Modelling the implied probability of stock market movements

In this paper we study risk-neutral densities (RNDs) for the German stock market. The use of option prices allows us to quantify the risk-neutral probabilities of various levels of the DAX index. For the period from December 1995 to November 2001, we implement the mixture of log-normals model and a volatility-smoothing method. We discuss the time series behaviour of the implied PDFs and we examine the relations between the moments and observable factors such as macroeconomic variables, the US stock markets and credit risk. We find that the risk-neutral densities exhibit pronounced negative skewness. Our second main observation is a significant spillover of volatility, as the implied volatility and kurtosis of the DAX RND are mostly driven by the volatility of US stock prices. JEL Classification: C22, C51, G13, G15Option prices, risk-neutral density, spillover, Volatility

Addressing the Multi-Channel Inverse Problem at High Energy Colliders: A Model Independent Approach to the Search for New Physics with Trileptons

We describe a method for interpreting trilepton searches at high energy colliders in a model-independent fashion and apply it to the recent searches at the Tevatron. The key step is to recognize that the trilepton signature is comprised of four experimentally very different channels defined by the number of tau-leptons in the trilepton state. Contributions from these multiple channels to the overall experimental sensitivity (cross section times branching ratio) are model-independent and can be parametrized in terms of relevant new particle masses. Given the trileptonic branching ratios of a specific model, these experimentally obtained multichannel sensitivities can be combined to obtain a cross section measurement that can be used to confront the model with data. Our model-independent results are more widely applicable than the current Tevatron trilepton results which are stated exclusively in terms of mSUGRA parameters of supersymmetry. The technique presented here can be expanded beyond trilepton searches to the more general "inverse problem" of experimentally discriminating between competing models that seek to explain new physics discovered in multiple channels.Comment: 17 pages, 7 figures Changed content cosmetic changes for submission to JHE

How frequently do consumer prices change in Austria? Evidence from micro CPI data

Based on individual price records collected for the computation of the Austrian CPI, average frequencies of price changes and durations of price spells are estimated to characterize price setting in Austria. Depending on the estimation method, prices are unchanged for 10 to 14 months on average. We find strong heterogeneity across sectors and products. Price increases occur only slightly more often than price decreases. The typical size of a price increase (decrease) is 11 (15) percent. The aggregate hazard function of prices is decreasing with time. Besides heterogeneity across products and price setters, this is due to oversampling of products with a high frequency of price changes. Accounting for unobserved heterogeneity in estimating the probability of a price change with a fixed-effects logit model, we find a positive effect of the duration of a price spell. During the Euro cash changeover the probability of price changes was higher. JEL Classification: C41, D21, E31, L11consumer prices, duration of price spells, frequency and synchronization of price changes, sticky prices

The forecasting performance of German stock option densities

In this paper the authors estimate risk-neutral densities (RND) for the largest euro-area stock market (the index of which is the German DAX), reporting their statistical properties, and evaluating their forecasting performance. The authors have applied an innovative test procedure to a new, rich, and accurate data set. They have two main results. First, They have recorded strong negative skewness in the densities. Second, they find evidence for a significant difference between the actual density and the risk-neutral density, leading to the conclusion that market participants were surprised by the extent of both the rise and the fall of the DAX.Stock market - Germany ; Stock options

Continuities on Subspaces

We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions

The Forecasting Performance of German Stock Option Densities

In this paper we will be estimating risk-neutral densities (RND) for the largest euro area stock market (the index of which is the German DAX), reporting their statistical properties, and evaluating their forecasting performance. We have applied an innovative test procedure to a new, rich, and accurate data set. We have two main results. First, we have recorded strong negative skewness in the densities. Second, we find evidence for significant differences between the actual density and the risk-neutral density, leading to the conclusion that market participants were surprised by the extent of both the rise and the fall of the DAX. -- In dieser Arbeit werden "risikoneutrale" Dichtefunktionen über künftige DAXIndexstände aus täglich beobachteten Preisen europäischer Kauf- und Verkaufsoptionen mit verschiedenen Restlaufzeiten abgeleitet. Das hierbei verwendete Berechnungsverfahren beruht auf der Mischung von zwei Log-Normalverteilung, bei dem fünf Parameter (der Mischungsparameter, zwei Mittelwerte und zwei Standardabweichungen) so bestimmt werden, dass der quadratische Abstand zwischen beobachteten und impliziten Optionspreisen minimal ist. Die Preisnotierungen für die Derivative werden der Eurex entnommen und der Untersuchungszeitraum erstreckt sich von Dezember 1995 bis Mai 2002, also sowohl über die Boom- als auch über die Niedergangsphase des DAX. Die Vorhersagehorizonte der Dichten sind auf Grund der Datenlage auf sechs bis acht Wochen begrenzt. Die Vorhersagegüte dieser Dichten wird über verschiedene neuartige statistische Evaluierungsverfahren abgeschätzt. Im Ergebnis stellt sich folgendes heraus: Erstens: Die Dichten weisen im Durchschnitt eine negative Schiefe (negatives drittes Moment) auf, so dass das linke Ende der Dichte "dicker" ist als das rechte und die Marktteilnehmer somit einen bestimmten prozentualen Kursverlust als wahrscheinlicher einschätzten als einen Kursgewinn. Zweitens: Die Evaluierungstests für die Dichten machen deutlich, dass die tatsächlichen Dichten im Mittel deutlich von den risikoneutralen Dichten abweichen. Dabei kann ausgeschlossen werden, dass es sich lediglich um einen "Mittelwert"fehler handelt. Vielmehr scheinen die Markteilnehmer sowohl in der Aufschwung- als auch in der Abschwungphase von den Kursbewegungen des DAX überrascht worden zu.option prices,risk-neutral density,density evaluation,overlapping data

Triphase catalysis: mass transfer and kinetic studies

The importance of phase transfer catalysis (PTC) in the production of high value chemicals has grown immensely over the past few years. PTC may be a suitable method to synthesize a product whenever each reactant is miscible in a different phase. By addition of a PT catalyst, which functions as a ferrying agent between the phases, significant rate enhancements can be achieved;The PT catalyst (e.g. a quaternary ammonium salt) is usually used in soluble form. Alternatively, it can be bound to a solid support. The latter technique is called triphase catalysis (TPC). It has operational advantages over conventional PTC due to its potential use in continuous processes. However, the solid support (usually a porous polymer) induces diffusional limitations and consequently reduces overall reaction rates;The objective of the present research is to develop a method to determine external mass transfer coefficients since many TPC systems may be film diffusion limited under typical reaction conditions. A rotating disk contactor (RDC) has been specifically designed for this purpose. From the data obtained from this unit, it is possible to calculate mass transfer coefficients of several reaction systems and to suggest a general equation that correlates the Sherwood number to the Reynolds and Schmidt numbers;In view of conflicting reports on the efficacy of supported PTC, a comparative assessment of heterogeneous and homogeneous catalysts has been made for different mechanistic categories of PTC systems. It is possible to identify conditions under which the supported catalyst performs distinctly better than its soluble counterpart. The solubility of the homogeneous catalyst in the organic phase is found to be the most important factor in determining catalytic activity. Under certain conditions, polarity changes of the organic bulk phase induces autocatalytic behavior, an observation not hitherto made. In conclusion, it can be stated that certain categories of heterogenized catalysts perform better than their soluble counterparts for some reactions, notwithstanding their natural predilection to hinder reaction by diffusional limitation. This fact, coupled with the operational advantages of triphase catalysis, opens up the distinct possibility of its acceptance by industry