Information Flow, Social Interactions and the Fluctuations of Prices in Financial Markets

We model how excess demand or excess supply can be generated in the presence of a social network of interactions, where agents are subject to external information and individual incentives. In this context we study price fluctuations in financial markets under equilibrium. In particular, we isolate the role of these different factors in the determination of price fluctuations and describe non trivial sensitivities to changes in equilibrium due to the existence of social interactions. We characterize equilibrium and distinguish between stable and unstable equilibrium. Crashes or bubbles are seen as out-of-equilibrium situations, preceeded by unstable equilibrium. Fluctuations under unstable equilibrium are shown to be abnormal and particulary large. Also, we show how fluctuations of the external information flows affect the fluctuations of the return process. In all cases we explain the well-known phenomena that prices do not fluctuate upwards in the same way as they fluctuate downwards. This asymmetry of price fluctuations is due to asymmetries in the price elasticity of demand and supply curves at the level defining equilibriumsocial network, excess demand, excess supply, price fluctuations

Super-replicating Bounds on European Option Prices when the Underlying Asset is Illiquid

We derive super-replicating bounds on European option prices when the underlying asset is illiquid. Illiquidity is taken as the impossibility of transacting the underlying asset at some points in time, generating market incompleteness. We conclude that option price bounds follow a Black-Scholes partial differential equation where the volatility term is adjusted to reflect different levels of illiquidity.

Equilibrium Bid-Ask Spread of European Derivatives in Dry Markets

In the framework of incomplete markets, due to the non-existence of trade at some points in time, and using a partial equilibrium analysis, we show how the bid-ask spread of an European derivative is generated. We also ¯nd conditons for the existence of the spread. These conditions concern the market structure of the maret-makers, which can be a oligolopoly with price competition or a monopoly, as well as the riskaversion of the demand and supply of the market.

Dry Markets and Statistical Arbitrage Bounds for European Derivatives

We derive statistical arbitrage bounds for the buying and selling price of European derivatives under incomplete markets. In this paper, incompleteness is generated due to the fact that the market is dry, i.e., the underlying asset cannot be transacted at certain points in time. In particular, we re¯ne the notion of statistical arbitrage in order to extend the procedure for the case where dryness is random, i.e., at each point in time the asset can be transacted with a given probability. We analytically characterize several properties of the statistical arbitragefree interval, show that it is narrower than the super-replication interval and dominates somehow alternative intervals provided in the literature. Moreover, we show that, for su±ciently incomplete markets, the statistical arbitrage interval contains the reservation price of the derivative.

Market Illiquidity and the Bid-Ask Spread of Derivatives

This paper analyzes the impact of illiquidity of a stock on the pricing of derivatives. In particular, it is shown how illiquidity generates a bid-ask spread in an option on this stock, even in the absence of other imperfections, such as transaction costs and asymmetry of information. Moreover, the spread is shown to be asymmetric with respect to the option price under perfect liquidity. This fact explains the appearance of a smile e$ect when the implied volatility is estimated from the mid-quote.

Dry Markets and Superreplication Bounds of American Derivatives

This paper studies the impact of dry markets for underlying assets on the pricing of American derivatives, using a disrete time framework. Dry markets are characterized by the possibility of non-existence of trading at certain dates. Such non-existence may be deterministic or probabilistic. Using superreplicating strategies, we derive expectation representations for the range of arbitrage-free values of the dervatives. In the probabilistic case, if we consider an enlarged filtration induced by the price process and the market existence process, ordinary stopping times are required. If not, randomized stopping times are required. Several comparisons of the ranges obtained with the two market restrictions are performed. Finally, we conclude that arbitrage arguments are not enough to define the optimal exercise policy.American derivatives, pricing, incomplete markets, dry markets, superreplication, randomized stopping times, strong duality

Testing the Markov property with ultra-high frequency financial data

This paper develops a framework to nonparametrically test whether discretevalued irregularly-spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.Bid-ask spread, nonparametric testing, price durations, Markov property, ultra-high frequency data

Consuming durable goods when stock markets jump: a strategic asset allocation approach

Agents derive their utilities from consumption over time. In this paper we consider an agent that invests in thefinancial market and in consumption goods. The agent has an infinite time horizon and a utility that depends on consumption at each point in time, consuming both a durable good and a perishable good. There are costs for transacting the durable good. We show that an agent who does not consider the impact of jumps in the return process of risky assets will make suboptimal decisions, not only regarding the fraction of wealth invested in the stock market, but also with respect to the timing for trading on the durable good.Optimal asset allocation, durable consumption good, transaction costs.

The Exact Value for European Options on a Stock Paying a Discrete Dividend

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.Comment: 14 pages,3 figure

Afinity, Animosity and Organizational Design

The behavior of the members of an organization is determined, not only by the objective situation facing them, but also by their attitudes. Thus, the objective of aligning collective goals and individual behavior translates into a problem of alignment of attitudes. An important dimension of the problem of organizational design is, therefore, to choose the organization that best contributes to the alignment of attitudes. This paper shows that the existence of animosity, as opposed to afinity, affects the optimal organizational design.