def getScheduleComplete(self):
myscheduler = Scheduler()
self.datelist = myscheduler.getSchedule(self.start, self.maturity,
self.freq, self.start)
self.ntimes = len(self.datelist)
fullset = sorted(
set(self.datelist).union([self.start]).union([self.maturity]))
return fullset, self.datelist
class CDSSwaption(object):
def __init__(self, option_start, cds_start,cds_end,strike,cds_freq,cds_flavor,cds_recovery,Q):
self.option_start = option_start
self.strike = strike
self.cds_start = cds_start
self.cds_end = cds_end
self.cds_freq = cds_freq
# payer to pay strike K, spread - k; receiver to receive strike K, k - spread
self.cds_flavor = cds_flavor
self.cds_recovery = cds_recovery
self.myScheduler = Scheduler()
self.cds_datelist = self.myScheduler.getSchedule(self.cds_start,self.cds_end,self.cds_freq,self.cds_start)
self.OIS = OIS(option_start,cds_end)
self.Q = Q
self.ntimes = np.shape(self.Q)[0]
self.ntrajectories = np.shape(self.Q)[1]
def getCDSSwaption(self,premium_rate):
Q_truncation = self.Q[self.cds_start:]
Q_truncation = Q_truncation.divide(Q_truncation.ix[0])
OIS_DCF_List = []
for cds_date in self.cds_datelist: OIS_DCF_List.append(self.OIS.getDF_trimstartDate(cds_date))
OIS_truncation = pd.Series(OIS_DCF_List,index=self.cds_datelist)
OIS_truncation = OIS_truncation.divide(OIS_truncation.ix[0])
# add one day since this is header not index
OIS_truncation = OIS_truncation[self.cds_start+datetime.timedelta(days=1):]
self.CDS = CDS(OIS_truncation, Q_truncation, self.cds_start, self.cds_end, self.cds_freq, self.cds_flavor, self.cds_recovery)
total_instance = 0
for i in range(self.ntrajectories):
cur_default = self.Q.loc[self.cds_start][i]
cur_discount = self.OIS.getDF_trimstartDate(self.cds_start)
cur_spread, cur_ra = self.CDS.getSingleSpread(self.CDS.Q[i])
if self.cds_flavor: total_instance += cur_discount * cur_default * max(cur_spread-premium_rate,0) * cur_ra
else: total_instance += cur_discount * cur_default * max(-cur_spread + premium_rate,0) * cur_ra
return total_instance / self.ntrajectories
from unittest import TestCase
from parameters import xR, simNumber, t_step, trim_start, trim_end, freq, periods, referenceDate, start, inArrears, WORKING_DIR
from MonteCarloSimulators.Vasicek.vasicekMCSim import MC_Vasicek_Sim
from Scheduler.Scheduler import Scheduler
mySchedule = Scheduler()
# Global Variables
mySchedule = mySchedule.getSchedule(start=trim_start, end=trim_end, freq="M")
mySimulator = MC_Vasicek_Sim(datelist=mySchedule,
x=xR,
simNumber=simNumber,
t_step=t_step)
mySimulator.getLibor()
mySimulator.getSmallLibor()
a = 1
class TestMC_Vasicek_Sim(TestCase):
def test_getLibor(self):
mySimulator.getLibor()
def test_getSmallLibor(self):
# Monte Carlo trajectories creation - R
Libor = mySimulator.getSmallLibor(mySchedule)
return Libor
myScheduler = Scheduler()
periods = '1Y'
freq = '1M'
t_step = 1.0 / 365.0
simNumber = 10
trim_start = date(2000, 1, 1)
trim_end = date(2000, 12, 31)
trim_endMC = date(2001, 12, 31)
effDay = date(2000, 4, 1)
referenceDate = date(2000, 1, 1)
testSched = pd.date_range(trim_start, trim_start)
scheduleComplete = pd.date_range(start=trim_start, end=trim_end)
xR = [3.0, 0.05, 0.04, 0.03]
datelist = myScheduler.getSchedule(start=trim_start,
end=trim_end,
freq=freq,
referencedate=referenceDate)
myMC = MC_Vasicek_Sim()
myMC.setVasicek(x=xR,
minDay=trim_start,
maxDay=trim_endMC,
simNumber=simNumber,
t_step=t_step)
myMC.getLibor()
myCorp = CorporateRates()
myCorp.getCorporatesFred(trim_start, trim_end)
testRatings = myCorp.getCorporateData("AAA", testSched)
testSurvival = myCorp.getCorporateQData("AAA", scheduleComplete, 0.4)
mySwap = IRSwap(zCurve=myMC.getLibor(),
startDate=trim_start,
class MC_CIR_Sim(object):
def __init__(self):
pass
def setCIR(self, minDay, maxDay, x, simNumber, t_step):
# dλ(t) = k(θ − λ(t))dt + σ*sqrt(λ(t))*dW(t)
self.kappa = x[0]
self.theta = x[1]
self.sigma = x[2]
self.r0 = x[3]
self.simNumber = simNumber
self.t_step = t_step
# creation of a fine grid for Monte Carlo integration
# Create fine date grid for SDE integration
self.Schedule = Scheduler()
self.datelistlong = self.Schedule.getSchedule(start=minDay,end=maxDay,freq="1M",referencedate=minDay)
self.datelistlong_daily = pd.date_range(minDay, maxDay).tolist()
self.datelistlong_daily = [x.date() for x in self.datelistlong_daily]
self.ntimes = len(self.datelistlong)
self.ntimes_daily = len(self.datelistlong_daily)
self.survival = []
self.smallSurvival = []
def getSurvival(self):
rd = np.random.standard_normal((self.ntimes, self.simNumber)) # array of numbers for the number of samples
r = np.zeros(np.shape(rd))
nrows = np.shape(rd)[0]
sigmaDT = self.sigma * np.sqrt(self.t_step)
#calculate λ(t)
r[1,:] = self.r0 + r[1,:]
for i in np.arange(2, nrows):
r[i,:] = r[i-1,:] + self.kappa * (self.theta - r[i-1,:]) * self.t_step + sigmaDT * rd[i,:]*np.sqrt(r[i-1,:])
# calculate integral(λ(s)ds)
integralR = r.cumsum(axis=0) * self.t_step
# calculate Survival Prob
self.survival = np.exp(-integralR)
self.survival = pd.DataFrame(data=self.survival, index=self.datelistlong)
return self.survival
def getSurvival_daily(self):
t_step = 1.0/365
rd = np.random.standard_normal((self.ntimes_daily, self.simNumber)) # array of numbers for the number of samples
r = np.zeros(np.shape(rd))
nrows = np.shape(rd)[0]
sigmaDT = self.sigma * np.sqrt(t_step)
#calculate λ(t)
r[1,:] = self.r0 + r[1,:]
for i in np.arange(2, nrows):
r[i,:] = r[i-1,:] + self.kappa * (self.theta - r[i-1,:]) * t_step + sigmaDT * rd[i,:]*np.sqrt(r[i-1,:])
# calculate integral(λ(s)ds)
integralR = r.cumsum(axis=0) * t_step
