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import array
import datetime
import math
import numpy as np
import pandas as pd
from .black import black
from .utils import GHquad
from .index import g, ForwardIndex
from yieldcurve import roll_yc
from pandas.tseries.offsets import BDay
from pyisda.curve import SpreadCurve
from pyisda.flat_hazard import pv_vec
from scipy.optimize import brentq
from scipy.integrate import simps
def calib(S0, fp, exercise_date : datetime.date, exercise_date_settle :datetime.date,
index, rolled_curve, tilt, w):
S = S0 * tilt * 1e-4
pv = pv_vec(S, rolled_curve, exercise_date, exercise_date_settle,
index.start_date, index.end_date, index.recovery,
index.fixed_rate * 1e-4)
return np.inner(pv, w) - fp
def ATMstrike(index, exercise_date : datetime.date):
exercise_date_settle = (pd.Timestamp(exercise_date) + 3* BDay()).date()
fp = index.forward_pv(exercise_date) / index.notional
closure = lambda S: g(index, S, exercise_date) - fp
eta = 1.1
a = index.spread
b = index.spread * eta
while True:
if closure(b) > 0:
break
b *= eta
return brentq(closure, a, b)
class Swaption(ForwardIndex):
"""Swaption class"""
def __init__(self, index, exercise_date : datetime.date, strike : float,
option_type="payer", strike_is_price = False):
ForwardIndex.__init__(self, index, exercise_date, strike_is_price)
self._exercise_date = exercise_date
self._forward_yc = roll_yc(index._yc, exercise_date)
self._T = None
self._strike_is_price = strike_is_price
self.strike = strike
self.option_type = option_type.lower()
self._Z, self._w = GHquad(50)
self.notional = 1
@property
def exercise_date(self):
return self._exercise_date
@exercise_date.setter
def exercise_date(self, d : datetime.date):
self._exercise_date = d
ForwardIndex.__init__(self, self.index, d)
self._forward_yc = roll_yc(self.index._yc, d)
self._G = g(self.index, self.strike, self.exercise_date, self._forward_yc)
@property
def strike(self):
if self._strike_is_price:
return 100 * (1 - self._G)
else:
return self._strike
@strike.setter
def strike(self, K : float):
if self._strike_is_price:
self._G = (100 - K) / 100
# we compute the corresponding spread to the strike price
def handle(S, index, forward_date, forward_yc):
return g(index, S, forward_date, forward_yc) - self._G
eta = 1.2
a = 250
b = eta * a
while True:
if handle(b, self.index, self.exercise_date, self._forward_yc) > 0:
break
b *= eta
self._strike = brentq(handle, a, b,
args = (self.index, self.exercise_date, self._forward_yc))
else:
self._G = g(self.index, K, self.exercise_date, self._forward_yc)
self._strike = K
@property
def intrinsic_value(self):
V = self.df * (self.forward_pv - self._G)
return max(V, 0) if self.option_type == "payer" else max(-V, 0)
@property
def pv(self):
T = self.T
tilt = np.exp(-self.sigma**2/2 * T + self.sigma * self._Z * math.sqrt(T))
args = (self.forward_pv, self.exercise_date, self.exercise_date_settle,
self.index, self._forward_yc, tilt, self._w)
eta = 1.05
a = self.index.spread
b = a * eta
while True:
if calib(*((b,) + args)) > 0:
break
b *= eta
S0 = brentq(calib, a, b, args)
if T == 0:
return self.notional * self.intrinsic
## Zstar solves S_0 exp(-\sigma^2/2 * T + sigma * Z^\star\sqrt{T}) = strike
Zstar = (math.log(self._strike/S0) + self.sigma**2/2 * T) / \
(self.sigma * math.sqrt(T))
if self.option_type == "payer":
Z = Zstar + np.logspace(0, math.log(4 / (self.sigma * math.sqrt(T)), 10), 300) - 1
elif self.option_type == "receiver":
Z = Zstar - np.logspace(0, math.log(4 / (self.sigma * math.sqrt(T)), 10), 300) + 1
else:
raise ValueError("option_type needs to be either 'payer' or 'receiver'")
S = S0 * np.exp(-self.sigma**2/2 * T + self.sigma * Z * math.sqrt(T))
r = pv_vec(S * 1e-4, self._forward_yc, self.exercise_date,
self.exercise_date_settle, self.index.start_date,
self.index.end_date, self.index.recovery, self.index.fixed_rate * 1e-4)
val = (r - self._G) * 1/math.sqrt(2*math.pi) * np.exp(-Z**2/2)
return self.notional * simps(val, Z) * self.df
@pv.setter
def pv(self, val: float):
if val < self.intrinsic_value:
raise ValueError("{}: is less than intrinsic value: {}".
format(val, self.intrinsic_value))
def handle(x):
self.sigma = x
return self.pv - val
# use sigma_black as a starting point
self.pv_black = val
eta = 1.1
a = self.sigma
while True:
if handle(a) < 0:
break
a /= eta
b = a * eta
while True:
if handle(b) > 0:
break
b *= eta
self.sigma = brentq(handle, a, b)
@property
def pv_black(self):
"""compute pv using black-scholes formula"""
strike_tilde = self.index.fixed_rate * 1e-4 + self._G / self.forward_annuity * self.df
return self.forward_annuity * black(self.forward_spread * 1e-4,
strike_tilde,
self.T,
self.sigma,
self.option_type) * self.notional
@pv_black.setter
def pv_black(self, val: float):
if val < self.intrinsic_value:
raise ValueError("{}: is less than intrinsic value: {}".
format(val, self.intrinsic_value))
def handle(x):
self.sigma = x
return self.pv_black - val
eta = 1.01
a = 0.1
b = a * eta
while True:
if handle(b) > 0:
break
b *= eta
self.sigma = brentq(handle, a, b)
@property
def delta(self):
old_index_pv = self.index.pv
old_pv = self.pv
self.index.spread += 0.1
notional_ratio = self.index.notional/self.notional
delta = (self.pv - old_pv)/(self.index.pv - old_index_pv) * notional_ratio
self.index.spread -= 0.1
return delta
@property
def T(self):
if self._T:
return self._T
else:
return ((self.exercise_date - self.index.trade_date).days + 1)/365
@property
def gamma(self):
pass
@property
def theta(self):
old_pv = self.pv
self._T = self.T - 1/365
theta = self.pv - old_pv
self._T = None
return theta
@property
def vega(self):
old_pv = self.pv
self.sigma += 0.01
vega = self.pv - old_pv
self.sigma -= 0.01
return vega
@property
def DV01(self):
old_pv = self.pv
self.index.spread += 1
dv01 = self.pv - old_pv
self.index.spread -= 1
return dv01
@property
def breakeven(self):
pv = self.pv / self.notional
if self._strike_is_price:
return self._G + pv
else:
aux = lambda S: g(self.index, S, self.exercise_date) - self._G - pv
eta = 1.1
a = self._strike
b = a * eta
while True:
if aux(b) > 0:
break
b *= eta
return brentq(aux, a, b)
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