4,016 research outputs found

    Nietzsche and Amor Fati

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    This paper identifies two central paradoxes threatening the notion of amor fati [love of fate]: it requires us to love a potentially repellent object (as fate entails significant negativity for us) and this, in the knowledge that our love will not modify our fate. Thus such love may seem impossible or pointless. I analyse the distinction between two different sorts of love (eros and agape) and the type of valuation they involve (in the first case, the object is loved because we value it; in the second, we value the object because we love it). I use this as a lens to interpret Nietzsche?s cryptic pronouncements on amor fati and show that while an erotic reading is, up to a point, plausible, an agapic interpretation is preferable both for its own sake and because it allows for a resolution of the paradoxes initially identified. In doing so, I clarify the relation of amor fati to the eternal return on the one hand, and to Nietzsche?s autobiographical remarks about suffering on the other. Finally, I examine a set of objections pertaining both to the sustainability and limits of amor fati, and to its status as an ideal

    Real Option Valuation of a Portfolio of Oil Projects

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    Various methodologies exist for valuing companies and their projects. We address the problem of valuing a portfolio of projects within companies that have infrequent, large and volatile cash flows. Examples of this type of company exist in oil exploration and development and we will use this example to illustrate our analysis throughout the thesis. The theoretical interest in this problem lies in modeling the sources of risk in the projects and their different interactions within each project. Initially we look at the advantages of real options analysis and compare this approach with more traditional valuation methods, highlighting strengths and weaknesses ofeach approach in the light ofthe thesis problem. We give the background to the stages in an oil exploration and development project and identify the main common sources of risk, for example commodity prices. We discuss the appropriate representation for oil prices; in short, do oil prices behave more like equities or more like interest rates? The appropriate representation is used to model oil price as a source ofrisk. A real option valuation model based on market uncertainty (in the form of oil price risk) and geological uncertainty (reserve volume uncertainty) is presented and tested for two different oil projects. Finally, a methodology to measure the inter-relationship between oil price and other sources of risk such as interest rates is proposed using copula methods.Imperial Users onl