# calculate Survival Prob
self.survival = np.exp(-integralR)
self.survival = pd.DataFrame(data=self.survival, index=self.datelistlong_daily)
# r = pd.DataFrame(data=r, index=self.datelistlong_daily)
return self.survival
def getHazard_daily(self):
t_step = 1.0/365
rd = np.random.standard_normal((self.ntimes_daily, self.simNumber)) # array of numbers for the number of samples
r = np.zeros(np.shape(rd))
nrows = np.shape(rd)[0]
sigmaDT = self.sigma * np.sqrt(t_step)
#calculate λ(t)
r[1,:] = self.r0 + r[1,:]
for i in np.arange(2, nrows):
r[i,:] = r[i-1,:] + self.kappa * (self.theta - r[i-1,:]) * t_step + sigmaDT * rd[i,:]*np.sqrt(r[i-1,:])
r = pd.DataFrame(data=r, index=self.datelistlong_daily)
return r
def getSmallSurvival(self,datelist = None):
# calculate indexes
if (datelist is None):
datelist = self.datelist
ind = self.return_indices1_of_a(self.datelistlong, datelist)
self.smallSruvival = self.survival.iloc[ind, :]
return self.smallSurvival
def saveMeExcel(self):
df = DataFrame(self.libor)
df.to_excel(os.path.join(WORKING_DIR,'MC_CIR_Sim.xlsx'), sheet_name='survival', index=False)
def return_indices1_of_a(self, a, b):
b_set = set(b)
ind = [i for i, v in enumerate(a) if v in b_set]
return ind
def return_indices2_of_a(self, a, b):
index = []
for item in a:
index.append(np.bisect.bisect(b,item))
return np.unique(index).tolist()
class CouponBond(object):
def __init__(self,
fee,
coupon,
start,
maturity,
freq,
referencedate,
observationdate,
rating,
notional=1,
recovery=0.4):
self.numSim = 10
self.t_step = 1.0 / 365
self.fee = fee
self.coupon = coupon
self.start = start
self.maturity = maturity
self.freq = freq
self.recovery = recovery
self.rating = rating
self.referencedate = referencedate
self.observationdate = observationdate
self.myScheduler = Scheduler()
self.delay = self.myScheduler.extractDelay(freq=freq)
self.referencedate = referencedate
self.getScheduleComplete()
self.fullDateList = self.datelist
self.ntimes = len(self.datelist)
self.pvAvg = 0.0
self.cashFlows = DataFrame()
self.cashFlowsAvg = []
self.yieldIn = 0.0
self.notional = notional
self.errorCurve = []
self.mcSim = MC_Vasicek_Sim()
def getScheduleComplete(self):
self.datelist = self.myScheduler.getSchedule(
start=self.start,
end=self.maturity,
freq=self.freq,
referencedate=self.referencedate)
self.ntimes = len(self.datelist)
fullset = sorted(
set(self.datelist).union([self.referencedate]).union([
self.start
]).union([self.maturity]).union([self.observationdate]))
a = 1
return fullset, self.datelist
def setLibor(self, libor):
self.libor = libor / libor.loc[self.referencedate]
#self.ntimes = np.shape(self.datelist)[0]
self.ntrajectories = np.shape(self.libor)[1]
self.ones = np.ones(shape=[self.ntrajectories])
def getExposure(self, referencedate):
if self.referencedate != referencedate:
self.referencedate = referencedate
self.getScheduleComplete()
deltaT = np.zeros(self.ntrajectories)
if self.ntimes == 0:
pdzeros = pd.DataFrame(data=np.zeros([1, self.ntrajectories]),
index=[referencedate])
self.pv = pdzeros
self.pvAvg = 0.0
self.cashFlows = pdzeros
self.cashFlowsAvg = 0.0
return self.pv
for i in range(1, self.ntimes):
deltaTrow = ((self.datelist[i] - self.datelist[i - 1]).days /
365) * self.ones
deltaT = np.vstack((deltaT, deltaTrow))
self.cashFlows = self.coupon * deltaT
principal = self.ones
if self.ntimes > 1:
self.cashFlows[-1:] += principal
else:
self.cashFlows = self.cashFlows + principal
if (self.datelist[0] <= self.start):
self.cashFlows[0] = -self.fee * self.ones
if self.ntimes > 1:
self.cashFlowsAvg = self.cashFlows.mean(axis=1) * self.notional
else:
self.cashFlowsAvg = self.cashFlows.mean() * self.notional
pv = self.cashFlows * self.libor.loc[self.datelist]
self.pv = pv.sum(axis=0) * self.notional
self.pvAvg = np.average(self.pv) * self.notional
return self.pv
def getPV(self, referencedate):
self.getExposure(referencedate=referencedate)
return self.pv / self.libor.loc[self.referencedate]
def getFullExposure(self):
fullExposure = pd.DataFrame(data=np.zeros(len(self.fullDateList)),
index=self.fullDateList)
for days in self.fullDateList:
fullExposure.loc[days] = self.getExposure(days)
self.fullExposure = fullExposure
def setCorpData(self, corpData):
self.corpData = corpData.loc[self.rating, :, "1 MO"]
def setxQ(self, xQ):
res = optimize.fmin(func=self.mcSim.errorFunction,
x0=np.array([xQ[0], xQ[1]]),
args=(self.corpData.values[:-1],
self.corpData.values[1:], self.t_step))
xQSigma = np.std(self.corpData.values[:-1] - self.corpData.values[1:])
self.xQ = np.append(res, np.array([xQSigma, xQ[3]]))
self.mcSim.setVasicek(minDay=self.start,
maxDay=self.maturity,
x=self.xQ,
simNumber=self.numSim,
t_step=self.t_step)
def setQCurve(self):
self.qCurve = self.mcSim.getLibor().loc[:, 0]
return
def getCVA(self):
self.CVA = (1 - self.recovery) * self.fullExposure.loc[
self.fullDateList, 0].values * self.qCurve.loc[
self.fullDateList] * self.libor.loc[self.fullDateList, 0]
def getLiborAvg(self, yieldIn, datelist):
self.yieldIn = yieldIn
time0 = datelist[0]
# this function is used to calculate exponential single parameter (r or lambda) Survival or Libor Functions
Z = np.exp(-self.yieldIn *
pd.DataFrame(np.tile([(x - time0).days / 365.0
for x in self.datelist],
reps=[self.ntrajectories, 1]).T,
index=self.datelist))
return Z
def getYield(self, price):
# Fit model to curve data
yield0 = 0.05 * self.ones
self.price = price
self.yieldIn = self.fitModel2Curve(x=yield0)
return self.yieldIn
def fitModel2Curve(self, x):
# Minimization procedure to fit curve to model
results = optimize.minimize(fun=self.fCurve, x0=x)
