Nonparametric Estimation of American Options Exercise Boundaries and Call Prices

Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. The paper focuses on the daily market option prices and exercise data on the S&P100 contract. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries. Contrairement à ce qu'il est possible d'obtenir dans un contexte d'évaluation de titres dérivés de type européen, il n'existe pas de formule analytique simple pour évaluer les options américaines, même si la volatilité de l'actif sous-jacent est supposée constante. La possibilité d'exercice prématuré qu'offre ce type de contrat complique considérablement son évaluation. La démarche adoptée dans cette étude consiste à dériver les prix d'option et les frontières d'exercice à partir de données financières, utilisées dans un cadre d'analyse statistique non-paramétrique. Plus particulièrement, l'étude utilise les observations quotidiennes du prix du contrat sur l'indice S&P100 ainsi que les observations sur l'exercice de ce contrat. Les résultats sont comparés à ceux obtenus à l'aide de techniques paramétriques dans un modèle où la volatilité est supposée constante. La conclusion est qu'il existe des différences stratégiques entre les prédictions des deux modèles, aussi bien en ce qui concerne le prix de l'option que la politique d'exercice qui lui est associée.Option Pricing, Derivative Securities, OEX Contract, Kernel Estimation, Prix d'options, titres dérivés, contrat OEX, estimation par méthode de noyau

American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation

In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility. Cet article examine les contrats optionnels de type américain lorsque l'actif sous-jacent paie des dividendes et a une volatilité stochastiques. Nous présentons une discussion complète des fondations théoriques de l'évaluation des options américaines et de leurs frontières d'exercice. Nous démontrons leur dépendance par rapport aux diverses sources d'incertitude qui déterminent le taux de dividendes et la volatilité, et dérivons les prix d'équilibre des actifs, titres dérivés ainsi que les politiques optimales d'exercice dans un modèle d'équilibre général. Les modèles théoriques conduisent à des expressions complexes qui sont difficiles à estimer. C'est pourquoi nous adoptons une approche non-paramétrique qui permet d'examiner des formes réduites. Nous utilisons des méthodes non-paramétriques pour estimer les prix d'options à l'achat et les frontières d'exercice conditionnelles aux dividendes et à la volatilité. Puisque cette dernière est un processus latent nous proposons plusieurs approches, fondées en particulier sur des estimateurs-filtres EGARCH, des volatilités implicites et historiques. L'approche non-paramétrique nous permet de tester si les prix d'options et les décisions d'exercice sont principalement déterminés par les dividendes, comme suggéré par Harvey et Whaley (1992a, b) et Fleming et Whaley (1994) pour le contrat OEX, ou si la volatilité stochastique complémente l'incertitude sur les dividendes. Nous établissons que les dividendes seuls ne rendent pas compte de tous les aspects de l'évaluation de ces options et des décisions d'exercice, ce qui suggère la nécessité d'inclure la volatilité stochastique.Option Pricing, Derivative Securities, OEX Contract, Kernel Estimation, Prix d'options, titres dérivés, contrat OEX, estimation par méthode de noyau

American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation

Cet article examine les contrats optionnels de type américain lorsque l'actif sous-jacent paie des dividendes et a une volatilité stochastiques. Nous présentons une discussion complète des fondations théoriques de l'évaluation des options américaines et de leurs frontières d'exercice. Nous démontrons leur dépendance par rapport aux diverses sources d'incertitude qui déterminent le taux de dividendes et la volatilité, et dérivons les prix d'équilibre des actifs, titres dérivés ainsi que les politiques optimales d'exercice dans un modèle d'équilibre général. Les modèles théoriques conduisent à des expressions complexes qui sont difficiles à estimer. C'est pourquoi nous adoptons une approche non-paramétrique qui permet d'examiner des formes réduites. Nous utilisons des méthodes non-paramétriques pour estimer les prix d'options à l'achat et les frontières d'exercice conditionnelles aux dividendes et à la volatilité. Puisque cette dernière est un processus latent nous proposons plusieurs approches, fondées en particulier sur des estimateurs-filtres EGARCH, des volatilités implicites et historiques. L'approche non-paramétrique nous permet de tester si les prix d'options et les décisions d'exercice sont principalement déterminés par les dividendes, comme suggéré par Harvey et Whaley (1992a, b) et Fleming et Whaley (1994) pour le contrat OEX, ou si la volatilité stochastique complémente l'incertitude sur les dividendes. Nous établissons que les dividendes seuls ne rendent pas compte de tous les aspects de l'évaluation de ces options et des décisions d'exercice, ce qui suggère la nécessité d'inclure la volatilité stochastique.In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility

Quantitative analysis of mixed niobium-titanium carbonitride solubility in HSLA steels based on atom probe tomography and electrical resistivity measurements

Solubility of mixed niobium-titanium carbonitrides in commercially relevant High Strength Low-Alloy (HSLA) steel was investigated by combined use of electrical re sistivity measurements and APT after interrupted quenching from soaking temperatures between 950 and 1250 C. Increasing electrical resistivity of the bulk material towards higher soaking temperatures was proportional to the nominal niobium addition which was varied between 0.002 and 0.022e0.043e0.085 wt.-%. Correlative APT analysis of the solutes in the steel matrix showed good agreement with electrical resistivity. Investigating numerous precipitate particles, APT also derived a precise composition for mixed niobium titanium-carbonitrides which constitute the steel microstructure after casting/before soaking. The scavenging of microalloy elements by insoluble titanium nitrides was cor rected by means of combined APT analysis of such precipitate and a quantitative image analysis for the estimation of the total volume fraction of titanium nitrides. For the first time, solute and precipitate composition together were used for solubility calculations of such mixed carbonitrides to derive an experimental solubility product. This was compared to solubility products of well-established simple carbides and nitrides and theoretical calculations of the solubility of multicomponent carbonitrides. The large discrepancy between experimentally derived and modelled solubility emphasizes the ne cessity of a robust methodology for the quantification of microalloy precipitation in HSLA steels

