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import cvxpy
import datetime
import math
import numpy as np
import pandas as pd
from pandas.tseries.offsets import BDay
from arch import arch_model
from db import dbengine, dbconn
from scipy.interpolate import interp1d
from analytics import Index, ForwardIndex
from index_data import index_returns
serenitasdb = dbengine('serenitasdb')
def realized_vol(index, series, tenor='5yr', date=None, years=None, return_type='spread'):
"""computes the realized spread volatility"""
if date is None:
if years is None:
raise ValueError("need to provide at least one of date or years")
date = (pd.Timestamp.now() - pd.DateOffset(years=years)).date()
returns = index_returns(index=index, series=series, tenor=tenor, years=None)
# GARCH(1,1) volatility process with constant mean
am = arch_model(returns[return_type+'_return'])
res = am.fit(update_freq=0, disp='off')
return (res.conditional_volatility * math.sqrt(252), res)
def lr_var(res):
""" computes long run variance of the garch process
.. math::
\sigma^2=\frac{\omega}{1-\sum_{i=1}^p \alpha_i + \sum_{i=1}^q \beta_i}
"""
names = res.model.volatility.parameter_names()
## names[0] is omega, rest is alpha[1],..., alpha[p], beta[1],...,beta[q]
var = res.params[names[0]]/(1 - res.params[names[1:]])
return math.sqrt(var * 252)
def atm_vol_fun(v, moneyness=0.2, index=None):
f = interp1d(v.strike.values, v.vol.values, fill_value='extrapolate')
if index is None:
atm_val = v['fwdspread'].iat[0]
otm_val = atm_val * (1 + moneyness)
else:
index.ref = v['ref'].iat[0]
atm_val = ForwardIndex(index, v.index.get_level_values('expiry')[0]).forward_spread
otm_val = atm_val * (1 + moneyness)
if index._quote_is_price:
index.spread = atm_val
atm_val = index.price
index.spread = otm_val
otm_val = index.price
return pd.Series(f(np.array([atm_val, otm_val])), index = ['atm_vol', 'otm_vol'])
def atm_vol(index, date, series=None, moneyness=0.2):
sql_str = "SELECT * from swaption_ref_quotes JOIN swaption_quotes " \
"USING (quotedate, index, series, expiry) WHERE index=%s " \
"and quotedate >=%s"
params = (index.upper(), date)
if series:
sql_str += ' AND series = %s'
params = params + (series,)
df = pd.read_sql_query(sql_str, serenitasdb,
index_col=['quotedate', 'expiry', 'series'],
params=params, parse_dates=['quotedate'])
df1 = atm_vol_calc(df, index)
return df1
def atm_vol_calc(df, index):
g_temp = {}
for s, g1 in df.groupby(level='series'):
index_obj = Index.from_name(index, s, '5yr')
for date, g2 in g1.groupby(g1.index.get_level_values(0)):
index_obj.trade_date = date.date()
for expiry, g3 in g2.groupby(g2.index.get_level_values(1)):
g_temp[(date, expiry, s)] = atm_vol_fun(g3, index=index_obj)
df = pd.concat(g_temp, names=['quotedate', 'expiry', 'series'])
df = df.unstack(-1)
df = df.reset_index(level=['expiry', 'series'])
return df
def rolling_vol(df, col='atm_vol', term=[3]):
"""compute the rolling volatility for various terms"""
df = df.groupby(df.index).filter(lambda x: len(x)>2)
def aux(s, col, term):
k = s.index[0]
f = interp1d(s.expiry.values.astype('float'), s[col].values, fill_value='extrapolate')
x = np.array([(k + pd.DateOffset(months=t)).to_datetime64().astype('float') \
for t in term])
return pd.Series(f(x), index=[str(t)+'m' for t in term])
df = df.groupby(level='quotedate').apply(aux, col, term)
# MS quotes don't have fwdspread so they end up as NA
return df.dropna()
def vol_var(percentile=0.975, index='IG', start_date=datetime.date(2014, 6, 11)):
"""compute lo and hi percentiles of atm volatility daily change
Probably overestimates:
- we don't check that the quotes come from the same dealer
- we should group it by series
"""
df = atm_vol(index, start_date)
df = rolling_vol(df, term=[1,2,3])
df = df.sort_index()
df = df.groupby(df.index.date).nth(-1)
return df.diff().quantile([1-percentile, percentile])
def get_index_spread(index, series, date, conn):
with conn.cursor() as c:
c.execute("SELECT closespread from index_quotes " \