    Valuation of financial derivatives through transmutation operator methods

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    Nowadays there is a fast development of the methods based on transmutation operators (TO) theory for solving differential equations. The possibility to construct the images of solutions for TO in certain cases allowed the construction of accurate numerical solutions to several problems that appear in different applied fields. In the present work, for the first time, it is shown that these methods can be effectively applied to the optimal stopping problems that appear in mathematical finance. The first part of the thesis (Chapter 2) consists of an application of the method to the valuation of European-style double-barrier knock-out options (DBKO). This is done by using the efficient computation of eigenvalues for the Shrodinger equation and a representation of solutions in terms of Neumann series of Bessel functions. This knowledge was used in the construction of a novel analytically tractable method for pricing (and hedging) DBKO, which can be applied to the whole class of one-dimensional timehomogeneous diffusions even for the cases where the corresponding transition density is not known. The proposed numerical method is shown to be efficient and simple to implement. To illustrate the flexibility and computational power of the algorithm it is constructed an extended jump to default model that is able to capture several empirical regularities commonly observed in the literature. The second part of the thesis (Chapters 3 and 4) is dedicated to the study of the more complicated problems: the free boundary problems. For this purpose, the method was first (in some certain sense) generalized and tested on the Stefan-like problem. The method consists in efficiently constructing a complete system of solutions for parabolic equation from known solutions for the heat equation, heat polynomials (HP). This way it was possible to extend the numerical method that existed only for the heat equation to the large class of parabolic equations. However, for the selected financial problem, Russian option with finite horizon (ROFH), the numerical computation from the method based on HP revealed to be non-efficient. This is due to the more complex structure of the problem, specifically the non-consistent boundary conditions. Hence, it was developed another variation of the method that uses different systems of solutions for the heat equation: the generalized exponential basis. The constructed method proved to be accurate, relatively easy to implement and can it can be applied to the large class of the free boundary problems. The value of the ROFH has been an important theme of discussion in the last decades. The application of the method to this problem confirmed several results that have appeared recently in the literature and shred some light on the differences that were present.The constructed methods have a large scope of applications not only in financial field, but also in other disciplines. Both studies also open a variety of future research and applications that are discussed in the text.Actualmente estamos a assistir a um rápido desenvolvimento de métodos baseados nos operadores de transmutação (OT) para a resolução de equações diferenciais. Em certos casos, é possível calcular as imagens de soluções para OT, o que permite construir soluções numéricas com um elevado grau de precisão para diversos problemas aplicados. No presente trabalho, pela primeira vez, e desenvolvida e ilustrada uma aplicação eficiente destes métodos aos problemas de paragem óptima que surgem na matemática financeira. A primeira parte da tese (Capítulo 2) consiste na aplicação do método ao problema de avaliação de opção com dupla barreira "knock-out" (DBKO) de estilo europeu. A construção do método passa por um apurado cálculo de valores próprios do respectivo problema de Schrodinger e a representação de soluções em termos de séries de Neumann de funções de Bessel. Esse conhecimento foi utilizado para construir um novo método de expressão analítica para definição de preço (e cobertura) de DBKO. O método pode ser aplicado a toda uma classe de difusões uni-dimensionais homogéneas no tempo, mesmo para os casos em que não é conhecida a função de densidade de transição. Neste capítulo é demonstrado que o método proposto é eficiente e simples de implementar. Para ilustrar a flexibilidade e a robustez computacional do respectivo algoritmo é construído um modelo estendido de salto para o incumprimento que oferece a possibilidade de captar certos efeitos empíricos presentes na literatura. A segunda parte da tese (Capítulos 3 e 4) e dedicada ao estudo de problemas mais complexos: problemas de fronteira livre. Para esse propósito, o método foi (em certo sentido) generalizado e testado no problema do tipo de Stefan. O método consiste numa construção eficiente de um sistema completo de soluções para uma equação diferencial parabólica a partir de um sistema completo de soluções para a equação de calor, os polinómios de calor (PC). Deste modo, foi possível estender o método numérico que existia apenas para equação de calor para uma larga classe de equações parabólicas. No entanto, para o problema financeiro seleccionado, a opção russa com horizonte finito (ORHF), o método baseado nos PCs revelou-se computacionalmente ineficiente. Isso deve-se a uma estrutura mais complicada do problema, nomeadamente as não-consistentes condições de fronteira. Como tal, foi desenvolvida uma outra variação do método que usa um sistema de soluções diferente de PCs: uma base exponencial generalizada. O método construído provou ser preciso, de relativamente fácil implementação e pode ser aplicado a uma larga classe de problemas de fronteira livre. O valor de ORHF foi e continua a ser um importante tema de discussão nas últimas décadas. A aplicação do método a esse problema confirmou vários resultados que surgiram recentemente na literatura e revelou o porque de algumas diferenças. Os métodos construídos têm uma larga gama de aplicações, tanto no âmbito de matemática financeira como em outras disciplinas. Ambos os estudos abrem várias possibilidades para futuras investigações e aplicações, as discussões das quais se encontram no texto

    Aspect and Case in Interlanguage Grammars: The Case of English Learners of Russian