Tracing Microalloy Precipitation in Nb-Ti HSLA Steel during Austenite Conditioning

The microalloying with niobium (Nb) and titanium (Ti) is standardly applied in low carbon steel high-strength low-alloy (HSLA) steels and enables austenite conditioning during thermo-mechanical controlled processing (TMCP), which results in pronounced grain refinement in the finished steel. In that respect, it is important to better understand the precipitation kinetics as well as the precipitation sequence in a typical Nb-Ti-microalloyed steel. Various characterization methods were utilized in this study for tracing microalloy precipitation after simulating different austenite TMCP conditions in a Gleeble thermo-mechanical simulator. Atom probe tomography (APT), scanning transmission electron microscopy in a focused ion beam equipped scanning electron microscope (STEM-on-FIB), and electrical resistivity measurements provided complementary information on the precipitation status and were correlated with each other. It was demonstrated that accurate electrical resistivity measurements of the bulk steel could monitor the general consumption of solute microalloys (Nb) during hot working and were further complemented by APT measurements of the steel matrix. Precipitates that had formed during cooling or isothermal holding could be distinguished from strain-induced precipitates by corroborating STEM measurements with APT results, because APT specifically allowed obtaining detailed information about the chemical composition of precipitates as well as the elemental distribution. The current paper highlights the complementarity of these methods and shows first results within the framework of a larger study on strain-induced precipitation

Effect of quenching strategy and Nb-Mo sdditions on phase transformations and quenchability of high-strength boron steels

The application of direct quenching after hot rolling of plates is being employed in the production of ultra-high-strength hot rolled plates. When heavy gauge plates are produced, the complexity involve in achieving high cooling rates in the plate core is increased and the formation of undesirable soft phases within martensite is common. In the current paper, both direct quenching and conventional quenching (DQ and CQ) processing routes were reproduced by dilatometry tests and continuous cooling transformation (CCT) diagrams were built for four different high-strength boron steels. The results indicate that the addition of Mo and Nb-Mo suppresses the ferritic region and considerably shifts the CCT diagram to lower transformation temperatures. The combination of DQ strategy and the Mo-alloying concept provides the best option to ensure hardenability and the formation of a fully martensitic microstructure, and to avoid the presence of soft phases in the center of thick plates

Charakterisierung von LaNiO3-basierten Übergittern mittels transmissionselektronenmikroskopischer Methoden

Diese Arbeit befasst sich mit der Charakterisierung der Mikrostruktur von Übergittern auf der Basis von LaNiO3 mittels Verfahren der Transmissionselektronenmikroskopie, wobei vor allem die rasternde Transmissionselektronenmikroskopie in Kombination mit Elektronenenergieverlustspektroskopie verwendet wurde. Da die Einzelschichtdicke, das verwendete Substratmaterial oder das Material, das mit LaNiO3 kombiniert wird, die makroskopischen Eigenschaften solcher Übergitter beeinflussen können, wird untersucht, inwiefern diese Parameter auch die Mikrostruktur verändern. Es wird die hohe Qualität der Übergitter wie unter anderem die perfekte Epitaxie nachgewiesen und gezeigt, dass die Schärfe der Grenzfläche, z.B. LaNiO3—LaAlO3 gegenüber LaAlO3—LaNiO3, unterschiedlich sein kann. Zudem stellt sich heraus, dass das Substrat einen wesentlichen Einfluss auf die Mikrostruktur der Schichten hat. So bilden sich in auf SrTiO3 aufgewachsenen Übergittern aufgrund der polaren Diskontinuität wenige Nanometer große Nickeloxidpartikel an der Grenzfläche zwischen Substrat und Schicht. Dagegen findet man in Schichten auf (La,Sr)AlO4 zwei Arten von Ruddlesden-Popper-Fehlern. An Oberflächenstufen des Substrats bilden sich ausgedehnte planare Ruddlesden-Popper-Fehler. Desweiteren führen lokale Stapelfehler, die sich durch kleine Unregelmäßigkeiten im Wachstumsprozess formen können, zu dreidimensionalen Ruddlesden-Popper-Fehlern

Nonparametric Estimation of American Options Exercise Boundaries and Call Prices

Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. The paper focuses on the daily market option prices and exercise data on the S&P100 contract. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries

Effect of Dynamic Recrystallization on Microstructural Evolution in B Steels Microalloyed with Nb and/or Mo

The dynamic recrystallization behavior of ultra-high strength boron-microalloyed steels optionally alloyed with niobium and molybdenum is analyzed in this paper. Multipass torsion tests were performed to simulate plate rolling conditions followed by direct quenching. The influence of alloy composition on the transformed microstructure was evaluated by means of EBSD, thereby characterizing the morphology of the austenite grain morphology after roughing and finishing passes. The results indicated that for Nb-microalloyed steel, partial dynamic recrystallization occurred and resulted in local clusters of fine-sized equiaxed grains dispersed within the pancaked austenitic structure. A recrystallized austenite fraction appeared and transformed into softer phase constituents after direct quenching. The addition of Mo was shown to be an effective means of suppressing dynamic recrystallization. This effect of molybdenum in addition to its established hardenability effects hence safeguards the formation of fully martensitic microstructures, particularly in direct quenching processes. Additionally, the circumstances initiating dynamic recrystallization were studied in more detail, and the interference of the various alloying elements with the observed phenomena and the potential consequences of dynamic recrystallization before quenching are discussed