Mastering Python for Finance - Second Edition

A class for pricing European options using the Crank-Nicolson method of finite differences

The Python implementation of the Crank-Nicolson method is given in the following FDCnEu class, which inherits from the FDExplicitEu class and overrides only the setup_coefficients and traverse_grid methods:

In [ ]:    import numpy as np    import scipy.linalg as linalg    """     Crank-Nicolson method of Finite Differences     """    class FDCnEu(FDExplicitEu):        def setup_coefficients(self):            self.alpha = 0.25*self.dt*(                (self.sigma**2)*(self.i_values**2) - \                self.r*self.i_values)            self.beta = -self.dt*0.5*(                (self.sigma**2)*(self.i_values**2) + self.r)            self.gamma = 0.25*self.dt*(                (self.sigma**2)*(self.i_values**2) +                self.r*self.i_values) self.M1 = -np.diag(self.alpha[2:self.M], ...