a = 1
return results.x
def fCurve(self, x):
# raw data error function
calcCurve = self.getLiborAvg(x, self.datelist)
thisPV = np.multiply(self.cashFlows,
calcCurve).mean(axis=1).sum(axis=0)
error = 1e4 * (self.price - thisPV)**2
self.errorCurve = error
return error
class CouponBond(object):
def __init__(self, fee, start,coupon, maturity, freq, referencedate, observationdate,notional):
self.fee = fee
self.coupon=coupon
self.start = start
self.maturity = maturity
self.freq= freq
self.referencedate = referencedate
self.observationdate = observationdate
self.myScheduler = Scheduler()
self.delay = self.myScheduler.extractDelay(freq=freq)
self.getScheduleComplete()
self.ntimes=len(self.datelist)
self.referencedate = referencedate
self.pvAvg=0.0
self.cashFlows = DataFrame()
self.cashFlowsAvg = []
self.yieldIn = 0.0
self.notional=notional
def getScheduleComplete(self):
self.datelist = self.myScheduler.getSchedule(start=self.start,end=self.maturity,freq=self.freq,referencedate=self.referencedate)
fullset = list(sorted(list(set(self.datelist)
.union([self.referencedate])
.union([self.start])
.union([self.maturity])
.union([self.observationdate])
)))
return fullset,self.datelist
def setLibor(self,libor):
self.libor = libor/libor.loc[self.referencedate]
self.ntimes = np.shape(self.datelist)[0]
self.ntrajectories = np.shape(self.libor)[1]
self.ones = np.ones(shape=[self.ntrajectories])
def getExposure(self, referencedate):
if self.referencedate!=referencedate:
self.referencedate=referencedate
self.getScheduleComplete()
deltaT= np.zeros(self.ntrajectories)
if self.ntimes==0:
pdzeros= pd.DataFrame(data=np.zeros([1,self.ntrajectories]), index=[referencedate])
self.pv=pdzeros
self.pvAvg=0.0
self.cashFlows=pdzeros
self.cashFlowsAvg=0.0
return self.pv
for i in range(1,self.ntimes):
deltaTrow = ((self.datelist[i]-self.datelist[i-1]).days/365)*self.ones
deltaT = np.vstack ((deltaT,deltaTrow) )
self.cashFlows= self.coupon*deltaT
principal = self.ones
if self.ntimes>1:
self.cashFlows[-1:]+= principal
else:
self.cashFlows = self.cashFlows + principal
if(self.datelist[0]<= self.start):
self.cashFlows[0]=-self.fee*self.ones
if self.ntimes>1:
self.cashFlowsAvg = self.cashFlows.mean(axis=1)*self.notional
else:
self.cashFlowsAvg = self.cashFlows.mean() * self.notional
pv = self.cashFlows*self.libor.loc[self.datelist]
self.pv = pv.sum(axis=0)*self.notional
self.pvAvg = np.average(self.pv)*self.notional
return self.pv
def getPV(self,referencedate):
self.getExposure(referencedate=referencedate)
return self.pv/self.libor.loc[self.observationdate]
def getLiborAvg(self, yieldIn, datelist):
self.yieldIn = yieldIn
time0 = datelist[0]
# this function is used to calculate exponential single parameter (r or lambda) Survival or Libor Functions
Z = np.exp(-self.yieldIn * pd.DataFrame(np.tile([(x - time0).days / 365.0 for x in self.datelist], reps=[self.ntrajectories,1]).T,index=self.datelist))
return Z
def getYield(self,price):
# Fit model to curve data
yield0 = 0.05 * self.ones
self.price = price
self.yieldIn = self.fitModel2Curve(x=yield0)
return self.yieldIn
def fitModel2Curve(self, x ):
# Minimization procedure to fit curve to model
results = minimize(fun=self.fCurve, x0=x)
return results.x
def fCurve(self, x):
# raw data error function
calcCurve = self.getLiborAvg(x, self.datelist)
thisPV = np.multiply(self.cashFlows,calcCurve).mean(axis=1).sum(axis=0)
error = 1e4 * (self.price - thisPV) ** 2
return error
class PortfolioLossCalculation(object):
def __init__(self, K1, K2, Fs, Rs, betas, start_dates, end_dates, freqs,
coupons, referenceDates, ratings, bootstrap):
self.bootstrap = bootstrap
self.K1 = K1
self.K2 = K2
self.Fs = Fs
self.Rs = Rs
self.betas = betas
self.referenceDates = referenceDates
self.freqs = freqs
self.coupons = coupons
self.start_dates = start_dates
self.end_dates = end_dates
self.ratings = ratings
self.R = Rs[0]
self.beta = betas[0]
self.referenceDate = referenceDates[0]
self.freq = freqs[0]
self.coupon = coupons[0]
self.start_date = start_dates[0]
self.end_date = end_dates[0]
self.rating = ratings[0]
self.maturity = end_dates[0]
self.myScheduler = Scheduler()
def setParameters(self, R, rating, coupon, beta, start_date, referenceDate,
end_date, freq):
self.R = R
self.beta = beta
self.referenceDate = referenceDate
self.freq = freq
self.coupon = coupon
self.start_date = start_date
self.end_date = end_date
self.rating = rating
self.maturity = end_date
def getQ(self, start_date, referenceDate, end_date, freq, coupon, rating,
R):
## Use CorporateDaily to get Q for referencedates ##
# print("GET Q")
# print(self.portfolioScheduleOfCF)
if self.bootstrap:
print("Q bootstrap")
CDSClass = CDS(start_date=start_date,
end_date=end_date,
freq=freq,
coupon=coupon,
referenceDate=referenceDate,
rating=rating,
R=R)
myLad = BootstrapperCDSLadder(start=self.start_date,
freq=[freq],
CDSList=[CDSClass],
R=CDSClass.R).getXList(x0Vas)[freq]
self.Q1M = MC_Vasicek_Sim(
x=myLad,
t_step=1 / 365,
datelist=[CDSClass.referenceDate, CDSClass.end_date],
simNumber=simNumber).getLibor()[0]
print(self.Q1M)
else:
myQ = CorporateRates()
myQ.getCorporatesFred(trim_start=referenceDate, trim_end=end_date)
## Return the calculated Q(t,t_i) for bonds ranging over maturities for a given rating
daterange = pd.date_range(start=referenceDate, end=end_date).date
myQ = myQ.getCorporateQData(rating=rating, datelist=daterange, R=R)
Q1M = myQ[freq]
print(Q1M)
return (Q1M)
def Q_lhp(self, t, K1, K2, R, beta, Q):
"""Calculates the Tranche survival curve for the LHP model.
