Valószínűség, esély, relatív súlyok. Opciók és reálopciók (Probability, chance, relative weights)

There is a long debate (going back to Keynes) how to interpret the concept of probability in economics, in business decisions, in finance. Iván Bélyácz suggested that the Black–Scholes– Merton analysis of fi nancial derivatives has a contribution to this risk vs. uncertainty debate. This article tries to interpret this suggestion, from the viewpoint of traded options, real options, Arrow–Debreu model, Heath–Jarrow–Morton model, insurance business. The article suggests making clear distinction and using different naming ● when the frequents approach and the statistics is relevant, ● when we just use consequent relative weights during the no-arbitrage pricing, and these weight are just interpreted as probabilities, ● when we just lack the necessary information, and there is a basic uncertainty in the business decision making process. The paper suggests making a sharp distinction between fi nancial derivatives used for market risk management and credit risk type derivatives (CDO, CDS, etc) in the reregulation process of the fi nancial markets.

A kockázat megjelenése a származtatott pénzügyi termékekben (The risk appearing in financial derivatives)

A pénzügyi kockázatok szerepe, modellezése, kezelése az utóbbi évtizedekben vált egyre hangsúlyosabbá az elméletben és a gyakorlatban egyaránt. A 2007-ben kezdődő pénzügyi válság egyik kiváltó oka a kockázatok nem megfelelő felmérése volt. A válság egyik tanulsága, hogy bár a matematika és a fizika hozzájárulása rendkívül mély módszertani apparátust biztosított a kockázatok számszerűsítésére, ezen eredmények pénzügyi alkalmazása csak akkor sikeres, ha pontosan értjük a modellek feltételeit és korlátait. Jelen cikk a pénzügyi derivatívák értékelésének alapelveit, valamint a származtatott ügyletekben megjelenő kockázatokat tekinti át, illetve bemutatja azokat a bizonytalansági tényezőket, amelyek megkérdőjelezik az értékelés objektivitását. / === / The modeling and management of financial risks became one of the most important topics of the last decade both in theory and fi nancial practice. The mismanagement of fi nancial risks can be mentioned among the reasons contributing to the eruption of the recent crisis. In order to use successfully the methodology of mathematics and physics in pricing of derivatives, we have to consider the assumptions and limits of the models. This paper introduces the main concepts – no arbitrage pricing and risk neutral valuation – in derivatives’ pricing, then presents and quantifies the risk of some derivative products. I am arguing that the assumptions of the Black–Scholes and Merton model are injured at several points, so the pricing can not be perfectly cleared from all the risk preferences. All those risks, deriving from the difference of the reality and the model are priced in the volatility parameter in the practice.

A kockázat mint látens fogalom (Risk - A latent concept)

A kockázat statisztikai értelemben közvetlenül nem mérhető, azaz látens fogalom éppen úgy, mint a gazdasági fejlettség, a szervezettség vagy az intelligencia. Mi bennünk a közös? A kockázat is komplex fogalom, több mérhető tényezőt foglal magában, és bár sok tényezőjét mérjük, fel sem tételezzük, hogy pontos eredményt kapunk. Ebben a megközelítésben az elemző kezdettől fogva tudja, hogy hiányos az ismerete. Ezt Bélyácz [2011[ nyomán úgy is megfogalmazhatjuk: „A statisztikusok tudják, hogy valamit éppen nem tudnak.” / === / From statistical point of view risk, like economic development is a latent concept. Typically there is no one number which can explicitly estimate or project risk. Variance is used as a proxy in finance to measure risk. Other professions are using other concepts for risk. Underwriting is the most important step in insurance business to analyse exposure. Actuaries evaluate average claim size and the probability of claim to calculate risk. Bayesian credibility can be used to calculate insurance premium combining frequencies and empirical knowledge, as a prior. Different types of risks can be classified into a risk matrix to separate insurable risk. Only this category can be analysed by multivariate statistical methods, which are based on statistical data. Sample size and frequency of events are relevant not only in insurance, but in pension and investment decisions as well.

A közvetlen külföldi befektetések és a korrupció közötti kapcsolat (The connection of Foreign Direct Investment and corruption)

A szerzők tanulmányának középpontjában a közvetlen külföldi befektetések és a korrupció kapcsolata áll. Feltételezésük az, hogy a közvetlen külföldi befektetők a kevésbé korrupt országokat kedvelik, mivel a korrupció egy további kockázati tényezőt jelent a befektetők számára, amely növelheti a befektetések költségeit. Megítélésük szerint ezt kvantitatív módszerekkel érdemes vizsgálni, így elemzésük során 79 országot vizsgálnak meg tíz évre vonatkozó átlagokkal a Gretl-program és az OLS becslőfüggvény segítségével. Több modell lefuttatása után azt az eredményt kapták, hogy a közvetlen külföldi befektetők döntéseiben a korrupció szignifikáns tényező, a két változó között negatív korrelációt figyeltek meg. / === / The study focuses on the connection of Foreign Direct Investment and corruption. The authors assume that investors prefer countries where corruption level is lower, as corruption an additional risk factor that might increase the cost of investment. They believe that the best way to prove the previous statement if they use quantitative methods, so they set up a model where 79 countries are tested for 10 years averages, with the help of the Gretl and OLS estimator. After running several models their finding was that corruption is a significant factor in the decisions of foreign investors, and there is a negative correlation between corruption and FDI.

