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

Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, reversible, volume-preserving analogue of Chirikov's standard map with one action and two angles. We investigate the preservation and destruction of tori under perturbation by computing the "residue" of nearby periodic orbits. We find tori with Diophantine rotation vectors in the "spiral mean" cubic algebraic field. The residue is used to generate the critical function of the map and find a candidate for the most robust torus.Comment: laTeX, 40 pages, 26 figure

The Destruction of Tori in Volume-Preserving Maps

Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional volume-preserving map, such tori are prevalent when the map is nearly "integrable," in the sense of having one action and $n-1$ angle variables. As the map is perturbed, numerical studies show that the originally connected image of the frequency map acquires gaps due to resonances and domains of nonconvergence due to chaos. We present examples of a three-dimensional, generalized standard map for which there is a critical perturbation size, $\epsilon_c$, above which there are no tori. Numerical investigations to find the "last invariant torus" reveal some similarities to the behavior found by Greene near a critical invariant circle for area preserving maps: the crossing time through the newly destroyed torus appears to have a power law singularity at $\epsilon_c$, and the local phase space near the critical torus contains many high-order resonances.Comment: laTeX, 16 figure

An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling properties. We numerically investigate the structure of the attracting set on the critical surface and find that it is a strange nonchaotic attractor. We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure

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