed. Their applicability is demonstrated using actuarial and financial time series data. The first group of algorithms involved hidden Markov models (HMM), where the parameters of an asset price model switch between regimes in accordance with the dynamics of a Markov chain. We start with the known HMM filtering set-up and extend the framework to the case where the drift and volatility have independent probabilistic behaviour. In addition, a non-normal noise term is considered and recursive formulae in the online re-estimation of model parameters are derived for the case of students’ t-distributed noise. Change of reference probability is employed in the construction of the filters. Both extensions are then tested on financial and actuarial data. The second group of filtering algorithms deals with sigma point filtering techniques. We propose a method to generate sigma points from symmetric multivariate distributions. The algorithm matches the first three moments exactly and the fourth moment approximately; this minimises the worst case mismatch using a semidefinite programming approach. The sigma point generation procedure is in turn applied to construct algorithms in the latent state estimation of nonlinear time series models; a numerical demonstration of the procedure’s effectiveness is given. Finally, we propose a partially linearised sigma point filter, which is an alternative technique for the optimal state estimation of a wide class of nonlinear time series models. In particular, sigma points are employed for generating samples of possible state values and then a linear programming-based procedure is utilised in the update step of the state simulation. The performance of the filtering technique is then assessed on simulated, highly non-linear multivariate interest rate process and is shown to perform significantly better than the extended Kalman filter in terms of computational time

Two-Stage Stochastic Program Optimizing the Total Cost of Ownership of Electric Vehicles in Commercial Fleets

The possibility of electric vehicles to technically replace internal combustion engine vehicles and to deliver economic benefits mainly depends on the battery and the charging infrastructure as well as on annual mileage (utilizing the lower variable costs of electric vehicles). Current studies on electric vehicles’ total cost of ownership often neglect two important factors that influence the investment decision and operational costs: firstly, the trade-off between battery and charging capacity; secondly the uncertainty in energy consumption. This paper proposes a two-stage stochastic program that minimizes the total cost of ownership of a commercial electric vehicle under uncertain energy consumption and available charging times induced by mobility patterns and outside temperature. The optimization program is solved by sample average approximation based on mobility and temperature scenarios. A hidden Markov model is introduced to predict mobility demand scenarios. Three scenario reduction heuristics are applied to reduce computational effort while keeping a high-quality approximation. The proposed framework is tested in a case study of the home nursing service. The results show the large influence of the uncertain mobility patterns on the optimal solution. In the case study, the total cost of ownership can be reduced by up to 3.9% by including the trade-off between battery and charging capacity. The introduction of variable energy prices can lower energy costs by 31.6% but does not influence the investment decision in this case study. Overall, this study provides valuable insights for real applications to determine the techno-economic optimal electric vehicle and charging infrastructure configuration

Algorithms for appliance usage prediction

Demand-Side Management (DSM) is one of the key elements of future Smart Electricity Grids. DSM involves mechanisms to reduce or shift the consumption of electricity in an attempt to minimise peaks. By so doing it is possible to avoid using expensive peaking plants that are also highly carbon emitting. A key challenge in DSM, however, is the need to predict energy usage from specific home appliances accurately so that consumers can be notified to shift or reduce the use of high energy-consuming appliances. In some cases, such notifications may be also need to be given at very short notice. Hence, to solve the appliance usage prediction problem, in this thesis we develop novel algorithms that take into account both users' daily practices (by taking advantage of the cyclic nature of routine activities) and the inter-dependency between the usage of multiple appliances (i.e., the user's typical consumption patterns). We propose two prediction algorithms to satisfy the needs for fast prediction and high accuracy respectively: i) a rule-based approach, EGH-H, for scenarios in which notifications need to be given at short notice, to find significant patterns in the use of appliances that can capture the user's behaviour (or habits), ii) a graphical{model based approach, GM-PMA (Graphical Model for Prediction in Multiple Appliances) for scenarios that require high prediction accuracy. We demonstrate through extensive empirical evaluations on real{world data from a prominent database of home energy usage that GM-PMA outperforms existing methods by up to 41%, and the runtime of EGH-H is 100 times lower on average, than that of other benchmark algorithms, while maintaining competitive prediction accuracy. Moreover, we demonstrate the use of appliance usage prediction algorithms in the context of demand{side management by proposing an Intelligent Demand Responses (IDR) mechanism, where an agent uses Logistic Inference to learn the user's preferences, and hence provides the best personalised suggestions to the user. We use simulations to evaluate IDR on a number of user types, and show that, by using IDR, users are likely to improve their savings significantly

