Market Completion with Derivative Securities

Let $S^F$ be a $\mathbb{P}$-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on model coefficients which guarantee the completeness of the market in which in addition to the primitive asset one may also trade a derivative contract $S^B$. Both $S^F$ and $S^B$ are defined in terms of the solution $X$ to a $2$-dimensional stochastic differential equation: $S^F_t = f(X_t)$ and $S^B_t:=\mathbb{E}[g(X_1) | \mathcal{F}_t]$. From a purely mathematical point of view we prove that every local martingale under $\mathbb{P}$ can be represented as a stochastic integral with respect to the $\mathbb{P}$-martingale $S := (S^F\ S^B)$. Notably, in contrast to recent results on the endogenous completeness of equilibria markets, our conditions allow the Jacobian matrix of $(f,g)$ to be singular everywhere on $\mathbf{R}^2$. Hence they cover, as a special case, the prominent example of a stochastic volatility model being completed with a European call (or put) option

Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach

We present a novel approach to the pricing of financial instruments in emission markets, for example, the EU ETS. The proposed structural model is positioned between existing complex full equilibrium models and pure reduced form models. Using an exogenously specified demand for a polluting good it gives a causal explanation for the accumulation of CO2 emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO2. We derive a forward-backward stochastic differential equation for the price process of the allowance certificate and solve the associated semilinear partial differential equation numerically. We also show that derivatives written on the allowance certificate satisfy a linear partial differential equation. The model is extended to emission markets with multiple compliance periods and we analyse the impact different intertemporal connecting mechanisms, such as borrowing, banking and withdrawal, have on the allowance price.Comment: Section 5 in this version is new and contains an asymptotic analysis of the problem under consideratio

Neither Reasonable nor Necessary: “Amateurism” in Big-Time College Sports

The NCAA and its member schools are a joint venture that fixes the compensation of its most important workers, the athletes, at a level that is substantially below what would otherwise occur in a competitive market. Claims of amateurism and the need for competitive balance obscure the more than $3.5 billion dollars in revenue generated mostly on the backs of those athletes. From the point of view of rule of reason antitrust analysis, the NCAA’s justification for its concerted wage fixing has obvious weaknesses. Recent phenomenal growth in revenue has made the claims of the necessity and reasonableness of concerted action to restrain wages increasingly dubious.amateurism; monopoly; cartel; NCAA; college sports; competitive balance; collusion

Illustrations of Price Discrimination in Baseball

Price discrimination of this nature, focused on differing degrees of quality, bundled goods, volume discounts, and other forms of second-degree price discrimination, is commonplace in MLB. Indeed, it is safe to say that every single MLB ticket is sold under some form of price discrimination. As teams grow increasingly sophisticated in their pricing strategies, price discrimination is becoming more precise, more wide-spread, and more profitable, while at the same time providing for more opportunities for more fans to find tickets at a price they are willing to pay. Unlike a baseball game, where one team must lose and one must win, price discrimination allows for win-win economic outcomes for teams and fans alike.price discrimination; bundling; variable pricing; dynamic pricing; secondary ticketing; two-part tariff; loaded ticket

Experiment on the Demand for Encompassment

The idea of political community is appealing on a gut-level. Hayek suggested that certain genes and instincts still dispose us toward the ethos and mentality of the hunter-gatherer band, and that modern forms of political collectivism have, in part, been atavistic reassertions of such tendencies. Picking up on Hayek, Klein (2005) has suggested a combination of yearnings: 1) a yearning for coordinated sentiment (like Smithian sympathy); and 2) a yearning that the sentiment encompass the whole group. This paper reports on an experiment designed to explore the demand for encompassment by having subjects sing together. In each trial, one person in the room was designated not to sing unless every one of the others in the room had made a payment sufficient so as to have that person sing. Subjects chose to sacrifice money to achieve encompassment 47.4 percent of the time, with 59.6 percent of the subjects doing so in at least one trial. An exit questionnaire showed that subjects’ chief reason for making such a sacrifice was a belief that the singing would be more enjoyable if it encompassed the whole group, and reported enjoyment is significantly higher with encompassment. We discuss the experiment as a parable for a penchant toward political collectivism.Encompassment; political psychology; Hayek; the people’s romance