We present a computational method for measuring financial risk by estimating
the Value at Risk and Expected Shortfall from financial series. We have made
two assumptions: First, that the predictive distributions of the values of an
asset are conditioned by information on the way in which the variable evolves
from similar conditions, and secondly, that the underlying random processes can
be described using piecewise Gaussian processes.
According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian
variety then its L-function must capture substantial part of the arithmetic
properties of A. The smallest number field L where A has all its endomorphisms
defined must also have a role. This article deals with the relationship between
these two objects in the specific case of modular abelian varieties A_f/Q
associated to weight 2 newforms for the modular group Gamma_1(N).