"WHERE index=%s and series=%s and date=%s and tenor='5yr'",
(index, series, date))
try:
spread, = c.fetchone()
except TypeError:
spread = None
conn.commit()
return spread
def get_index_ref(index, series, date, expiry, conn):
with conn.cursor() as c:
c.execute("SELECT ref, fwdspread from swaption_ref_quotes " \
"WHERE index=%s and series=%s and quotedate::date=%s "\
"AND expiry=%s ORDER BY quotedate desc",
(index, series, date, expiry))
try:
ref, fwdspread = c.fetchone()
except TypeError:
ref, fwdspread = None, None
conn.commit()
return ref, fwdspread
def get_option_pnl(strike, expiry, index, series, start_date, engine):
for s in [strike, strike+2.5, strike-2.5, strike+5]:
df = pd.read_sql_query("SELECT quotedate, (pay_bid+pay_offer)/2 AS pay_mid, " \
"(rec_bid+rec_offer)/2 AS rec_mid FROM swaption_quotes " \
"WHERE strike=%s and expiry=%s and index=%s and series=%s" \
"and quotedate>=%s", engine,
params=(s, expiry, index, series, start_date),
index_col='quotedate',
parse_dates=['quotedate'])
if not df.empty and df.index[0].date() == start_date:
strike = s
break
else:
raise ValueError("Couldn't find data starting from that date")
if not pd.api.types.is_datetime64tz_dtype(df.index):
df.index = df.index.tz_localize('utc')
df = df.groupby(df.index.normalize()).nth(-1)
if expiry < datetime.date.today():
spread = get_index_spread(index, series, expiry, engine.raw_connection())
underlying = Index.from_name(index, series, "5yr", expiry, 1e4)
underlying.spread = spread
pv = underlying.pv
underlying.spread = strike
if spread > strike:
pay_mid, rec_mid = pv-underlying.pv, 0
else:
pay_mid, rec_mid = 0, underlying.pv - pv
pv = underlying.pv
df = df.append(pd.DataFrame([[pay_mid, rec_mid]],
columns=['pay_mid', 'rec_mid'],
index=[pd.Timestamp(expiry, tz='UTC')]))
return df, strike
def sell_vol_strategy(index="IG", months=3):
engine = dbengine('serenitasdb')
conn = engine.raw_connection()
with conn.cursor() as c1, conn.cursor() as c2:
c1.execute("SELECT DISTINCT series, expiry FROM " \
"swaption_quotes ORDER BY expiry, series desc")
d = {}
for series, expiry in c1:
start_date = BDay().rollback(expiry - pd.DateOffset(months=months)).date()
if start_date > datetime.date.today():
break
c2.execute("SELECT max(quotedate::date) FROM swaption_quotes WHERE " \
"index=%s AND series=%s AND expiry=%s AND quotedate<=%s",
(index, series, expiry, start_date))
actual_start_date, = c2.fetchone()
if actual_start_date is None or (start_date - actual_start_date).days > 5:
continue
ref, fwdspread = get_index_ref(index, series, actual_start_date, expiry, conn)
if fwdspread is None:
fwdspread = ref + months / 50 #TODO: use actual values
strike = round(fwdspread/2.5) * 2.5
pnl, strike = get_option_pnl(strike, expiry, index, series, actual_start_date, engine)
d[(series, strike, expiry)] = pnl
conn.commit()
return d
def aggregate_trades(d):
r = pd.Series()
for v in d.values():
r = r.add(-v.sum(1).diff().dropna(), fill_value=0)
return r
def compute_allocation(df):
Sigma = df.cov().values
gamma = cvxpy.Parameter(sign='positive')
mu = df.mean().values
w = cvxpy.Variable(3)
ret = mu.T*w
risk = cvxpy.quad_form(w, Sigma)
prob = cvxpy.Problem(cvxpy.Maximize(ret - gamma * risk),
[cvxpy.sum_entries(w) == 1,
w >= -2,
w <= 2])
gamma_x = np.linspace(0, 0.02, 500)
W = np.empty((3, gamma_x.size))
for i, val in enumerate(gamma_x):
gamma.value = val
prob.solve()
W[:,i] = np.asarray(w.value).squeeze()
fund_return = mu @ W
fund_vol= np.array([math.sqrt(W[:,i] @ Sigma @W[:,i]) for i in range(gamma_x.size)])
return (W, fund_return, fund_vol)
if __name__ == "__main__":
d1 = sell_vol_strategy(months=1)
d2 = sell_vol_strategy(months=2)
d3 = sell_vol_strategy(months=3)
all_tenors = pd.concat([aggregate_trades(d) for d in [d1, d2, d3]], axis=1)
all_tenors.columns = ['1m', '2m', '3m']
all_tenors['optimal'] = ((1.2*all_tenors['1m']).
sub(1.2*all_tenors['2m'], fill_value=0).
add(all_tenors['3m'], fill_value=0))
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