from analytics.index_data import index_returns
from statsmodels.distributions.empirical_distribution import ECDF
from scipy.stats import norm
from scipy.optimize import brentq

df = index_returns(index="IG", tenor=["5yr"])
df = df.reset_index(['index', 'tenor'], drop=True)
spreads = df.dropna().groupby(['date']).nth(-1)['spread_return']
monthly_returns = spreads.rolling('30D').apply(lambda s: (1 + s).prod() - 1)
mu = monthly_returns.median()
ecdf = ECDF(monthly_returns)

def implied_vol(q):
    """ computes the equivalent vol such that P(r \leq \mu + \sigma x) = \Phi(x)"""
    x0, r = brentq(lambda sigma: ecdf(mu + sigma * q) - norm.cdf(q), 0, 2, full_output=True)
    return x0