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    This dissertation presents the results of an empirical study on the acquisition of aspect and case by English speaking adult second language learners (L2) of Russian. Richardson (2007) argues that in Russian, structural Accusative case is aspectually relevant and that it is linked to the compositional event structure of the base form of a verb. The base form of a verb is compositionally determined when addition of a lexical or telic prefix changes the grammatical aspect of a verb from imperfective to perfective and lexical aspect from atelic to telic. I refer to these verbs as Condition 1 verbs. Alternatively, the base form of a verb is not compositionally determined when it merges with a superlexical prefix that changes the grammatical aspect of a verb from imperfective to perfective but does not change the telicity of an inherently atelic verb. I refer to these verbs as Condition 2 verbs. Direct objects of Condition 1 verbs are marked with structural Accusative case, whereas direct objects of inherently atelic Condition 2 verbs are assigned lexical case. The question that is investigated in the study is whether the knowledge of Condition 1 and Condition 2 verbs is part of the interlanguage (IL) grammars of L2 learners of Russian. Specifically, whether L2 English learners understand that in Russian, perfectivity is not always equated with telicity, and a base form of verbs whose event structure is (not) compositionally determined has different case assigning mechanisms. Six native speakers of Russian and 29 L1-English L2 learners of Russian performed the following experimental tasks: a Logical Entailment task, a Grammaticality Judgement task, and an Elicited Production task. Each task included sentences with Condition 1 and Condition 2 verbs. A repeated measures ANOVA, where Condition 1 verbs or Condition 2 verbs were used as a within subject factor and the proficiency group as a between subject factor, showed a significant effect for Condition 1 or Condition 2 verbs with the participants performing better on Condition 1 verbs across the three tasks. The superior performance on Condition 1 verbs is explained by the accessibility of the universal semantic feature [telic], the less marked cluster of features [+telic, +perfective] and the availability of structural Accusative case in English. A decline in performance on Condition 2 verbs is explained by the difficulties in acquiring a more marked cluster of features [-telic, +perfective], and the idiosyncrasy of lexical case

    TAU METHOD FOR PRICING AMERICAN OPTIONS UNDER COMPLEX MODELS

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    The European option can be exercised only at the expiration date while an American option can be exercised on or at any time before the expiration date.In this paper, we will study the numerical solutions of a class of complex partial differential equations (PDE) systems with free boundary conditions. This kind of problems arise naturally in pricing (finite-maturity) American options, which is applies to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump-diffusion (HEJD) and the finite moment log stable (FMLS) models. Developing efficient numerical schemes will have significant applications in finance computation. These equations have already been solve by the Hybrid Laplace transformfinite difference methods and the Laplace transform method(LTM). In this paper we will introduce a method to solve these equations by Tau method. Also, we will show that using this method will end up to a faster convergence. Numerical examples demonstrate the accuracy and velocity of the method in CEV models

