dates = np.array(db_invariants_series.index)
db_invariants_nextstep = pd.read_csv(path + 'db_invariants_nextstep.csv')
# -
# ## [Step 1](https://www.arpm.co/lab/redirect.php?permalink=s_checklist_scenariobased_step03-implementation-step01): Set the flexible probabilities
# +
# time and state conditioning on smoothed and scored VIX returns
# state indicator: VIX compounded return realizations
db_vix['c_vix'] = np.log(db_vix).diff()
# extract data for analysis dates
c_vix = db_vix.c_vix[dates].values
# smoothing
z_smooth = smoothing(c_vix, tau_hl_smooth)
# scoring
z = scoring(z_smooth, tau_hl_score)
# target value
z_star = z[-1]
# prior probabilities
p_prior = exp_decay_fp(t_, tau_hl_prior)
# posterior probabilities
p = conditional_fp(z, z_star, alpha, p_prior)
# effective number of scenarios
ens = effective_num_scenarios(p)
print('Effective number of scenarios is', int(round(ens)))
# -
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_checklist_scenariobased_step03-implementation-step02): Estimate the marginal distributions for stocks, S&P 500 and implied volatility
# merging datasets spx_vix = pd.merge(spx, vix, how='inner', on=['date']) date = spx_vix.date # ## [Step 1](https://www.arpm.co/lab/redirect.php?permalink=s_smooth_kernel_fp-implementation-step01): Compute the S&P 500 compounded return and the VIX compounded return epsi = np.diff(np.log(spx_vix.SPX_close)) # S&P 500 index compounded return v_vix = np.array(spx_vix.VIX_close) # VIX index value c = np.diff(np.log(v_vix)) # VIX index compounded return t_ = len(epsi) # ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_smooth_kernel_fp-implementation-step02): Compute the risk factor by smoothing and scoring VIX compounded return tau_hl_smoo = 15 tau_hl_scor = 100 z_smooth = smoothing(c, tau_hl_smoo) # smoothing z = scoring(z_smooth, tau_hl_scor) # scoring # ## [Step 3](https://www.arpm.co/lab/redirect.php?permalink=s_smooth_kernel_fp-implementation-step03): Compute the smooth kernel probabilities p_smooth = smooth_kernel_fp(z, z_star, h, gamma=gamma) # ## [Step 4](https://www.arpm.co/lab/redirect.php?permalink=s_smooth_kernel_fp-implementation-step04): Compute the effective number of scenarios ens = effective_num_scenarios(p_smooth) # ## [Step 5](https://www.arpm.co/lab/redirect.php?permalink=s_smooth_kernel_fp-implementation-step05): Compute flexible probabilities histogram f_eps, x_eps = histogram_sp(epsi, p=p_smooth, k_=10*np.log(t_)) # ## Plots