1 files changed, 16 insertions, 0 deletions
diff --git a/python/exploration/realized_vol_quantiles.py b/python/exploration/realized_vol_quantiles.py
new file mode 100644
index 00000000..18298abf
--- /dev/null
+++ b/python/exploration/realized_vol_quantiles.py
@@ -0,0 +1,16 @@
+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