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

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

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

Financial distress and the cross section of equity returns,”

Abstract In this paper, we provide a new perspective for understanding cross-sectional properties of equity returns. We explicitly introduce financial leverage in a simple equity valuation model and consider the likelihood of a firm defaulting on its debt obligations as well as potential deviations from the absolute priority rule (APR) upon the resolution of financial distress. We show that financial leverage amplifies the magnitude of the book-to-market effect and hence provide an explanation for the empirical evidence that value premia are larger among firms with a higher likelihood of financial distress. By further allowing for APR violations, our model generates two novel predictions about the cross section of equity returns: (i) the value premium (computed as the difference between expected returns on mature and growth firms), is humpshaped with respect to default probability, and (ii) firms with a higher likelihood of deviation from the APR upon financial distress generate stronger momentum profits. Both predictions are confirmed in our empirical tests. These results emphasize the unique role of financial distressand the nonlinear relationship between equity risk and firm characteristics-in understanding cross-sectional properties of equity returns. JEL Classification Codes: G12, G14, G3

Approximation of invariant surfaces by periodic orbits in high-dimensional maps. Some rigorous results.

The existence of an invariant surface in high-dimensional systems greatly influences the behavior in a neighborhood of the invariant surface. We prove theorems that explain the behavior of periodic orbits in the vicinity of an invariant surface for symplectic maps and quasi-periodic perturbations of symplectic maps. Our results allow for efficient numerical algorithms that can serve as an indication for the breakdown of invariant surfaces

Numerical Study of Invariant Sets of a Quasiperiodic Perturbation of a Symplectic Map

this paper we investigate numerically the domains of existence of two-dimensional tori in a particular two-parameter family of volume-preserving c fl A K Peters, Ltd. 1058-6458/96 $0.50 per page 212 Experimental Mathematics, Vol. 5 (1996), No. 3 maps, and the behavior that occurs at breakdown. The maps we study are quasiperiodic perturbations of a family of symplectic maps. Our numerical algorithms are based on analytical results described in [Falcolini and Llave 1992a] and [Tompaidis 1996] (the preceding article in this issue). The main idea is to use another landmark of longterm behavior, periodic orbits, to determine the existence and breakdown of tori. For symplectic maps in two dimensions, it was originally observed in [Greene 1979] that existence of invariant circles has a strong influence on periodic orbits close to the circle. In [Tompaidis 1996] we prove that in symplectic maps of any dimension, as well as in quasiperiodic perturbations of them, existence of an invariant torus implies that the behavior of the map in a neighborhood of the torus is close to that of an integrable map. We will make use of this result as an indication of breakdown. The system we will study is a three-dimensional model of a family of volume-preserving maps. Motion in one of the coordinates is rigid rotation with rotation number given by an appropriate diophantine number. The other two coordinates of the map are described by a perturbation of the standard map. Properties of the map and existence of tori have also been investigated in [Artuso et al. 1991]. Our rationale for studying this map (henceforth called the rotating standard map) is similar to that used in experimental physics, where one carefully prepares a sample in order to observe certain phenomena. In our case, the rotati..