Args:
T (datetime.date): Should be given in "days" (no hours, minutes, etc.)
K1 (float): The starting value of the tranche. Its value should be
between 0 & 1.
K2 (float): The final value of the tranche.
beta (float): Correlation perameter. Its value should be between 0 and 1.
R (float): Recovery rate. Usually between 0 and 1.
Q (callable function): A function Q that takes in a dateime.date and
outputs a float from 0 to 1. It is assumed that Q(0) = 1 and Q is
decreasing. Represents survival curve of each credit.
"""
if Q(t) == 1:
return 1 # prevents infinity
def emin(K):
# Calculates E[min(L(T), K)] in LHP model
C = norm.ppf(1 - Q(t))
A = (1 / beta) * (C - sqrt(1 - beta * beta) * norm.ppf(K /
(1 - R)))
return (1 - R) * mvn.mvndst(
upper=[C, -1 * A],
lower=[0, 0],
infin=[0, 0], # set lower bounds = -infty
correl=-1 * beta)[1] + K * norm.cdf(A)
return 1 - (emin(K2) - emin(K1)) / (K2 - K1)
def Q_gauss(self, t, K1, K2, Fs, Rs, betas, Qs):
""" Calculate the tranche survival probability in the Gaussian heterogenous model.
Arguments:
t (float): Time. Positive.
K1 (float): Starting tranche value. Between 0 and 1.
K2 (float): Ending tranche value. Between 0 and 1.
Fs (list): List of fractional face values for each credit. Each entry must be
between 0 and 1.
Rs (list): List of recovery rates for each credit. Each entry must be between
0 and 1.
betas (list): Correlation perameters for each credit. Each entry must be between
0 and 1.
Qs (list): Survival curves for each credit. Each entry must be a callable function
that takes in a datetime.date argument and returns a number from 0 to 1.
"""
Cs = [norm.ppf(1 - q(t)) for q in Qs]
N = len(Fs)
def f(K, z):
ps = [
norm.cdf((C - beta * z) / sqrt(1 - beta**2))
for C, beta in zip(Cs, betas)
]
mu = 1 / N * sum([p * F * (1 - R) for p, F, R in zip(ps, Fs, Rs)])
sigma_squared = 1 / N / N * sum([
p * (1 - p) * F**2 * (1 - R)**2 for p, F, R in zip(ps, Fs, Rs)
])
sigma = sqrt(sigma_squared)
return -1 * sigma * norm.pdf(
(mu - K) / sigma) - (mu - K) * norm.cdf((mu - K) / sigma)
emin = lambda K: quad(lambda z: norm.pdf(z) * f(K, z), -10, 10)[0]
return 1 - (emin(K2) - emin(K1)) / (K2 - K1)
def Q_adjbinom(self, t, K1, K2, Fs, Rs, betas, Qs):
""" Calculates the tranche survival probability under the adjusted
binomial model.
Arguments:
t (datetime.date): Time.
K1 (float): Starting tranche value (0 to 1).
K2 (float): Final tranche value (0 to 1).
Fs (list): List of fractional face values (floats) for each credit.
Rs (list): List of recovery rates (floats) for each credit.
betas (list): List of correlation perameters
Qs (list): List of survival probabilities. These are callable functions that
takes in a single datetime.date argument and returns a float.
Returns:
float: The value of the tranche survival curve.
"""
if Qs[0](t) == 1:
return 1.0 # initial value -- avoids weird nan return
N = len(Fs)
Cs = [norm.ppf(1 - Q(t)) for Q in Qs]
L = sum([(1 - R) * F for R, F in zip(Rs, Fs)]) / N
def choose(n, k): # Calculates binomial coeffecient: n choose k.
