Risk quantification of an option portfolio through the introduction of the fuzzy Black-Scholes formula

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2018-2019, Tutor: Ana María Gil LafuenteThe aim of this thesis is to quantify the market risk of an option portfolio under uncertainty. The fuzzy sets theory is introduced to model the parameters of the Black-Scholes option-pricing formula. Since the option price is calculated through the fuzzy Black-Scholes formula, we can compute the Value-at-Risk as a fuzzy number. By doing so, we aim to capture extra information that is lost in traditional models given the uncertainty derived from the fluctuations of financial markets. Finally, we want to conclude whether the introduction of the fuzzy sets theory is useful in order to improve the risk management

Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation

Option pricing is irreversible, fuzzy, and flexible. The fuzzy measure which is used for real option pricing is a useful supplement to the traditional real option pricing method. Based on the review of the concepts of the mean and variance of trapezoidal fuzzy number and the combination with the Carlsson-Fuller model, the trapezoidal fuzzy variable can be used to represent the current price of land expropriation and the sale price of land on the option day. Fuzzy Black-Scholes option pricing model can be constructed under fuzzy environment and problems also can be solved and discussed through numerical examples

Compound Option Pricing under Fuzzy Environment

Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each α, the α-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment

Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments

In this doctoral dissertation characteristics of very large industrial real investments (VLIRI) are investigated and a special group of VLIRI is defined as giga-investments. The investment decision-making regarding to giga-investments is discussed from the points of view of discounted cash-flow based methods and real option valuation. Based on the bacground of establishing giga-investments, state-of-the-art in capital budgeting (including real options) and by applying fuzzy numbers a novel method for the evaluation and profitability analysis of giga-investments is presented. Application of the method is illustrated and issues regarding investment decision-making of large industrial real investments are discussed.Real Options; Fuzzy Real Option Valuation; Giga-Investments; Very Large Industrial Real Investments; Dissertation

Real options valuation for South African nuclear waste management using a fuzzy mathematical approach

The feasibility of capital projects in an uncertain world can be determined in several ways. One of these methods is real options valuation which arose from financial option valuation theory. On the other hand fuzzy set theory was developed as a mathematical framework to capture uncertainty in project management. The valuation of real options using fuzzy numbers represents an important refinement to determining capital projects' feasibility using the real options approach. The aim of this study is to determine whether the deferral of the decommissioning time (by a decade) of an electricity-generating nuclear plant in South Africa increases decommissioning costs. Using the fuzzy binomial approach, decommissioning costs increase when decommissioning is postponed by a decade whereas use of the fuzzy Black-Scholes approach yields the opposite result. A python code was developed to assist in the computation of fuzzy binomial trees required in our study and the results of the program are incorporated in this thesis.KMBT_363Adobe Acrobat 9.54 Paper Capture Plug-i

Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification

We present a fuzzy version of the Garman-Kohlhagen (FG-K) formula for pricing European currency option based on the extension principle. In order to keep consistent with the real market, we assume that the interest rate, the spot exchange rate, and the volatility are fuzzy numbers in the FG-K formula. The conditions of a basic proposition about the fuzzy-valued functions of fuzzy subsets are modified. Based on the modified conditions and the extension principle, we prove that the fuzzy price obtained from the FG-K formula for European currency option is a fuzzy number. To simplify the trade, the weighted possibilistic mean (WPM) value with a weighting function is adopted to defuzzify the fuzzy price to a crisp price. The numerical example shows our method makes the α-level set of fuzzy price smaller, which decreases the fuzziness. The example also indicates that the WPM value has different approximation effects to real market price by taking different values of weighting parameter in the weighting function. Inspired by this example, we provide a method, which can identify the optimal parameter

Intra- and extra-organisational knowledge exchange within an agent based system from an option-theoretic point of view

Die vorliegende Diplomarbeit analysiert das Konzept der Business Transaction Theory (BTT). Diese Theorie besagt, dass der Austausch von Wissen zwischen Menschen durch finanzmathematische Evaluierungsmodelle bewertet werden kann. Darüber hinaus kombiniert die Diplomarbeit, durch einen interdisziplinären Ansatz, die Gebiete des Wissensmanagements (repräsentiert durch die BTT), der Finanzmathematik (repräsentiert durch das Black-Scholes Modell) und der agentenbasierten Simulation (ABS), um den Wissensaustausch innerhalb einer Firma mittels des ABS zu simulieren. Nachdem die drei erwähnten Modelle im Detail analysiert wurden, wurde die Kompatibilität der BTT und des B-S Modells kontrolliert. Dies wurde nachgewiesen, indem eine Überprüfung aller finanzmathematischen Anforderungen auf deren Transferierbarkeit in ein Wissensaustausch-Szenario durchgeführt wurde. Die Diplomarbeit bezieht sich nicht nur auf den intra-organisationalen Wissensaustausch, sondern schafft ein Modell eines virtuellen Informationsmarktes, auf dem Angestellte und Firmen Informationen aus externen Quellen, zur Erweiterung des eigenen Wissensstandes, akquirieren können. Durch eine kritische Analyse der dargelegten Konzepte und durch eine Auseinandersetzung mit den, bei der Kombination der unterschiedlichen Forschungsgebiete entstandenen Problemen, versucht diese Diplomarbeit einen innovativen Ansatz, sowie einen Beitrag zur wissenschaftlichen Forschung zu leisten.This diploma thesis analyses the concept of the Business Transaction Theory (BTT). This theory states that human knowledge exchange can be evaluated by finance mathematic evaluation models. Through an interdisciplinary approach, it combines the areas of knowledge management (represented by the BTT), finance mathematics (represented by the Black-Scholes option evaluation formula) and agent based simulations (ABS), in order to create a possibility to simulate knowledge exchanges within a company. After having analysed the three above mentioned models in detail, the compatibility of the BTT and the B-S model has been proved. This was done by verifying that all necessary requirements and assumptions that arose from the finance mathematic side were transferable into a knowledge exchange setup within an ABS. The diploma thesis not only focuses on the intra-organisational knowledge exchange, but also introduces the model of a virtual information market, where employees and companies can acquire additional information from external sources, in order to increase their own knowledge level. By analysing critically all concepts used, as well as addressing occurring problems that arose with combining the different areas, this diploma thesis represents an innovative approach and contribution to academic research