Impacts of energy taxation in the enlarged European Union, evaluation with GEM-E3 Europe

The objective of this study is twofold: first to analyze how the implementation of the EU energy tax policies will affect the EU and its Member States and secondly to analyze how energy tax policies can contribute to climate policy objectives in the enlarged EU.

The Shapley value for airport and irrigation games

In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).

Every hierarchy of beliefs is a type

When modeling game situations of incomplete information one usually considers the players’ hierarchies of beliefs, a source of all sorts of complications. Harsányi (1967-68)’s idea henceforth referred to as the ”Harsányi program” is that hierarchies of beliefs can be replaced by ”types”. The types constitute the ”type space”. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.

Tőkeallokáció nem likvid portfóliók esetén (Risk capital allocation in case of illiquid portfolios)

A kockázat jó mérése és elosztása elengedhetetlen a bankok, biztosítók, befektetési alapok és egyéb pénzügyi vállalkozások belső tőkeallokációjához vagy teljesítményértékeléséhez. A cikkben bemutatjuk, hogy a koherens kockázati mértékek axiómáit nem likvid portfóliók esetén is el lehet várni. Így mérve a kockázatot, ismertetünk a kockázatelosztásra vonatkozó két kooperatív játékelméleti cikket. Az első optimista, eszerint mindig létezik stabil, az alegységek minden koalíciója által elfogadható, általános módszer a kockázat (tőke) elosztására. A második cikk pesszimista, mert azt mondja ki, hogy ha a stabilitás mellett igazságosak is szeretnénk lenni, akkor egy lehetetlenségi tételbe ütközünk. / === / Measuring and allocating risk properly are crucial for performance evaluation and internal capital allocation of portfolios held by banks, insurance companies, investment funds and other entities subject to fi nancial risk. We argue that the axioms of coherent measures of risk are valid for illiquid portfolios as well. Then, we present the results of two papers on allocating risk measured by a coherent measure of risk. Assume a bank has some divisions. According to the fi rst paper there is always a stable allocation of risk capital, which is not blocked by any coalition of the divisions, that is there is a core compatible allocation rule (we present some examples for risk allocation rules). The second paper considers two more natural requirements, Equal Treatment Property and Strong Monotonicity. Equal Treatment Property makes sure that similar divisions are treated symmetrically, that is if two divisions make the same marginal risk contribution to all the coalition of divisions not containing them, then the rule should allocate them the very same risk capital. Strong Monotonicity requires that if the risk environment changes in such a way that the marginal contribution of a division is not decreasing, then its allocated risk capital should not decrease either. However, if risk is evaluated by any coherent measure of risk, then there is no risk allocation rule satisfying Core Compatibility, Equal Treatment Property and Strong Monotonicity, we encounter an impossibility result.

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models.

Type space on a purely measurable parameter space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Opportunity Knocks: An Economic Analysis of Television Advertisements

Certain aspects of advertising–especially on television–are not easily explained with conventional economic models. In particular, much of the imagery and repetitive thematic content seen in advertisements suggests it is "psychological" in nature, as opposed to "informative". To understand the economic rationale for incorporating such material, we develop a theory of preferences in which information about threshold payoffs induces sudden shifts in demand. These threshold payoffs are best understood in the context of human evolutionary history. Furthermore, the presence of threshold payoffs in consumer preferences gives firms incentive for providing threshold-type information. To examine the use of threshold-related content in television advertisements, we look for this con- tent in a sample of 370 television advertisements. We find considerable evidence that advertisers make strategic use of threshold-type content in television advertisements. Specifically, threshold-related content occurred in 83% of food and beverage advertisements for children and in 71% of advertisements for general audiences. Furthermore, the threshold-related content in children’s food and beverage advertisements occurred with statistically greater frequency than factual content, which isn’t true for food and beverage advertisements for general audiences.

The political districting problem: A survey

Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which the connections and the differences between the two approaches are highlighted.

Does timing of decisions in a mixed duopoly matter?

We determine the endogenous order of moves in a mixed pricesetting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payo equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists.

On the completeness of the universal knowledge-belief space

Meier (2008) shows that the universal knowledge-belief space exists. However, besides the universality there is an other important property might be imposed on knowledge-belief spaces, inherited also from type spaces, the completeness. In this paper we introduce the notion of complete knowledge-belief space, and demonstrate that the universal knowledge-belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge-belief space are not knowledge-belief types.