def test_SA():
m = Markovian(f, n_Markov_states, 5)
n = Markovian(g, n_Markov_states, 5)
m.SA()
n.SA()
def generator_augmented(random_state, size):
# (r_it, r_Mt, epsilon_Mt, sigma^2_Mt)
process = generator(random_state, size)
market_return = process[:,:,0]
process_aug = numpy.concatenate(
(beta*(market_return[:,:,numpy.newaxis]-rf) + rf,process),
axis=-1,
)
return process_aug
# Markov chain discretization
sample_paths = generator(numpy.random.RandomState(0),size=1000)
return_sample_paths = sample_paths[:,:,0]
var_sample_paths = sample_paths[:,:,2]
price_sample_paths = numpy.cumprod(numpy.exp(return_sample_paths),axis=1)
markovian = Markovian(generator,n_Markov_states=[1]+[100]*(T-1),n_sample_paths=1000000)
markovian.SA()
# augment to 103 dimension
Markov_states = [None for _ in range(T)]
transition_matrix = markovian.transition_matrix
for t in range(T):
market_return = markovian.Markov_states[t][:,0].reshape(-1,1)
asset_return_market_exposure = beta*(market_return-rf) + rf
Markov_states[t] = numpy.concatenate(
(asset_return_market_exposure,markovian.Markov_states[t]), axis=1)
# comparison of the true process vs the Markov chain approximation
fig, ax = plt.subplots(1,2,figsize=(10,5),sharey=True)
fig = fan_plot(return_sample_paths, ax=ax[0])
s = markovian.simulate(1000)
fig = fan_plot(s[:,:,-3], ax=ax[1])
ax[0].set_xlabel("stages")
ax[0].set_ylabel("returns")