diff options
Diffstat (limited to 'python/analytics')
| -rw-r--r-- | python/analytics/option.py | 70 | ||||
| -rw-r--r-- | python/analytics/sabr.py | 89 |
2 files changed, 154 insertions, 5 deletions
diff --git a/python/analytics/option.py b/python/analytics/option.py index 6f52bf3d..2ffbe462 100644 --- a/python/analytics/option.py +++ b/python/analytics/option.py @@ -8,6 +8,7 @@ import pandas as pd from db import dbengine from .black import black, Nx +from .sabr import sabr from .utils import GHquad, build_table from .index import g, ForwardIndex, Index, engine from yieldcurve import roll_yc @@ -26,6 +27,7 @@ import matplotlib.pyplot as plt from multiprocessing import Pool from functools import partial from itertools import chain +from scipy.optimize import least_squares from scipy.special import logit, expit @@ -437,13 +439,16 @@ def compute_vol(option, strike, mid): else: return np.array([option.sigma, option.tail_prob, option.vega, option.moneyness, option.strike]) -def _get_keys(df): +def _get_keys(df, models=["black", "precise"]): for quotedate, source in (df[['quotedate', 'quote_source']]. drop_duplicates(). itertuples(index=False)): for option_type in ["payer", "receiver"]: - for model in ["black", "precise"]: - yield (quotedate, source, option_type, model) + if models: + for model in models: + yield (quotedate, source, option_type, model) + else: + yield (quotedate, source, option_type) class VolatilitySurface(ForwardIndex): def __init__(self, index_type, series, tenor='5yr', trade_date=datetime.date.today()): @@ -529,9 +534,9 @@ class VolatilitySurface(ForwardIndex): swaption_class = Swaption moneyness, T, r = [], [], [] if option_type == "payer": - quotes = quotes.assign(mid = quotes[['pay_bid','pay_offer']].mean(1) * 1e-4) + quotes = quotes.assign(mid=quotes[['pay_bid','pay_offer']].mean(1) * 1e-4) else: - quotes = quotes.assign(mid = quotes[['rec_bid','rec_offer']].mean(1) * 1e-4) + quotes = quotes.assign(mid=quotes[['rec_bid','rec_offer']].mean(1) * 1e-4) quotes = quotes.dropna(subset=['mid']) with Pool(4) as p: for expiry, df in quotes.groupby(['expiry']): @@ -556,3 +561,58 @@ class VolatilitySurface(ForwardIndex): else: return self._surfaces[surface_id] +def calib_sabr(x, option, strikes, pv, beta): + alpha, rho, nu = x + F = option.forward_spread + T = option.T + r = np.empty_like(strikes) + for i, K in enumerate(strikes): + option.strike = K + option.sigma = sabr(alpha, beta, rho, nu, F, option._strike, T) + r[i] = option.pv - pv[i] + return r + +class SABRVolatilitySurface(VolatilitySurface): + def __init__(self, index_type, series, tenor='5yr', + trade_date=datetime.date.today(), beta=None): + VolatilitySurface.__init__(self, index_type, series, tenor='5yr', + trade_date=datetime.date.today()) + if index_type == "HY": + self.beta = 3.19 + elif index_type == "IG": + self.beta = 1.84 + + def list(self, source=None, option_type=None): + """returns list of vol surfaces""" + r = [] + for k in _get_keys(self._quotes, []): + if (source is None or k[1] == source) and \ + (option_type is None or k[2] == option_type): + r.append(k) + return r + + def __getitem__(self, surface_id): + if surface_id not in self._surfaces: + quotedate, source, option_type = surface_id + quotes = self._quotes[(self._quotes.quotedate == quotedate) & + (self._quotes.quote_source == source)] + self._index.ref = quotes.ref.iat[0] + + T, r = [], [] + if option_type == "payer": + quotes = quotes.assign(mid=quotes[['pay_bid','pay_offer']].mean(1) * 1e-4) + else: + quotes = quotes.assign(mid=quotes[['rec_bid','rec_offer']].mean(1) * 1e-4) + quotes = quotes.dropna(subset=['mid']) + for expiry, df in quotes.groupby(['expiry']): + option = BlackSwaption(self._index, expiry.date(), 100, option_type) + prog = least_squares(calib_sabr, (0.01, 0.3, 3.5), + bounds=([0, -1, 0], [np.inf, 1, np.inf]), + args=(option, df.strike.values, df.mid.values, self.beta)) + T.append(option.T) + r.append(prog.x) + print(prog) + self._surfaces[surface_id] = (T, r) + return self._surfaces[surface_id] + else: + return self._surfaces[surface_id] diff --git a/python/analytics/sabr.py b/python/analytics/sabr.py new file mode 100644 index 00000000..eba32bac --- /dev/null +++ b/python/analytics/sabr.py @@ -0,0 +1,89 @@ +import datetime
+import math
+import numpy as np
+from numba import jit, float64
+
+@jit(float64(float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+def sabr_lognormal(alpha, rho, nu, F, K, T):
+ A = 1 + (0.25 * (alpha * nu * rho) + nu * nu * (2 - 3 * rho * rho) / 24.) * T
+ if F == K:
+ VOL = alpha * A
+ elif F != K:
+ nulogFK = nu * math.log(F/K)
+ z = nulogFK / alpha
+ x = math.log( ( math.sqrt(1-2*rho*z+z**2) + z - rho ) / (1-rho) )
+ VOL = (nulogFK * A) / x
+ return VOL
+
+@jit(float64(float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+def sabr_normal(alpha, rho, nu, F, K, T):
+ if F == K:
+ V = F
+ A = 1 + (alpha * alpha / (24. * V * V) + nu * nu * (2 - 3 * rho * rho) / 24.) * T
+ VOL = (alpha / V) * A
+ elif F != K:
+ V = math.sqrt(F * K)
+ logFK = math.log(F/K)
+ z = (nu/alpha)*V*logFK
+ x = math.log( ( math.sqrt(1-2*rho*z+z**2) + z - rho ) / (1-rho) )
+ A = 1 + ( (alpha * alpha) / (24. * (V * V)) + ((nu * nu) * (2 - 3 * (rho * rho)) / 24.) ) * T
+ logFK2 = logFK * logFK
+ B = 1/1920. * logFK2 + 1/24.
+ B = 1 + B * logFK2
+ VOL = (nu * logFK * A) / (x * B)
+ return VOL
+
+@jit(float64(float64, float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+def sabr(alpha, beta, rho, nu, F, K, T):
+ if beta == 0.:
+ return sabr_normal(alpha, rho, nu, F, K, T)
+ elif beta == 1.:
+ return sabr_lognormal(alpha, rho, nu, F, K, T)
+ else:
+ if F == K: # ATM formula
+ V = F**(1-beta)
+ A = 1 + ( ((1-beta)**2*alpha**2)/(24.*(V**2)) + (alpha*beta*nu*rho) / (4.*V) +
+ ((nu**2)*(2-3*(rho**2))/24.) ) * T
+ VOL = (alpha/V)*A
+ elif F != K: # not-ATM formula
+ V = (F*K)**((1-beta)/2.)
+ logFK = math.log(F/K)
+ z = (nu/alpha)*V*logFK
+ x = math.log( ( math.sqrt(1-2*rho*z+z**2) + z - rho ) / (1-rho) )
+ A = 1 + ( ((1-beta)**2*alpha**2)/(24.*(V**2)) + (alpha*beta*nu*rho)/(4.*V) +
+ ((nu**2)*(2-3*(rho**2))/24.) ) * T
+ B = 1 + (1/24.)*(((1-beta)*logFK)**2) + (1/1920.)*(((1-beta)*logFK)**4)
+ VOL = (nu*logFK*A)/(x*B)
+ return VOL
+
+if __name__ == "__main__":
+ from analytics.option import BlackSwaption
+ from analytics import Index
+ from scipy.optimize import least_squares
+
+ underlying = Index.from_name("IG", 28, "5yr")
+ underlying.spread = 67.5
+ exercise_date = datetime.date(2017, 9, 20)
+ option = BlackSwaption(underlying, exercise_date, 70)
+
+ strikes = np.array([50, 55, 57.5, 60, 62.5, 65, 67.5, 70, 75, 80, 85])
+ pvs = np.array([44.1, 25.6, 18.9, 14, 10.5, 8.1, 6.4, 5, 3.3, 2.2, 1.5]) * 1e-4
+
+ strikes = np.array([50, 55, 57.5, 60, 62.5, 65, 67.5, 70, 75, 80, 85, 90, 95, 100])
+ pvs = np.array([53.65, 37.75, 31.55, 26.45, 22.25, 18.85, 16.15, 13.95, 10.55,
+ 8.05, 6.15, 4.65, 3.65, 2.75]) * 1e-4
+
+ def calib(x, option, strikes, pv, beta):
+ alpha, rho, nu = x
+ F = option.forward_spread
+ T = option.T
+ r = np.empty_like(strikes)
+ for i, K in enumerate(strikes):
+ option.strike = K
+ option.sigma = sabr(alpha, beta, rho, nu, F, K, T)
+ r[i] = option.pv - pv[i]
+ return r
+
+ prog = least_squares(calib, (0.3, 0.5, 0.3),
+ bounds=(np.zeros(3), [np.inf, 1, np.inf]),
+ args=(option, strikes, pvs, 1))
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