Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

Authoritarian Responses to Foreign Pressure: Spending, Repression, and Sanctions

This paper explores how international sanctions affect authoritarian rulers’ decisions concerning repression and public spending composition, and how different authoritarian rulers respond to foreign pressure. If sanctions are assumed to increase the price of loyalty to the regime, then rulers whose budgets are not severely constrained by sanctions will tend to increase spending in those categories that most benefit their core support groups. In contrast, when constraints are severe due to reduced aid and trade, dictators are expected to greatly increase their levels of repression. Using data on regime types, public expenditures and spending composition (1970–2000) as well as on repression levels (1976–2001), we show that the empirical patterns conform well to our theoretical expectations. Single-party regimes, when targeted by sanctions, increase spending on subsidies and transfers which largely benefit more substantial sectors of the population and especially the urban classes. Likewise, military regimes increase their expenditures on goods and services, which include military equipment and soldiers’ and officers’ wages. Conversely, personalist regimes reduce spending in all categories, especially capital expenditures, while increasing repression much more than other regime types when targeted by sanctions.

Trade disclosure and price dispersion

This paper determines the effects of post-trade opaqueness on market performance. We find that the degree of market transparency has important effects on market equilibria. In particular, we show that dealers operating in a transparent structure set regret-free prices at each period making zero expected profits in each of the two trading rounds, whereas in the opaque market dealers invest in acquiring information at the beginning of the trading day. Moreover, we obtain that if there is no trading activity in the first period, then market makers only change their quotes in the opaque market. Additionally, we show that trade disclosure increases the informational efficiency of transaction prices and reduces volatility. Finally, concerning welfare of market participants, we obtain ambiguous results. Keywords: Market microstructure, Post-trade transparency, Price experimentation, Price dispersion.

Tacit collusion and capacity withholding in repeated uniform price auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor

Double implementation in a market for indivisible goods with a price constraint

I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envy-free with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.

Collusion and fights in an experiment with price-setting firms and production in advance

We present results from 50-round market experiments in which firms decide repeatedly both on price and quantity of a completely perishable good. Each firm has capacity to serve the whole market. The stage game does not have an equilibrium in pure strategies. We run experiments for markets with two and three identical firms. Firms tend to cooperate to avoid fights, but when they fight bankruptcies are rather frequent. On average, pricing behavior is closer to that for pure quantity than for pure price competition and price and efficiency levels are higher for two than for three firms. Consumer surplus increases with the number of firms, but unsold production leads to higher efficiency losses with more firms. Over time prices tend to the highest possible one for markets both with two and three firms.

Elicited bid functions in (a)symmetric first-price auctions

We report on a series of experiments that examine bidding behavior in first-price sealed bid auctions with symmetric and asymmetric bidders. To study the extent of strategic behavior, we use an experimental design that elicits bidders' complete bid functions in each round (auction) of the experiment. In the aggregate, behavior is consistent with the basic equilibrium predictions for risk neutral or homogenous risk averse bidders (extent of bid shading, average seller's revenues and deviations from equilibrium). However, when we look at the extent of best reply behavior and the shape of bid functions, we find that individual behavior is not in line with the received equilibrium models, although it exhibits strategic sophistication.

Bidding at sequential first-price auctions with(out) supply uncertainty: a laboratory analysis

We report on a series of experiments that test the effects of an uncertain supply on the formation of bids and prices in sequential first-price auctions with private-independent values and unit-demands. Supply is assumed uncertain when buyers do not know the exact number of units to be sold (i.e., the length of the sequence). Although we observe a non-monotone behavior when supply is certain and an important overbidding, the data qualitatively support our price trend predictions and the risk neutral Nash equilibrium model of bidding for the last stage of a sequence, whether supply is certain or not. Our study shows that behavior in these markets changes significantly with the presence of an uncertain supply, and that it can be explained by assuming that bidders formulate pessimistic beliefs about the occurrence of another stage.

Price competition under cost uncertainty: A laboratory analysis

We study the relation between the number of firms and price-cost margins under price competition with uncertainty about competitors' costs. We present results of an experiment in which two, three and four identical firms repeatedly interact in this environment. In line with the theoretical prediction, market prices decrease with the number of firms, but on average stay above marginal costs. Pricing is less aggressive in duopolies than in triopolies and tetrapolies. However, independently from the number of firms, pricing is more aggressive than in the theoretical equilibrium. Both the absolute and the relative surpluses increase with the number of firms. Total surplus is close to the equilibrium level, since enhanced consumer surplus through lower prices is counteracted by occasional displacements of the most efficient firm in production.

