Global ETD Search

21	Pricing in (in)complete markets : structural analysis and applications / Esser, Angelika. January 2004 (has links) Univ., Diss.--Frankfurt (Main), 2003. / Literaturverz. S. [105] - 107.
22	Stable Parameter Identification Evaluation of Volatility Rückert, Nadja, Anderssen, Robert S., Hofmann, Bernd 29 March 2012 (has links) (PDF) Using the dual Black-Scholes partial differential equation, Dupire derived an explicit formula, involving the ratio of partial derivatives of the evolving fair value of a European call option (ECO), for recovering information about its variable volatility. Because the prices, as a function of maturity and strike, are only available as discrete noisy observations, the evaluation of Dupire’s formula reduces to being an ill-posed numerical differentiation problem, complicated by the need to take the ratio of derivatives. In order to illustrate the nature of ill-posedness, a simple finite difference scheme is first used to approximate the partial derivatives. A new method is then proposed which reformulates the determination of the volatility, from the partial differential equation defining the fair value of the ECO, as a parameter identification activity. By using the weak formulation of this equation, the problem is localized to a subregion on which the volatility surface can be approximated by a constant or a constant multiplied by some known shape function which models the local shape of the volatility function. The essential regularization is achieved through the localization, the choice of the analytic weight function, and the application of integration-by-parts to the weak formulation to transfer the differentiation of the discrete data to the differentiation of the analytic weight function. Parameteridentifikation Volatilitätsfunktion Dupire Formel Finite Differenzen Parameter identification Volatility surfaces Dupire’s equation Finite difference Localization approach ddc:510 Volatilität Parameteridentifikation Black-Scholes-Modell
23	Illustration of stochastic processes and the finite difference method in finance Kluge, Tino 22 January 2003 (has links) The presentation shows sample paths of stochastic processes in form of animations. Those stochastic procsses are usually used to model financial quantities like exchange rates, interest rates and stock prices. In the second part the solution of the Black-Scholes PDE using the finite difference method is illustrated. / Der Vortrag zeigt Animationen von Realisierungen stochstischer Prozesse, die zur Modellierung von Groessen im Finanzbereich haeufig verwendet werden (z.B. Wechselkurse, Zinskurse, Aktienkurse). Im zweiten Teil wird die Loesung der Black-Scholes Partiellen Differentialgleichung mittels Finitem Differenzenverfahren graphisch veranschaulicht. info:eu-repo/classification/ddc/510 ddc:510 Animation Black-Scholes-Modell Finite-Differenzen-Methode Pfad <Mathematik> Stochastik Stochastischer Prozess
24	Dynamic optimal portfolios benchmarking the stock market Gabih, Abdelali, Richter, Matthias, Wunderlich, Ralf 06 October 2005 (has links) The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results. info:eu-repo/classification/ddc/510 ddc:510 Black-Scholes-Modell Portfolio Selection benchmarking dynamic strategy martingale method optimal portfolio shortfall risk
25	A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets Krämer, Romy, Richter, Matthias 19 May 2008 (has links) In this paper, we study mathematical properties of a generalized bivariate Ornstein-Uhlenbeck model for financial assets. Originally introduced by Lo and Wang, this model possesses a stochastic drift term which influences the statistical properties of the asset in the real (observable) world. Furthermore, we generali- ze the model with respect to a time-dependent (but still non-random) volatility function. Although it is well-known, that drift terms - under weak regularity conditions - do not affect the behaviour of the asset in the risk-neutral world and consequently the Black-Scholes option pricing formula holds true, it makes sense to point out that these regularity conditions are fulfilled in the present model and that option pricing can be treated in analogy to the Black-Scholes case. info:eu-repo/classification/ddc/510 ddc:510 Black-Scholes-Modell Optionspreistheorie Black-Scholes formula financial analysis generalized Ornstein-Uhlenbeck process hedging option pricing
26	Stable Parameter Identification Evaluation of Volatility Rückert, Nadja, Anderssen, Robert S., Hofmann, Bernd January 2012 (has links) Using the dual Black-Scholes partial differential equation, Dupire derived an explicit formula, involving the ratio of partial derivatives of the evolving fair value of a European call option (ECO), for recovering information about its variable volatility. Because the prices, as a function of maturity and strike, are only available as discrete noisy observations, the evaluation of Dupire’s formula reduces to being an ill-posed numerical differentiation problem, complicated by the need to take the ratio of derivatives. In order to illustrate the nature of ill-posedness, a simple finite difference scheme is first used to approximate the partial derivatives. A new method is then proposed which reformulates the determination of the volatility, from the partial differential equation defining the fair value of the ECO, as a parameter identification activity. By using the weak formulation of this equation, the problem is localized to a subregion on which the volatility surface can be approximated by a constant or a constant multiplied by some known shape function which models the local shape of the volatility function. The essential regularization is achieved through the localization, the choice of the analytic weight function, and the application of integration-by-parts to the weak formulation to transfer the differentiation of the discrete data to the differentiation of the analytic weight function. info:eu-repo/classification/ddc/510 ddc:510 Volatilität Parameteridentifikation Black-Scholes-Modell
