Asian options with jumps: A closed form formula

In this article Marena, Roncoroni, and Fusai derive a closed-form formula for the fair value of call and put options written on the arithmetic average of security prices driven by jump diffusion processes displaying (possibly periodical) trend, time varying volatility, and mean reversion. The model allows one for jointly fitting quoted futures curve and the time structure of spot price volatility. These result extends the no-jump case put forward in [Fusai, G., Marena, M., Roncoroni, A. 2008. Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets. Journal of Banking and Finance 32 (10), 2033-2045]. A few tests based on commodity price data assess the importance of introducing a jump component on the resulting option prices

A Serrin-type symmetry result on model manifolds: an extension of the Weinberger argument

We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $\Delta u=-1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable "compatibility" assumption between the solution and the geometry of the model.Comment: 9 page

A Numerical Method for Pricing Electricity Derivatives for Jump-Diffusion Processes Based on Continuous Time Lattices

We present a numerical method for pricing derivatives on electricity prices. The method is based on approximating the generator of the underlying process and can be applied for stochastic processes that are combinations of diusions and jump processes. The method is accurate even in the case of processes with fast mean-reversion and jumps of large magnitude. We illustrate the speed and accuracy of the method by pricing European and Bermudan options and calculating the hedge ratios of European options for the Geman-Roncoroni model for electricity prices.Electricity derivatives; operator methods

On the umbilic set of immersed surfaces in three-dimensional space forms

We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated Hopf theorem

Spatial firm competition in two dimensions with linear transportation costs: simulations and analytical results

Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the most straightforward linear transportation costs are assumed. We show by simulations and also analytically that if periodic boundary conditions in two dimensions are assumed, the equilibrium exists for a pair of firms at any distance. When a larger number of firms is considered, we find that their total equilibrium profit is inversely proportional to the square root of the number of firms. We end with a numerical investigation of the system's behavior for a general transportation cost exponent.Comment: 7 pages, 4 figure

Understanding the fine structure of electricity prices

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a "jump-reversion" component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets

Modelling electricity prices with forward looking capacity constraints.

We present a spot price model for wholesale electricity prices which incorporates forward looking information that is available to all market players. We focus on information that measures the extent to which the capacity of the England and Wales generation park will be constrained over the next 52 weeks. We propose a measure of ‘tight market conditions’, based on capacity constraints, which identifies the weeks of the year when price spikes are more likely to occur. We show that the incorporation of this type of forward looking information, not uncommon in the electricity markets, improves the modeling of spikes (timing and magnitude) and the different speeds of mean reversionCapacity constraints; Mean reversion; Electricity indicated demand; Electricity indicated generation; Regime switching model;

Outlier Treatment and Robust Approaches for Modeling Electricity Spot Prices

We investigate the effects of outlier treatment on the estimation of the seasonal component and stochastic models in electricity markets. Typically, electricity spot prices exhibit features like seasonality, mean-reverting behavior, extreme volatility and the occurrence of jumps and spikes. Hence, an important issue in the estimation of stochastic models for electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, in regression analysis, classical estimation routines like OLS are very sensitive to extreme observations and outliers. Improved robustness of the model can be achieved by (a) cleaning the data with some reasonable procedure for outlier rejection, and then (b) using classical estimation and testing procedures on the remainder of the data. We examine the effects on model estimation for different treatment of extreme observations in particular on determining the number of outliers and descriptive statistics of the remaining series after replacement of the outliers. Our findings point out the substantial impact the treatment of extreme observations may have on these issues.Electricity; price modeling; seasonal decomposition; price spike