Mastering Python for Finance by Unknown

Author:Unknown
Language: eng
Format: mobi, epub, pdf
Publisher: Packt Publishing

With these methods defined, we can now run our code and price a callable zero-coupon bond by the Vasicek model.

The implementation of the VasicekCZCB class in Python is given as follows:

""" Price a callable zero coupon bond by the Vasicek model """ import math import numpy as np import scipy.stats as st class VasicekCZCB: def __init__(self): self.norminv = st.distributions.norm.ppf self.norm = st.distributions.norm.cdf def vasicek_czcb_values(self, r0, R, ratio, T, sigma, kappa, theta, M, prob=1e-6, max_policy_iter=10, grid_struct_const=0.25, rs=None): r_min, dr, N, dtau = \ self.vasicek_params(r0, M, sigma, kappa, theta, T, prob, grid_struct_const, rs) r = np.r_[0:N]*dr + r_min v_mplus1 = np.ones(N) for i in range(1, M+1): K = self.exercise_call_price(R, ratio, i*dtau) eex = np.ones(N)*K subdiagonal, diagonal, superdiagonal = \ self.vasicek_diagonals(sigma, kappa, theta, r_min, dr, N, dtau) v_mplus1, iterations = \ self.iterate(subdiagonal, diagonal, superdiagonal, v_mplus1, eex, max_policy_iter) return r, v_mplus1 def vasicek_params(self, r0, M, sigma, kappa, theta, T, prob, grid_struct_const=0.25, rs=None): (r_min, r_max) = (rs[0], rs[-1]) if not rs is None \ else self.vasicek_limits(r0, sigma, kappa, theta, T, prob) dt = T/float(M) N = self.calculate_N(grid_struct_const, dt, sigma, r_max, r_min) dr = (r_max-r_min)/(N-1) return r_min, dr, N, dt def calculate_N(self, max_structure_const, dt, sigma, r_max, r_min): N = 0 while True: N += 1 grid_structure_interval = dt*(sigma**2)/( ((r_max-r_min)/float(N))**2) if grid_structure_interval > max_structure_const: break return N def vasicek_limits(self, r0, sigma, kappa, theta, T, prob=1e-6): er = theta+(r0-theta)*math.exp(-kappa*T) variance = (sigma**2)*T if kappa==0 else \ (sigma**2)/(2*kappa)*(1-math.exp(-2*kappa*T)) stdev = math.sqrt(variance) r_min = self.norminv(prob, er, stdev) r_max = self.norminv(1-prob, er, stdev) return r_min, r_max def vasicek_diagonals(self, sigma, kappa, theta, r_min, dr, N, dtau): rn = np.r_[0:N]*dr + r_min subdiagonals = kappa*(theta-rn)*dtau/(2*dr) - \ 0.5*(sigma**2)*dtau/(dr**2) diagonals = 1 + rn*dtau + sigma**2*dtau/(dr**2) superdiagonals = -kappa*(theta-rn)*dtau/(2*dr) - \ 0.5*(sigma**2)*dtau/(dr**2) # Implement boundary conditions. if N > 0: v_subd0 = subdiagonals[0] superdiagonals[0] = superdiagonals[0] - \ subdiagonals[0] diagonals[0] += 2*v_subd0 subdiagonals[0] = 0 if N > 1: v_superd_last = superdiagonals[-1] superdiagonals[-1] = superdiagonals[-1] - \ subdiagonals[-1] diagonals[-1] += 2*v_superd_last superdiagonals[-1] = 0 return subdiagonals, diagonals, superdiagonals def check_exercise(self, V, eex): return V > eex def exercise_call_price(self, R, ratio, tau): K = ratio*np.exp(-R*tau) return K def vasicek_policy_diagonals(self, subdiagonal, diagonal, superdiagonal, v_old, v_new, eex): has_early_exercise = self.check_exercise(v_new, eex) subdiagonal[has_early_exercise] = 0 superdiagonal[has_early_exercise] = 0 policy = v_old/eex policy_values = policy[has_early_exercise] diagonal[has_early_exercise] = policy_values return subdiagonal, diagonal, superdiagonal def iterate(self, subdiagonal, diagonal, superdiagonal, v_old, eex, max_policy_iter=10): v_mplus1 = v_old v_m = v_old change = np.zeros(len(v_old)) prev_changes = np.zeros(len(v_old)) iterations = 0 while iterations <= max_policy_iter: iterations += 1 v_mplus1 = self.tridiagonal_solve(subdiagonal, diagonal, superdiagonal, v_old) subdiagonal, diagonal, superdiagonal = \ self.vasicek_policy_diagonals(subdiagonal, diagonal, superdiagonal, v_old, v_mplus1, eex) is_eex = self.check_exercise(v_mplus1, eex) change[is_eex] = 1 if iterations > 1: change[v_mplus1 != v_m] = 1 is_no_more_eex = False if True in is_eex else True if is_no_more_eex: break v_mplus1[is_eex] = eex[is_eex] changes = (change == prev_changes) is_no_further_changes = all((x == 1) for x in changes) if is_no_further_changes: break prev_changes = change v_m = v_mplus1 return v_mplus1, (iterations-1) def tridiagonal_solve(self, a, b, c, d): nf = len(a) # Number of equations ac, bc, cc, dc = map(np.array, (a, b, c, d))

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.