Facilitating Brownfield Redevelopment Projects: Evaluation, Negotiation, and Policy

A risky project evaluation technique called the fuzzy real options analysis is developed to evaluate brownfield redevelopment projects. Other decision making techniques, such as multiple criteria analysis and conflict analysis, can be incorporated into fuzzy real options analysis to facilitate negotiations on brownfield redevelopment among decision makers (DMs). The value of managerial flexibility, which is important in negotiations and policy making for brownfield redevelopment, is overlooked when the traditional evaluation method, net present value (NPV), is employed. Findings of this thesis can be used to promote brownfield redevelopment, thereby helping to eliminate environmental threats and enhance regional sustainability. A brownfield is an abandoned or underutilized property that contains, or may contain, pollutants, hazardous substances, or contaminants from previous usage, typically industrial activity. Brownfields often occur when the local economy transits from industrial to service-oriented seeking more profit. Governments actively promote brownfield redevelopment to eliminate public health threats, help economic transition, and enhance sustainability. However, developers are reluctant to participate in brownfield redevelopment because they often regard these projects as unprofitable when using classic evaluation techniques. On the other hand, case studies show that brownfield redevelopment projects can be good business opportunities for developers. An improved evaluation method is developed in order to estimate the value of a brownfield more accurately. The main reason that makes the difference between estimates and ''actual'' values lies in the failure of the deterministic project evaluation tool to price the value of uncertainty, which leads to efforts to enhance the decision making under uncertainty. Real options modelling, which extends the ability of option pricing models in real asset evaluation, is employed in risky project evaluation because of its capacity to handle uncertainties. However, brownfield redevelopment projects contain uncertain factors that have no market price, thus violating the assumption of option pricing models for which all risks have been reflected in the market. This problem, called private risk, is addressed by incorporating fuzzy numbers into real options in this thesis, which can be called fuzzy real options. Fuzzy real options are shown to generalize the original model to deal with additional kinds of uncertainties, making them more suitable for project evaluation. A numerical technique based on hybrid variables is developed to price fuzzy real options. We proposed an extension of Least Squares Monte-Carlo simulation (LSM) that produces numerical evaluations of options. A major advantage of this methodology lies in its ability to produce results regardless of whether or not an analytic solution exists. Tests show that the generalized LSM produces similar results to the analytic valuation of fuzzy real options, when this is possible. To facilitate parameter estimation for the fuzzy real options model, another numerical method is proposed to represent the likelihood of contamination of a brownfield using fuzzy boundaries. Linguistic quantifiers and ordered weighted averaging (OWA) techniques are utilized to determine the likelihood of pollution at sample locations based on multiple environmental indicators, acting as a fuzzy deduction rule to calculate the triangle membership functions of the fuzzy parameters. Risk preferences of DMs are expressed as different ''ORness'' levels of OWA operators, which affect likelihood estimates. When the fuzzy boundaries of a brownfield are generated by interpolation of sample points, the parameters of fuzzy real options, drift rate and volatility, can be calculated as fuzzy numbers. Hence, this proposed method can act as an intermediary between DMs and the fuzzy real options models, making this model much easier to apply. The values of DMs to a brownfield can be input to the graph model for conflict resolution (GMCR) to identify possible resolutions during brownfield redevelopment negotiation among all possible states, or combinations of DMs' choices. Major redevelopment policies are studied using a brownfield redevelopment case, Ralgreen Community in Kitchener, Ontario, Canada. The fuzzy preference framework and probability-based comparison method to rank fuzzy variables are employed to integrate fuzzy real options and GMCR. Insights into this conflict and general policy suggestions are provided. A potential negotiation support system (NSS) implementing these numerical methods is discussed in the context of negotiating brownfield redevelopment projects. The NSS combines the computational modules, decision support system (DSS) prototypes, and geographic information systems (GIS), and message systems. A public-private partnership (PPP) will be enhanced through information sharing, scenario generation, and conflict analysis provided by the NSS, encouraging more efficient brownfield redevelopment and leading to greater regional sustainability. The integrated usage of fuzzy real options, OWA, and GMCR takes advantage of fuzziness and randomness, making better evaluation technique available in a multiple DMs negotiation setting. Decision techniques expand their range from decision analysis, multiple criteria analysis, to a game-theoretic approach, contributing to a big picture on decision making under uncertainty. When these methods are used to study brownfield redevelopment, we found that creating better business opportunities, such as allowing land use change to raise net income, are more important in determining equilibria than remediation cost refunding. Better redevelopment policies can be proposed to aid negotiations among stakeholders

Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments

In this doctoral dissertation characteristics of very large industrial real investments (VLIRI) are investigated and a special group of VLIRI is defined as giga-investments. The investment decision-making regarding to giga-investments is discussed from the points of view of discounted cash-flow based methods and real option valuation. Based on the bacground of establishing giga-investments, state-of-the-art in capital budgeting (including real options) and by applying fuzzy numbers a novel method for the evaluation and profitability analysis of giga-investments is presented. Application of the method is illustrated and issues regarding investment decision-making of large industrial real investments are discussed