if k == 0 or k == n:
return 1
return choose(n - 1, k - 1) + choose(n - 1, k)
def g(k, z):
ps = [
norm.cdf((C - beta * z) / sqrt(1 - beta * beta))
for C, beta in zip(Cs, betas)
]
p_avg = sum([(1 - R) * F / L * p
for R, F, p in zip(Rs, Fs, ps)]) / N
f = lambda k: choose(N, k) * p_avg**k * (1 - p_avg)**(N - k)
vA = p_avg * (1 - p_avg) / N
vE = 1 / N / N * sum([((1 - R) * F / L)**2 * p * (1 - p)
for R, F, p in zip(Rs, Fs, ps)])
m = p_avg * N
l = int(m)
u = l + 1
o = (u - m)**2 + ((l - m)**2 - (u - m)**2) * (u - m)
alpha = (vE * N + o) / (vA * N + o)
if k == l:
return f(l) + (1 - alpha) * (u - m)
if k == u:
return f(u) - (1 - alpha) * (l - m)
return alpha * f(k)
I = lambda k: quad(lambda z: norm.pdf(z) * g(k, z), -10, 10)[0]
emin = lambda K: sum([I(k) * min(L * k, K) for k in range(0, N + 1)])
return 1 - (emin(K2) - emin(K1)) / (K2 - K1)
def gcd(self, a, b):
if a * b == 0:
return max(a, b)
if a < b:
return self.gcd(a, b % a)
return self.gcd(a % b, b)
def Q_exact(self, t, K1, K2, Fs, Rs, betas, Qs):
Cs = [norm.ppf(1 - Q(t)) for Q in Qs]
N = len(Fs)
g = round(3600 * Fs[0] * (1 - Rs[0]))
for j in range(1, N):
g = self.gcd(g, round(3600 * Fs[j] * (1 - Rs[j])))
g = g / 3600
ns = [round(F * (1 - R) / g) for F, R in zip(Fs, Rs)]
def f(j, k, z):
if (j, k) == (0, 0):
return 1.0
if j == 0:
return 0.0
ps = [
norm.cdf((C - beta * z) / sqrt(1 - beta**2))
for C, beta in zip(Cs, betas)
]
if k < ns[j - 1]:
return f(j - 1, k, z) * (1 - ps[j - 1])
return f(j - 1, k, z) * (1 - ps[j - 1]) + f(
j - 1, k - ns[j - 1], z) * ps[j - 1]
I = [
quad(lambda z: norm.pdf(z) * f(N, k, z), -12, 12)[0]
for k in range(sum(ns))
]
emin = lambda K: sum([I[k] * min(k * g, K) for k in range(sum(ns))])
return 1 - (emin(K2) - emin(K1)) / (K2 - K1)
def getZ_Vasicek(self):
### Get Z(t,t_i) for t_i in datelist #####
## Simulate Vasicek model with paramters given in workspace.parameters
# xR = [5.0, 0.05, 0.01, 0.05]
# kappa = x[0]
# theta = x[1]
# sigma = x[2]
# r0 = x[3]
vasicekMC = MC_Vasicek_Sim(
datelist=[self.referenceDate, self.end_date],
x=xR,
simNumber=10,
t_step=t_step)
self.myZ = vasicekMC.getLibor()
self.myZ = self.myZ.loc[:, 0]
def getScheduleComplete(self):
datelist = self.myScheduler.getSchedule(
start=self.start_date,
end=self.maturity,
freq=self.freq,
referencedate=self.referenceDate)
ntimes = len(datelist)
fullset = list(
sorted(
list(
set(datelist).union([self.referenceDate]).union([
self.start_date
]).union([self.maturity]).union([self.referenceDate]))))
return fullset, datelist
def getPremiumLegZ(self, myQ):
Q1M = myQ
# Q1M = self.myQ["QTranche"]
fulllist, datelist = self.getScheduleComplete()
portfolioScheduleOfCF = fulllist
timed = portfolioScheduleOfCF[portfolioScheduleOfCF.
index(self.referenceDate):]
Q1M = Q1M.loc[timed]
zbarPremLeg = self.myZ / self.myZ.loc[self.referenceDate]
zbarPremLeg = zbarPremLeg.loc[timed]
## Calculate Q(t_i) + Q(t_(i-1))
Qplus = []
out = 0
for i in range(1, len(Q1M)):
out = out + (Q1M[(i - 1)] + Q1M[i]) * float(
(timed[i] - timed[i - 1]).days / 365) * zbarPremLeg[i]
zbarPremLeg = pd.DataFrame(zbarPremLeg, index=timed)
# print("Premium LEg")
PVpremiumLeg = out * (1 / 2)
# print(PVpremiumLeg)
## Get coupon bond ###
print(PVpremiumLeg)
return PVpremiumLeg
# //////////////// Get Protection leg Z(t_i)( Q(t_(i-1)) - Q(t_i) )
def getProtectionLeg(self, myQ):
print("Protection Leg ")
Q1M = myQ
#Qminus = np.gradient(Q1M)
zbarProtectionLeg = self.myZ
out = 0
for i in range(1, zbarProtectionLeg.shape[0]):
#out = -Qminus[i] * zbarProtectionLeg.iloc[i]*float(1/365)
out = out - (Q1M.iloc[i] -
Q1M.iloc[i - 1]) * zbarProtectionLeg.iloc[i]
## Calculate the PV of the premium leg using the bond class
print(out)
return out
def CDOPortfolio(self):
self.setParameters(R=self.Rs[0],
rating=self.ratings[0],
coupon=self.coupons[0],
beta=self.betas[0],
start_date=start_dates[0],
referenceDate=referenceDates[0],
end_date=end_dates[0],
freq=self.freqs[0])
## price CDOs using LHP
Q_now1 = self.getQ(start_date=self.start_dates[0],
referenceDate=self.referenceDates[0],
end_date=self.end_dates[0],
freq=self.freqs[0],
coupon=self.coupons[0],
rating=self.ratings[0],
R=self.Rs[0])
## Estimate default probabilites from Qtranche list ###
## Assume that lambda is constant over a small period of time
def getApproxDefaultProbs(Qvals, freq, tvalues):
t_start = tvalues[0]
delay = self.myScheduler.extractDelay(freq)
delay_days = ((t_start + delay) - t_start).days
## Estimate constant lambda
lam = -(1 / delay_days) * np.log(Qvals[t_start])
Qvals = [
((Qvals[t_start] * exp(-lam * (t - t_start).days)) / Qvals[t])
for t in tvalues
]
return (Qvals)
########################################################
print(Q_now1)
### Create Q dataframe
tvalues = Q_now1.index.tolist()
Cs = pd.Series(Q_now1, index=tvalues)
for cds_num in range(1, len(Fs)):
Q_add = self.getQ(start_date=self.start_dates[cds_num],
referenceDate=self.referenceDates[cds_num],
end_date=self.end_dates[cds_num],
freq=self.freqs[cds_num],
coupon=self.coupons[cds_num],
rating=self.ratings[cds_num],
R=self.Rs[cds_num])
Q_add = pd.Series(Q_add, index=tvalues)
Cs = pd.concat([Cs, Q_add], axis=1)
def expdecay(n):
return lambda t: Cs.ix[t, n]
##
#Qs = [expdecay(0),expdecay(1)]
Qs = [expdecay(n) for n in range(0, Cs.shape[1])]
self.getZ_Vasicek()
###### LHP Method #####################################################################
Rs_mean = np.mean(self.Rs)
betas_mean = np.mean(betas)
lhpcurve = [
self.Q_lhp(t, self.K1, self.K2, R=Rs[0], beta=betas[0], Q=Qs[0])
for t in tvalues
]
lhpcurve = pd.Series(lhpcurve, index=tvalues)
lhpcurve = getApproxDefaultProbs(lhpcurve,
freq=self.freq,
tvalues=tvalues)
lhpcurve = pd.Series(lhpcurve, index=tvalues)
ProtectionLeg = self.getProtectionLeg(myQ=lhpcurve)
PremiumLeg = self.getPremiumLegZ(myQ=lhpcurve)
spreads = ProtectionLeg / PremiumLeg
print("The spread for LHP is: ", 10000 * spreads, ".")