    경로에 의존하는 미국형 옵션의 해석적 가치 평가

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    학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 강명주.American options are type of options that can be exercised anytime during their life. Therefore, the valuation of such options is usually classified as optimal stopping problems or free boundary problems. I derive the analytic pricing formulas and integral equations of American chained options, Russian options with finite time horizon, American floating strike lookback options, and American maximum quanto options. To verify the derived pricing formula and the integral equation satisfied by the free boundary are correct, we numerically solve the derived integral equations using recursive integration method or simple iterative method.Chapter 1 Introduction 1 Chapter 2 Chained knock-in barrier option 3 2.1 Preliminaries 4 2.2 Analytic Valuation of Chained American Barrier Options 6 2.2.1 Crossing a single barrier 6 2.2.2 Crossing two barriers 10 2.3 Numerical results 14 2.4 Summary 19 Chapter 3 Russian option with finite time horizon 22 3.1 Model Formulation: Free Boundary Problem 23 3.2 Inhomogeneous Black-Scholes Partial Differential Equation:Mixed Boundary Problem 26 3.3 Integral Equation of Russian Options with Finite Time Horizon:Premium Decomposition 34 3.3.1 Case of r 6= q 35 3.3.2 Case of r = q 37 3.4 Valuing Russian Options: Perpetual Case 42 3.5 Numerical Results 47 3.5.1 Recursive Integration Method for Russian Option with Finite Time Horizon 47 3.5.2 Results : Qualitative analysis 51 3.5.3 Results : Comparison with Other Methods 51 3.6 Summary 59 Chapter 4 American floating strike lookback option 60 4.1 Model formulation 62 4.2 Inhomogeneous Black-Scholes equation with Neumann boundary condition 65 4.3 Integral equation representation of American floating strike lookback option 71 4.4 Perpetual American floating strike lookback option 78 4.5 Summary 85 Chapter 5 American maximum exchange rate quanto lookback option 87 5.1 Model Formulation : Free boundary problem 89 5.2 Derivation of analytic solution for two-dimensional inhomogeneous Black-Scholes PDE 93 5.2.1 Two-dimensional Inhomogeneous Black-Scholes parabolic PDE on Unrestricted Domain 93 5.2.2 Two-dimensional inhomogeneous Black-Scholes parabolic PDE : Dirichlet Boundary Conditions 95 5.2.3 Two-dimensional inhomogeneous Black-Scholes parabolic PDE : Mixed Boundary Conditions 98 5.3 Analytic Pricing of American Maximum Exchange-Rate Quanto Lookback Options 105 5.3.1 European Maximum Exchange Rate Quanto Lookback Options 106 5.3.2 American Maximum Exchange Rate Quanto Lookback Options 109 5.4 Numerical Results 114 5.4.1 An iterative method 114 5.4.2 Forward shooting grid method for two-state model 116 5.4.3 Implications 118 5.5 Summary 126 Appendix A Basic Properties of Mellin Transforms 133 A.1 Properties of Mellin transform 133 A.2 Properties of double Mellin transform 135 Appendix B Some useful lemmas 137 Abstract (in Korean) 138Docto

    Damodaran Discount Cash Flow valuation

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    Context-linked grammar

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    Language is context free in the sense that it builds well-formed structures like "ideas sleep" and "ghosts live" (NP + VP) without regard to meaning and specific contexts (Chomslcy, 1957). However, it is also context sensitive in the sense that it makes use of linguistic objects such as personal pronouns and other indexical expressions that cannot have any reference unless they are embedded in some specific context. This (apparent) context-free/context-sensitive paradox is the focus of this essay. It pursues the idea that phases in the sense of Chomsky (2001) and related work - the minimal computational domains of language - are equipped with silent linking edge features that enable syntax to compute elements of a phase in relation to other phases, thereby also enabling narrow syntax to link to context and build the structures of broad syntax. Evidence for the edge linkers comes from overt phase internal effects, including person and tense marking, person shift of pronouns (indexical shift), the syntax of inclusiveness, and gender agreement across clause (phase) boundaries. Scrutiny of these phenomena suggests that nominal reference is exhaustively syntactic. Syntax therefore communicates with context, but it does so indirectly, via silent edge linkers. The inherent silence of these linkers, in turn, is the reason why the context-syntax relation has been such an opaque problem in linguistics and philosophy. (C) 2014 Elsevier Ltd. All rights reserved

    Valuation Strategies for Small Businesses\u27 Intangible Assets

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    Small business owners who attempt to sell their businesses may not receive full value if they do not adequately value their intangible assets. The purpose of this multiple case study was to explore effective strategies business leaders used to value intangible assets when considering the sale of their businesses. The participants for this study were 5 business owners in a metropolitan area in the southeastern United States who had successful valuation experiences during the sale of their businesses. Data were collected through semistructured interviews with participants, methodological triangulation, observations, and review of company documents. Data were analyzed using thematic analysis, coding narrative segments, and reviewing secondary data. The themes that emerged from data analysis include collecting and using company data concerning intangible assets; hiring a reputable accounting firm to assist in valuation; understanding the values of brand, customer base, and goodwill; and choosing the appropriate asset valuation approach. To accurately value the intangible assets of their businesses, the most significant and recurring theme in the participants\u27 responses was the need for assistance from a reputable accounting firm. The implications of this study for positive social change include the potential to enhance the economic investment in local areas where business owners appropriately value intangible assets
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