The valuation of clean spread options: linking electricity, emissions and fuels

The purpose of the paper is to present a new pricing method for clean spread options, and to illustrate its main features on a set of numerical examples produced by a dedicated computer code. The novelty of the approach is embedded in the use of a structural model as opposed to reduced-form models which fail to capture properly the fundamental dependencies between the economic factors entering the production process

Land markets and agrarian backwardness (Spain, 1900-1936)

To what extent were land markets the cause of Spanish agrarian backwardness? This paper uses new provincial data on average real land prices, together with provincial level variation in land productivity, to analyse land markets efficiency. To address this unresolved issue, we test whether land markets were spatially integrated and whether their prices can be explained with the present value model. Our results suggest that land prices converged across provinces and that variations were driven by fundamentals. In consequence, we conclude that institutional failure in land markets was not the cause of the relatively poor productivity performance of Spanish agricultur

Was land reform necessary? : access to land in Spain, 1860 to 1931.

In Spain, land reform involving the break-up of large southern estates was a central issue during the first decades of the twentieth century. It was justified on the grounds of economic efficiency, social equity and the distribution of political power. This paper uses new provincial data on landless workers, land prices and agrarian wages to consider if government intervention was desirable because land redistribution did not take place. Our evidence shows that the relative amount of landless workers decreased largely from 1890 to 1930. This was due to two interrelated market forces: structural change that drained rural population and a decrease in the ratio between land prices and rural wages, which made land cheaper for landless workers. So, given that rural markets did not restrict access to land, the government-initiated land redistribution had no clear-cut justification.Land markets; Structural change; Land prices; Landless peasants;

Land markets and agrarian backwardness (Spain, 1900-1936)

To what extent were land markets the cause of Spanish agrarian backwardness? This paper uses new provincial data on average real land prices, together with provincial level variation in land productivity, to analyse land markets efficiency. To address this unresolved issue, we test whether land markets were spatially integrated and whether their prices can be explained with the present value model. Our results suggest that land prices converged across provinces and that variations were driven by fundamentals. In consequence, we conclude that institutional failure in land markets was not the cause of the relatively poor productivity performance of Spanish agricultureLand prices determinants, Price convergence, Panel unit-roots, Present value model

The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Spanish housing markets during the first phase of the rural-urban transition process

This paper discusses how Spain’s housing markets reacted to the far-reaching changes that affected the demand for dwellings during the first phase of the rural-urban transition process. To this end, we construct a new hedonic index of real housing prices and assemble a cross-regional panel dataset of price fundamentals. The results of our econometric analysis suggest that housing markets did not face supply constraints, responded swiftly to the growing demand for accommodation and were efficient. In light of this new evidence, we conclude that housing markets were not a burden for Spanish economic development and that Spain’s institutional and regulatory frameworks were suitable for the housing needs at the time.Hedonic prices, Demand and supply of housing, Regulation in housing markets