########################################################################################
###### Gaussian Method #####################################################################
print('Gaussian progression: ', end="")
gaussiancurve = [
self.Q_gauss(t,
self.K1,
self.K2,
Fs=self.Fs,
Rs=self.Rs,
betas=self.betas,
Qs=Qs) for t in tvalues
]
gaussiancurve = pd.Series(gaussiancurve, index=tvalues)
gaussiancurve = getApproxDefaultProbs(gaussiancurve,
freq=self.freq,
tvalues=tvalues)
gaussiancurve = pd.Series(gaussiancurve, index=tvalues)
ProtectionLeg = self.getProtectionLeg(myQ=gaussiancurve)
PremiumLeg = self.getPremiumLegZ(myQ=gaussiancurve)
spreads = ProtectionLeg / PremiumLeg
print("The spread for Gaussian is: ", 10000 * spreads, ".")
########################################################################################
###### Adjusted Binomial Method #####################################################################
adjustedbinomialcurve = [
self.Q_adjbinom(t,
self.K1,
self.K2,
Fs=self.Fs,
Rs=self.Rs,
betas=self.betas,
Qs=Qs) for t in tvalues
]
adjustedbinomialcurve = pd.Series(adjustedbinomialcurve, index=tvalues)
adjustedbinomialcurve = getApproxDefaultProbs(adjustedbinomialcurve,
freq=self.freq,
tvalues=tvalues)
adjustedbinomialcurve = pd.Series(adjustedbinomialcurve, index=tvalues)
#adjustedbinomialcurve = adjustedbinomialcurve.to_frame(self.freqs[0])
ProtectionLeg = self.getProtectionLeg(myQ=adjustedbinomialcurve)
PremiumLeg = self.getPremiumLegZ(myQ=adjustedbinomialcurve)
spreads = ProtectionLeg / PremiumLeg
print("The spread for Ajusted Binomial is: ", 10000 * spreads, ".")
########################################################################################
###### Exact Method #####################################################################
exactcurve = [
self.Q_exact(t,
self.K1,
self.K2,
Fs=self.Fs,
Rs=self.Rs,
betas=self.betas,
Qs=Qs) for t in tvalues
]
exactcurve = pd.Series(exactcurve, index=tvalues)
exactcurve = getApproxDefaultProbs(exactcurve,
freq=self.freq,
tvalues=tvalues)
exactcurve = pd.Series(exactcurve, index=tvalues)
#exactcurve = exactcurve.to_frame(self.freqs[0])
ProtectionLeg = self.getProtectionLeg(myQ=exactcurve)
PremiumLeg = self.getPremiumLegZ(myQ=exactcurve)
spreads = ProtectionLeg / PremiumLeg
print("The spread for Exact is: ", 10000 * spreads, ".")
class IRSwap(object):
def __init__(self,
startDate,
endDate,
referenceDate,
effectiveDate,
freq,
notional,
recovery=0.4):
"""
effective date is the start of the payments, startDate is when the contract is entered, endDate is maturity
referenceDate is the date when the PV is taken
We are paying a fixed rate to receive a floating rate
"""
self.recovery = recovery
self.simNum = 10
self.xR = []
self.xQ = []
# use MC to generate scenarios for exposure
self.mcSim = MC_Vasicek_Sim()
#self.mcSim.setVasicek(minDay=startDate,maxDay=endDate,x=xR,t_step=1.0/365, simNumber=self.simNum)
# z is discount curve
self.zCurve = []
self.swapRate = []
self.freq = freq
self.notional = notional
self.fixedLeg = []
self.floatingLeg = []
self.startDate = startDate
self.endDate = endDate
self.referenceDate = referenceDate
self.effctiveDate = effectiveDate
self.initialSpread = []
self.myScheduler = Scheduler()
self.datelist = pd.date_range(start=effectiveDate,
end=endDate,
freq=freq)
def getScheduleComplete(self):
self.datelist = self.myScheduler.getSchedule(
start=self.startDate,
end=self.endDate,
freq=self.freq,
referencedate=self.referenceDate)
self.ntimes = len(self.datelist)
fullset = sorted(
set(self.datelist).union([self.referenceDate]).union([
self.startDate
]).union([self.endDate]).union([self.referenceDate]))
return fullset, self.datelist
def setLibor(self, libor):
self.zCurve = libor / libor.loc[self.referenceDate]
def setxR(self, xR):
self.xR = xR
self.mcSim.setVasicek(minDay=self.startDate,
maxDay=self.endDate,
x=xR,
t_step=1.0 / 365,
simNumber=self.simNum)
def setSwapRate(self):
# getting initial spread at time zero
floatLegPV = (self.zCurve.loc[self.effctiveDate,
0]) - (self.zCurve.loc[self.endDate, 0])
fixedLegPV = 0
delta = (self.datelist[1] - self.datelist[0]).days / 365
for payDate in self.datelist:
fixedLegPV += delta * self.zCurve.loc[payDate.date(), 0]
swapRate = floatLegPV / fixedLegPV
self.swapRate = swapRate
return
def setCashFlows(self):
fixedLegCF = np.ones(len(self.datelist)) * self.swapRate
floatLegCF = []
delta = (self.datelist[1] - self.datelist[0]).days / 365
for payDate in self.datelist:
if payDate.date() == self.endDate:
floatLegCF.append(
((self.zCurve.loc[payDate.date(), 0] / self.zCurve.loc[
payDate.date() + timedelta(delta * 365), 0]) - 1) /
delta)
else:
floatLegCF.append(
(self.zCurve.loc[payDate.date(), 0] / self.zCurve.loc[
(payDate + 1).date(), 0] - 1) / delta)
fixedLegCF = pd.DataFrame(data=fixedLegCF, index=self.datelist)
floatLegCF = pd.DataFrame(data=floatLegCF, index=self.datelist)
self.fixedLeg = fixedLegCF
self.floatingLeg = floatLegCF
return
def getExposure(self):
fullDate = pd.date_range(start=self.startDate,
end=self.endDate,
freq=self.freq)
EE = np.zeros((len(fullDate), self.simNum))
for i in range(0, self.simNum):
zCurveNew = self.mcSim.getLibor()
row = 0
for day in fullDate:
if day < self.datelist[0]:
npv = (np.sum(
(self.floatingLeg - self.fixedLeg).values.ravel() *
zCurveNew.loc[self.datelist, 0].values))
elif day >= self.datelist[0] and day < self.datelist[-1]:
fixedPartial = self.fixedLeg.loc[day.date():]
floatPartial = self.floatingLeg.loc[day.date():]
npv = (np.sum(
(floatPartial - fixedPartial).values.ravel() *
zCurveNew.loc[fixedPartial.index, 0].values))
else:
npv = 0
#if npv < 0:
# npv = 0
EE[row, i] = npv
row += 1
EE = pd.DataFrame(data=EE, index=fullDate)
self.fullDate = fullDate
self.fullExposure = EE
self.avgExposure = EE.mean(axis=1)
return
def getCVA(self, survCurve):
# CVA = LGD * EE * PD * Discount, LGD =1-R
CVA = self.notional * (
1 - self.recovery) * self.avgExposure.values * survCurve.loc[
self.fullDate].values * self.zCurve.loc[self.fullDate,
0].values
CVA = pd.DataFrame(data=CVA, index=self.fullDate)
self.CVA = CVA
return
from IPython.core.pylabtools import figsize
figsize(15, 4)
from pandas import ExcelWriter
import numpy.random as nprnd
from pprint import pprint
t_step = 1.0 / 365.0
simNumber = 10
trim_start = date(2005, 3, 10)
trim_end = date(2010, 12, 31) # Last Date of the Portfolio
start = date(2005, 3, 10)
referenceDate = date(2005, 3, 10)
myScheduler = Scheduler()
ReferenceDateList = myScheduler.getSchedule(start=referenceDate,
end=trim_end,
freq="1M",
referencedate=referenceDate)
# Create Simulator
xOIS = [3.0, 0.07536509, -0.208477, 0.07536509]
myVasicek = MC_Vasicek_Sim(datelist=[trim_start, trim_end],
x=xOIS,
simNumber=simNumber,
t_step=1 / 365.0)
#myVasicek.setVasicek(x=xOIS,minDay=trim_start,maxDay=trim_end,simNumber=simNumber,t_step=1/365.0)
myVasicek.getLibor()
# Create Coupon Bond with several startDates.
SixMonthDelay = myScheduler.extractDelay("6M")
TwoYearsDelay = myScheduler.extractDelay("2Y")
startDates = [
referenceDate + nprnd.randint(0, 3) * SixMonthDelay for r in range(10)
class CDS(object):
def __init__(self,
start_date,
end_date,
freq,
coupon,
referenceDate,
rating,
R=.4):
### Parameters passed to external functions
self.start_date = start_date
self.end_date = end_date
self.freq = freq
self.R = R
self.notional = 1
self.fee = fee
self.rating = rating
self.coupon = coupon
self.referenceDate = referenceDate
self.observationDate = referenceDate
## Get datelist ##
self.myScheduler = Scheduler()
# ReferenceDateList = self.myScheduler.getSchedule(start=referenceDate,end=end_date,freq=freq, referencedate=referenceDate)
## Delay start and maturity
delay = self.myScheduler.extractDelay(self.freq)
cashFlowDays = self.myScheduler.extractDelay("3M")
## Delay maturity and start date
# self.start_date = self.start_date +SixMonthDelay
# self.maturity =self.start_date + delay
self.maturity = self.start_date + delay
fulllist, datelist = self.getScheduleComplete()
self.datelist = datelist
self.portfolioScheduleOfCF = fulllist
self.myZ = None
self.myQ = None
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////// SET FUNCTIONS ///////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
def setZ(self, Zin):
## Zin needs to be a pandas dataframe
self.myZ = Zin
def setQ(self, Qin):
self.myQ = Qin
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////// GET FUNCTIONS ///////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
# ////////////////////////////////////////////////////////////////////////////////////////////#
# //////////////// Get Vasicek simulated Z(t,t_j)
def getZ_Vasicek(self):
### Get Z(t,t_i) for t_i in datelist #####
## Simulate Vasicek model with paramters given in workspace.parameters
# xR = [5.0, 0.05, 0.01, 0.05]
# kappa = x[0]
# theta = x[1]
# sigma = x[2]
# r0 = x[3]
vasicekMC = MC_Vasicek_Sim(
datelist=[self.referenceDate, self.maturity],
x=xR,
simNumber=100,
t_step=t_step)
self.myZ = vasicekMC.getLibor()
self.myLibor = self.myZ
self.myZ = self.myZ.loc[:, 0]
## get Libor Z for reference dates ##
# self.myZ = vasicekMC.getSmallLibor(datelist= self.portfolioScheduleOfCF).loc[:,0]
# //////////////// Get Corporates simulated Q(t,t_j)
def getQ_Corporate(self):
## Use CorporateDaily to get Q for referencedates ##
# print("GET Q")
# print(self.portfolioScheduleOfCF)
myQ = CorporateRates()
myQ.getCorporatesFred(trim_start=self.referenceDate,
trim_end=self.end_date)
## Return the calculated Q(t,t_i) for bonds ranging over maturities for a given rating
daterange = pd.date_range(start=self.referenceDate,
end=self.maturity).date
self.myQ = myQ.getCorporateQData(rating=self.rating,
datelist=daterange,
R=self.R)
return (self.myQ)
# //////////////// Get Premium leg Z(t_i)( Q(t_(i-1)) + Q(t_i) )
def getPremiumLegZ(self):
## Check if Z and Q exists
if self.myZ is None:
self.getZ_Vasicek()
if self.myQ is None:
self.getQ_Corporate()
## Choose 1month Q
'''
Q1M = self.myQ[self.freq]
# Q1M = self.myQ["QTranche"]
timed = self.portfolioScheduleOfCF[self.portfolioScheduleOfCF.index(self.referenceDate):]
Q1M = Q1M.loc[timed]
Q1M = Q1M.cumprod(axis=0)
zbarPremLeg = self.myZ / self.myZ.loc[self.referenceDate]
zbarPremLeg = zbarPremLeg.loc[timed]
## Calculate Q(t_i) + Q(t_(i-1))
out = 0
for i in range(1, len(Q1M)):
out = out + (Q1M[(i - 1)] + Q1M[i]) * float((timed[i] - timed[i - 1]).days / 365) * zbarPremLeg[i]
## Calculate the PV of the premium leg using the bond class
# zbarPremLeg = zbarPremLeg.cumsum(axis=0)
zbarPremLeg = pd.DataFrame(zbarPremLeg, index=timed)
# print("Premium LEg")
PVpremiumLeg = out * (1 / 2)
# print(PVpremiumLeg)
## Get coupon bond ###
return PVpremiumLeg
'''
Q1M = self.myQ[self.freq]
# Q1M = self.myQ["QTranche"]
timed = self.portfolioScheduleOfCF[self.portfolioScheduleOfCF.
