Term Projects

Financial Engineering

A Model for the Three-Portfolios Matching Problem

Author: Ch. Vögeli / Contact: Jörg Doege & Michael Guarisco

Introduction

A typical problem arising in financial planning and banking industry for private investors is the fact that the investor’s original portfolio, the one determined by the consulting process of the financial advisor and the universe of instruments, i.e. investment possibilities, made available to the investor have to be matched when determining the relevant portfolio choice. This problem is called the three-portfolios matching problem (TPMP). TPMP focuses at a resulting portfolio that is as close as possible to the optimal asset allocation determined by the consulting process of the financial advisor. This matching process is complicated by the existence of transaction costs and some additional restrictions. Traditionally portfolio selection processes are structured by different aggregation levels which make selection even more difficult.

One way of approaching the TPMP is by minimizing the distance between the optimal and the current asset allocation satisfying certain restrictions as outlined before. Such an approach is straightforward and easy to implement. The solution will consist of one or many “optimal” current asset allocations for the private investor. Intuitively the investor can choose any but he does not know anything about the quality of his choice.

In order to bring light into the dark the investor needs to know the expected return of each asset allocation and the associated risk in order to determine his choice. This is why additional constraints with respect to risk and expected return have to be added to the TPMP in order to guarantee the optimality of the asset allocation. As a risk measure one should preferably use a coherent one, e.g. Conditional Value-at-Risk (CVaR), due to its favorable properties.

Goal of the Term Project

The goals of this work are three-folded: First, a mathematical model has to be developed for the problem stated above (particularly with regard to the above additional restrictions). Then, an appropriate optimization algorithm has to be derived and implemented in order to solve the problem. Finally, the coded model has to be tested and validated using real-world data.

Credit Risk Portfolio Optimization Using CVaR

Author: S. Grundel / Contact: Jörg Doege & Vania Eleuterio

The objective of portfolio optimization models is to maximize expected profit given a certain level of risk the investor is willing to take, or vice versa. Usually they are either formulated as linear or as convex optimization problems, depending of the risk measure being applied. Using Conditional Value-at-Risk (CVaR) as risk measure, the problem can be written as an instance of linear programming if the profit is a linear function in the “decision” variables. This fact makes CVaR of computational ease. Although CVaR has been widely used in banking industry the concept has not been studied much in credit risk management due to the difficulty of linear modeling of credit exposure. Hence, the goal of this term project is two-folded. On the one hand, a CVaR-based portfolio optimization framework has to be developed that is capable of dealing with credit risk. This will typically result in a large-scale problem as e.g. the number of customers with credit exposure is quite large. Although there are many different LP-solvers available, large-scale problems often cannot be solved efficiently with standard approaches. Hence, the second goal of the term project is to test a new gradient-based algorithm that approximates those kinds of linear programs very fast.

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Energy Risk Engineering

Evaluating Different Valuation Methods for Hydro Pump Storages

Author: V. Lörtscher / Contact: Jörg Doege & Dr. Juri Hinz

Introduction

Long term valuation of power generation assets is typically done with the well-known and well-documented discounted cash-flow method or also known as net present value. The net present value is the present value of the benefits minus the present value of the costs. Whereas the long-term determination of costs is not too difficult the benefits are hard to determine. Appropriate forecasts for (electricity) prices have to be made. Subsequently the net present value can easily determine a value for the generation asset.

The disadvantage of the net present value method is that it will overestimate the generation asset. Operations and feasibility is not taken into account. This is due to the fact that the asset might produce electricity1 even when it is not possible. This is especially the case for hydro power plants where a reservoir might be empty and hence no production is possible. In order to incorporate this fact one has to evaluate a hydro power plant based on real options theory. This methodology will with come up the correct value of the generation asset. Another advantage of real options theory is that it immediately gives a hedging strategy while keeping the risk at a certain level.

Real options theory for generation assets can be approximated by linear programming where a dispatch policy is determined that is comparable to a series of American put options. This means that the holder of the option, i.e. the owner of the generation asset, has the right but not the obligation to produce electricity, to pump water, or to do nothing. The linear programming method is a portfolio optimization approach which means that the expected profit is maximized given the technical setup of the plant and the risk will never exceed a certain value. This method for power portfolio optimization was first introduced by Unger (2002) and had been extended by Doege (2004).

The real options approach suggested by Unger (2002) and Doege (2004) is a purely microeconomic approach, i.e. it determines the value of the hydro (pump) storages from the company’s perspective. The market price of this generation facility is totally neglected. This fair price can be above or below the microeconomic value. In order to determine this market price, the most recent and sophisticated approach is suggested by Hinz et.al.(2004) who suggest an interest-rate based method to price those generation assets.

Goal of the Term Project

Goal of this term project is to extend the existing 1-year models for the real option valuation of hydro pump storages to a long-term horizon of 50 years. Moreover new multi-stage hydro pump storages have to be modeled accordingly and evaluated for a time period of 50 years. The next step is to compare the results from the real options model to those from the net present value method. Additionally investments in hydro (pump) storages have to be taken into account and evaluated appropriately. Rules for optimal investment strategies have to be developed and discussed in detail.

The second part of this project is to compare the microeconomic real options approach to the fair market price of the hydro (pump) storage. A consistent framework has to be developed that is able of highlighting the differences. Moreover explanations for the differences have to be given.