Structural inferences from first-price auction experiments

We use structural methods to assess equilibrium models of bidding with data from first-price auction experiments. We identify conditions to test the Nash equilibrium models for homogenous and for heterogeneous constant relative risk aversion when bidders private valuations are independent and uniformly drawn. The outcomes of our study indicate that behavior may have been affected by the procedure used to conduct the experiments and that the usual Nash equilibrium model for heterogeneous constant relative risk averse bidders does not consistently explain the observed overbidding. From an empirical standpoint, our analysis shows the possible drawbacks of overlooking the homogeneity hypothesis when testing symmetric equilibrium models of bidding and it puts in perspective the sensitivity of structural inferences to the available information.

Pressure groups and experts in environmental regulation

We study a problem of adverse selection in the context of environmental regulation, where the firm may suffer from a certain degree of ignorance about its own type. In a framework like the construction of a certain infrastructure project, the presence of ignorance about its impact on the environment, can play an important role in the determination of the regulatory policy. First, an optimal contract is constructed for any exogenous level of ignorance. Second, the presence of potentially informed third-parties is studied from the perspective of the regulator, which allows us to analyze the impact on the efficiency of the contract, of the presence of environmentalists and of experts. Then, we obtain some insights on how the problem differs when the degree of ignorance is a choice variable for the firm. We finally use our results to derive policy implications concerning the existing envoronmental regulation, and the potential role of interested parties as information providers.

Economic impacts of alternative water policy scenarios in the Spanish production system: an input-output analysis

The objective of this paper is to analyse the economic impacts of alternative water policies implemented in the Spanish production system. The methodology uses two versions of the input-output price model: a competitive formulation and a mark-up formulation. The input-output framework evaluates the impact of water policy measures on production prices, consumption prices, intermediate water demand and private welfare. Our results show that a tax on the water used by sectors considerably reduces the intermediate water demand, and increases the production and consumption prices. On the other hand, according to Jevons' paradox, an improvement in technical efficiency, which leads to a reduction in the water requirements of all sectors and an increase in water production, increases the amount of water consumed. The combination of a tax on water and improved technical efficiency takes the pressure off prices and significantly reduces intermediate water demand. JEL Classification: C67 ; D57 ; Q25. Keywords: Production prices; Consumption prices; Water uses; Water policy; Water taxation.

Effect of high pressure processing on the microbiology of skin-vacuum packaged sliced meat products: cooked pork ham, dry cured pork ham and marinated beef loin

High hydrostatic pressure is being increasingly investigated in food processing. It causes microbial inactivation and therefore extends the shelf life and enhances the safety of food products. Yeasts, molds, and vegetative cells of bacteria can be inactivated by pressures in the range of 200 to 700 MPa. Microorganisms are more or less sensitive to pressure depending on several factors such as type, strain and the phase or state of the cells. In general, Gram-positive organisms are usually more resistant than Gram-negative. High pressure processing modifies the permeability of the cell membrane, the ion exchange and causes changes in morphology and biochemical reactions, protein denaturations and inhibition of genetic mechanisms. High pressure has been used successfully to extend the shelf life of high-acid foods such as refrigerated fruit juices, jellies and jams. There is now an increasing interest in the use of this technology to extend the shelf life of low-acid foods such as different types of meat products.

Bioequivalence of meat products treated with high pressure processing

The effects of high pressure on the composition of food products have not been evaluated extensively. Since, it is necessary to take in consideration the possible effects in basis to the changes induced in the bio molecules by the application of high pressures. The main effect on protein is the denaturation, because the covalent bonds are not affected; however hydrogen bonding, hydrophobic and intermolecular interactions are modified or destroyed. 1 High pressure can modify the activity of some enzymes. If this is done the proteolysis and lipolysis could be more or less intense and the content of free amino acids and fatty acids will be different. This could be related to the bioavailability of these compounds. Low pressures (100 MPa) have been shown to activate some enzymes (monomeric enzymes). Higher pressures induce loss of the enzyme activity. However some enzymes are very stable (ex. Lipase ~ 600 - 1000 MPa). Lipoxygenase is less stable, and there is little information about the effects on antioxidant enzymes. Other important issue is the influence of high pressure on oxidation susceptibility. This could modify the composition of lipids if the degree of the oxidation would have been higher or lower than in the traditional product. Pressure produces the damage of cell membranes favouring the contact between substrates and enzymes, exposure to oxidation of membrane fatty acids and loos of the efficiency of vitamin E. These effects can also affect to protein oxidation. In this study different compounds were analysed to establish the differences between non-treated and high-pressure treated products.