27	Hedging Foreign Exchange Exposure in Private Equity Using Financial Derivatives / Hedging av valutaexponering inom private equity med finansiella derivat Kwetczer, Filip, Åkerlind, Carl January 2018 (has links) This thesis sets out to examine if and how private equity funds should hedge foreign exchange exposure. To our knowledge the field of foreign exchange hedging within private equity, from the private equity firms’ point of view, is vastly unexplored scientifically. The subject is important since foreign ex-change risk has a larger impact on private equity returns now than historically due to increased competition, cross-boarder investments and foreign exchange volatility. In order to answer the research question a simulation model is constructed and implemented under different scenarios. Foreign exchange rates are simulated and theoretical private equity funds are investigated and com-pared under different performance measures. The underlying mathematical theory originates from the work of Black and Scholes. The main result of this thesis is that private equity funds cannot achieve a higher internal rate of return on average through hedging of foreign exchange exposure independent of the slope of the foreign exchange forward curve. However, hedging strategies yielding the same mean internal rate of return but performing better in terms of performance measures accounting for volatility of returns have been found. Furthermore, we found that the conclusions are independent of whether the current or forward foreign exchange rate is a better approximation for the future foreign exchange rate. / Uppsatsens syfte är att undersöka om och i sådana fall hur private equity fonder ska hedgea valutaexponering. Ämnet är såvitt vi vet ej tidigare undersökt inom vetenskaplig forskning ur private equity företagens synvinkel. Ämnet är viktigt eftersom valutarisk har fått en större påverkan på private equity företagens avkastning jämfört med hur det har sett ut historiskt på grund av högre konkurrens, mer internationella investeringar samt ökad volatilitet i valutakurser. En simuleringsmodell har konstruerats och implementerats under olika scenarier för att besvara forskningsfrågan. Valutakurser simuleras och teoretiska private equity fonder undersöks samt jämförs utefter olika nyckeltal. Den underliggande matematiska modelleringen härstammar från Black och Scholes forskning. Uppsatsens viktigaste resultat är att private equity fonder inte kan uppnå en högre avkastning genom att hedgea valutaexponering oavsett lutningen av den förväntade valutautvecklingskurvan. Vi har dock funnit att det existerar hedgingstrategier som ger samma avkastning med lägre volatilitet. Vidare är slutsatserna oberoende av om nuvarande eller förväntad framtida valutakurs är den bästa approximationen av den framtida valutakursen. Private Equity Foreign Exchange Exposure Hedging Black-Scholes Model Financial Derivatives Private Equity Valutaexponering Hedging Black-Scholes Modell Finansiella Derivat Computational Mathematics Beräkningsmatematik
28	Three essays on financial econometrics / Yu, Jialin. January 2005 (has links) (PDF) NJ, Univ., Dep. of Economics, Diss.--Princeton, 2005. / Kopie, ersch. im Verl. UMI, Ann Arbor, Mich. - Enth. 3 Beitr.
29	Studies on two specific inverse problems from imaging and finance Rückert, Nadja 20 July 2012 (has links) (PDF) This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial diﬀerential equation. The option prices are only available as discrete noisy observations so that the main diﬃculty is the ill-posedness of the numerical diﬀerentiation. Finite diﬀerence schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these diﬃculties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial diﬀerential equation and evaluate the performance of the ﬁnite diﬀerence schemes and the new algorithm for synthetic and real option prices. Tikhonov-Regularisierung Kullback-Leibler Totale Variation Poissonverteilte Daten Bildverarbeitung Wahl des Regularisierungsparameters Diskrepanzprinzip L-Kurve Quasi-Optimalitätskriterium PET Black-Scholes-Modell Volatilität Dupire Call-Option Regularisierung durch Diskretisierung Parameter Identifikationsalgorithmus Tikhonov-Regularization Kullback-Leibler Total Variation Poisson distributed data discrepancy principle L-curve method quasi-optimality criterion PET Black-Scholes model volatility Dupire call option regularization by discretization imaging finance ddc:515 ddc:519 Tichonov-Regularisierung Black-Scholes-Modell Volatilität Regularisierungsverfahren Poisson-Verteilung Bildverarbeitung Call-Option Parameter <Mathematik>
30	Studies on two specific inverse problems from imaging and finance Rückert, Nadja 16 July 2012 (has links) This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial diﬀerential equation. The option prices are only available as discrete noisy observations so that the main diﬃculty is the ill-posedness of the numerical diﬀerentiation. Finite diﬀerence schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these diﬃculties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial diﬀerential equation and evaluate the performance of the ﬁnite diﬀerence schemes and the new algorithm for synthetic and real option prices. info:eu-repo/classification/ddc/515 ddc:515 info:eu-repo/classification/ddc/519 ddc:519

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