Optimal Auctioning in the European Electricity Transmission Market

Author: Th. Bietenhader & Ch. Portmann / Contact: Jörg Doege

Goal of the Term Project

The goal of this term project is to develop a theoretical methodology for the optimal transfer strategy of a cross-border (or inter-regional) power trading company and implement it into a simulation tool. The output should give the amount of money per MWh that has to be bidden (with respect to profit maximization) in order to make sure that the trading company will get its capacity during the auction.

Description of the Term Projects

Due to the liberalization of the European Energy Market the electric industry is facing dramatic changes nowadays. The foundation of power exchanges has led to the occurence of trading companies. Power traders buy electricity at different European energy markets depending on the current market situation and sell it to their customers throughout the whole continent.
In cross-border (or inter-regional) transactions trading companies also have to assure that they are capable of transporting the electricity to its final destination. However, as those interconnectors between countries or transfer regions have low capacities most of the time congestions will occur. Thus, auctions are made by each Transmission System Operator (TSO) in order to determine which participant will get the capacity that is available. But those auction methods vary from TSO to TSO. Moreover at those transmission auctions every participant can only make one bid. Additionally entry/exit rights for fixed capacities are also traded by the TSO's.
The result is that the risk involved in power trading will dramatically increase due to the fact that a trader might have bought electricity in country/region A but he is not able to deliver everything to country/region B (i.e. where he sold it) or only by making a significant loss. So it is essential for trading companies to have a method that will reduce this risk by optimizing the transfer strategies of electricity in order to assure delivery

Portfolio Optimization and Optimal Dispatch for Thermal Power Plants

(Authors: Frank Haeusler / Contact: Jörg Doege)

Im Zuge der Deregulierung des Elektrizitätsmarktes werden die Strompreise in Zukunft nicht mehr regulativ festgelegt, sondern durch den freien Markt bestimmt. Durch die resultierende Preisvolatilität werden zukünftige Einkommen unsicher und die verschiedenen Stromproduzenten stehen vor der Aufgabe ein aktives Risiko Management zu etablieren. Unter der Annahme, dass operationelle Flexibilitäten eine Möglichkeit bieten auf die zunehmenden Unsicherheiten zu reagieren, wird in dieser Semesterarbeit untersucht, wie entsprechende Flexibilitäten eingesetzt werden sollen. Gesucht ist insbesondere eine "optimale" Nutzung der operationellen Flexibilitäten, d.h. eine möglichst gute "Dispatch Strategy", die unter Begrenzung des Risikos (gemessen in CVaR) die erwarteten Gewinne maximiert.

Während in früheren Arbeiten vor allem Wasserkraftwerke betrachtet wurden, gilt der Fokus dieser Semesterarbeit der Betrachtung von sogenannten semiflexiblen Kraftwerken, wie z.B. thermische Kraftwerke. Auch wenn verschiedene Konzepte kraftwerktypenunabhängig Gültigkeit haben, machen es unterschiedliche Produktionsmethoden unabdingbar, kraftwerkspezifische "Dispatch Strategy" zu entwickeln. Insbesondere die bei thermischen Kraftwerken auftretenden Aufstart- und Abstellkosten beeinflussen die "Dispatch Strategy" nachhaltig und machen es bei der Modellierung nötig, binäre Variablen einzuführen.

Aufbauend auf den für Wasserkraftwerke entwickelten Modellen und Konzepten, wurden in dieser Arbeit - in einem ersten Schritt - die grundlegenden Einflussfaktoren für semiflexible Kraftwerke bestimmt. Die daraus resultierenden Erkenntnisse wurden dann in einem zweiten Schritt - in einem gemischt ganzzahligen Linearen Programm - zusammengefasst.

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Capacity Management

Risk Assessment of Strategic Decisions in Production Management

(Authors: Marcel Bieri / Contact: Philippe Schiltknecht)

In this study an integrated logistics model for locating production and distribution facilities was considered. Such a logistics system requires two essential decisions: one strategic e.g. where to locate plants and warehouses; and the other operational e.g. distribution strategy from plants to customer outlets through warehouses. In general, such models are formulated as Mixed Integer Programs and solved using mathematical programming methods. An inherent assumption of such methods is that all the necessary information is known a-priori and with certainty. In cases where the actual value of a parameter is stochastic, frequently the expected value of the parameter is taken and used in the mathematical program. The problem with this approach is that strategic decisions are taken based on expectations, and can turn out to be disastrous for the company if expectations are not realized in the future. In other words, decisions are made based on one state of nature (the expected state), and reality in the future can be completely different (actual state).

The task of this project was to develop an instrument to assess the risk of strategic decisions taken under expected conditions. Product demands and prices were identified as parameters that can be expected to be stochastic in nature. An industrial case was considered, and a stochastic distribution (in this case uniform) for the demands of the various products was assumed. Since part of the project was to generate many scenarios based on the stochastic variables, considerable effort was spent in developing a Visual Basic routine that could generate and store these scenarios. Performance measures were identified and test cases were run. The computational time for even a moderate number of scenarios was quite large, which necessitated the investigation of size reduction. In examining the production - distribution network of the model, it was observed that certain connections and production quantities were invariant of the scenario. As such, after examining a few scenarios, the connections on the network were labeled as either variant or invariant. This allowed the reduction of the model and also gave a better understanding of the effect of the various investments under study. Initial computational problems and time restrictions did not permit the final implemen-tation of a risk measure, and the topic will be pursued in a follow up work.