INVESTMENT PORTFOLIO REBALANCING DECISION MAKING

Nowadays financial markets’ volatility and significant stock prices’ fluctuations allow improving investment return actively managing investment portfolio, rather than choosing long term investment strategy. Active portfolio management also allows personal investor’s development and gives opportunity to avoid losses in terms of market instability. However active portfolio management is more risky. Rebalancing the investment portfolio investor incurs real costs for expected return, so actively managing the investment portfolio it is crucial to use a good, investor needs meeting portfolio rebalancing method. Dealing with mentioned problem scientific information sources analysis is made and a new portfolio rebalancing method is suggested in the article

Techno-economic optimization and environmental evaluation of electric vehicles in commercial fleets

Die Einführung von batterieelektrischen Fahrzeugen (E-Pkw) gilt als eine wichtige Maßnahme zur Emissionsverringerung im Straßenverkehr. Gewerbliche Flotten in Deutschland bilden hierfür einen vielversprechenden Markt. Um dieses Potential zu realisieren, ist sowohl eine techno-ökonomische Optimierung als auch eine ökologische Bewertung über den Lebenszyklus erforderlich. Das Ziel der Dissertation ist es, hierfür ein methodisches Rahmenwerk zu liefern. Die kumulative Dissertation besteht aus fünf Artikeln, die sich den einzelnen Bestandteilen des Rahmenwerks widmen und großteils auf Technologie- und Nutzungsdaten aus eigenen Messungen aufbauen. Der erste Artikel, Schücking et al. (2016) [Paper I], ist eine technische Analyse. Sie untersucht den realen Energieverbrauch von E-Pkws im Vergleich zu konventionellen Fahrzeugen und identifiziert optimale Betriebspunkte. Die Ergebnisse heben den Einfluss verschiedener Faktoren auf den Energieverbrauch als wichtige Komponente detaillierter techno-ökonomischer und ökologischer Betrachtungen hervor. Der zweite und der dritte Artikel haben einen techno-ökonomischen Fokus. Sie beschäftigen sich mit der Frage, wie E-Pkws einen schnelleren wirtschaftlichen Break-even im Vergleich zu konventionellen Fahrzeugen erreichen können. Der zweite Artikel, Schücking et al. (2017) [Paper II], stellt Ladestrategien vor, welche eine höhere Auslastung der E-Pkw ermöglichen und damit zu geringen Gesamtkosten im Vergleich zu konventionellen Pkw führen können. Unsicherheiten in Fahrprofilen und Energieverbrauch begrenzen die Anwendbarkeit dieser Strategien. Der dritte Artikel, Schücking & Jochem (2020) [Paper III], knüpft hieran an. Er schlägt ein zweistufiges stochastisches Optimierungsmodell zur Minimierung der Investition und Betriebskosten eines E-Pkw unter Berücksichtigung dieser Unsicherheiten vor. Neben der stochastischen Betrachtung ist auch die Abwägung zwischen Batteriekapazität und Ladeleistung in der Investitionsentscheidung ein neuer Beitrag zur Forschung. Im Kontext der stochastischen Optimierung werden ein Hidden Markov Modell zur Generierung komplexer Fahrprofile und eine neue Szenario-Reduktionsheuristik als methodische Weiterentwicklungen angewandt. Artikel vier und fünf liefern eine ökologische Bewertung. Die empirischen Daten sowie der Fokus auf den deutsch-französischen Grenzverkehr zeichnen beide Artikel aus. Der vierte Artikel, Ensslen et al. (2017) [Paper IV], konzentriert sich auf die E-Pkw Nutzungsphase. Er verdeutlicht den Einfluss unterschiedlicher Strommixe und Ladezeitpunkte auf die CO2- Emissionen und Reduktionspotentiale. Der fünfte Artikel, Held & Schücking (2019) [Paper V], betrachtet verschiedene ökologische Wirkungskategorien (wie z.B. Klimawandel, Versauerung Eutrophierung) über den gesamten Lebenszyklus mittels eines modularen Screening-Modells. Die Ergebnisse unterstreichen den Einfluss der Batterie und der Nutzungsphase auf die ökologische Gesamtbilanz. Dem übergreifenden Forschungsziel folgend, zeigen die Ergebnisse der einzelnen Artikel in ihrer Kombination, dass die Optimierung des wirtschaftlichen Nutzens auch die ökologischen Vorteile erhöhen kann. Die ex-ante Ermittlung der optimalen Batteriekapazität sowie ein hoher Betriebsgrad erhöhen nicht nur die Wettbewerbsfähigkeit von E-Pkw, sondern beschleunigen unter bestimmten Voraussetzungen auch den ökologischen Break-even in einem Großteil der betrachteten Wirkungskategorien. Die Eigenschaften, die gewerbliche Anwendungen aus wirtschaftlicher Sicht zu einem vielversprechenden Einführungsmarkt für E-Pkws machen, können damit auch die angestrebten ökologischen Vorteile unterstützen