index(self.referenceDate):]
Q1M = Q1M.loc[timed]
Q1M = Q1M.cumprod()
zbarPremLeg = self.myZ / self.myZ.loc[self.referenceDate]
zbarPremLeg = zbarPremLeg.loc[timed]
## Calculate Q(t_i) + Q(t_(i-1))
Qplus = []
out = 0
for i in range(1, len(Q1M)):
out = out + (Q1M[(i - 1)] + Q1M[i]) * float(
(timed[i] - timed[i - 1]).days / 365) * zbarPremLeg[i]
## Calculate the PV of the premium leg using the bond class
# zbarPremLeg = zbarPremLeg.cumsum(axis=0)
zbarPremLeg = pd.DataFrame(zbarPremLeg, index=timed)
# print("Premium LEg")
PVpremiumLeg = out * (1 / 2)
# print(PVpremiumLeg)
## Get coupon bond ###
return PVpremiumLeg
# //////////////// Get Protection leg Z(t_i)( Q(t_(i-1)) - Q(t_i) )
def getProtectionLeg(self):
if self.myZ is None:
self.getZ_Vasicek()
if self.myQ is None:
self.getQ_Corporate()
# Q1M = self.myQ["QTranche"]
## Calculate Q(t_i) + Q(t_(i-1))
# Qminus = np.gradient(np.array(Q1M))
# print(Qminus)
# QArray = np.array(Q1M)
# QArray = np.insert(QArray, obj = 0, values = 1)
# print(QArray)
# Q1M = self.myQ["QTranche"]
'''
Q1M = self.myQ[self.freq]
Q1M = Q1M.cumprod()
timed = Q1M.index.tolist()
timed = self.portfolioScheduleOfCF[self.portfolioScheduleOfCF.index(self.referenceDate):]
Q1M = Q1M.loc[timed]
zbarPremLeg = self.myZ / self.myZ.loc[self.referenceDate]
zbarPremLeg = zbarPremLeg.loc[timed]
## Calculate Q(t_i) + Q(t_(i-1))
Qplus = []
out = 0
for i in range(1, len(Q1M)):
out = out + (Q1M[(i-1)] - Q1M[(i)]) * float((timed[i] - timed[i - 1]).days / 365) * zbarPremLeg[i]
return(out)
## Calculate Z Bar ##
Qminus = np.gradient(Q1M)
zbarProtectionLeg = self.myZ / self.myZ.loc[self.referenceDate]
for i in range(1,zbarProtectionLeg.shape[0]):
zbarProtectionLeg.iloc[i] = -Qminus[i] * zbarProtectionLeg.iloc[i] * (1/365)
## Calculate the PV of the premium leg using the bond class
zbarProtectionLeg = zbarProtectionLeg.cumsum(axis=0)
zbarProtectionLeg = pd.DataFrame(zbarProtectionLeg, index=Q1M.index)
PVprotectionLeg = (1 - self.R) * zbarProtectionLeg
## Get coupon bond ###
return PVprotectionLeg.loc[self.maturity]
'''
Q1M = self.myQ[self.freq]
Q1M = Q1M.cumprod()
Qminus = np.gradient(Q1M)
zbarProtectionLeg = self.myZ / self.myZ.loc[self.referenceDate]
for i in range(zbarProtectionLeg.shape[0]):
zbarProtectionLeg.iloc[
i] = -Qminus[i] * zbarProtectionLeg.iloc[i] * (1 / 365)
## Calculate the PV of the premium leg using the bond class
zbarProtectionLeg = zbarProtectionLeg.cumsum(axis=0)
zbarProtectionLeg = pd.DataFrame(zbarProtectionLeg, index=Q1M.index)
PVprotectionLeg = (1 - self.R) * zbarProtectionLeg
## Get coupon bond ###
return PVprotectionLeg.loc[self.maturity]
# /////////////////////// Functions to get the exposure sum [delta Z(t,t_j)( Q(t,t_(j-1)) +/- Q(t,t_j) )
# ////// These are copied from Coupon bond
def getScheduleComplete(self):
self.datelist = self.myScheduler.getSchedule(
start=self.start_date,
end=self.maturity,
freq='3M',
referencedate=self.referenceDate)
self.ntimes = len(self.datelist)
fullset = list(
sorted(
list(
set(self.datelist).union([self.referenceDate]).union([
self.start_date
]).union([self.maturity]).union([self.observationDate]))))
return fullset, self.datelist
# /////// Get exposure
def getExposure(self, referencedate, libor):
self.ntrajectories = np.shape(libor)[1]
self.ones = np.ones(shape=[self.ntrajectories])
deltaT = np.zeros(self.ntrajectories)
if self.ntimes == 0:
pdzeros = pd.DataFrame(data=np.zeros([1, self.ntrajectories]),
index=[referencedate])
self.pv = pdzeros
self.pvAvg = 0.0
self.cashFlows = pdzeros
self.cashFlowsAvg = 0.0
return self.pv
for i in range(1, self.ntimes):
deltaTrow = ((self.datelist[i] - self.datelist[i - 1]).days /
365) * self.ones
deltaT = np.vstack((deltaT, deltaTrow))
self.cashFlows = self.coupon * deltaT
principal = self.ones
if self.ntimes > 1:
self.cashFlows[-1:] += principal
else:
self.cashFlows = self.cashFlows + principal
if (self.datelist[0] <= self.start_date):
self.cashFlows[0] = -self.fee * self.ones
if self.ntimes > 1:
self.cashFlowsAvg = self.cashFlows.mean(axis=1) * self.notional
else:
self.cashFlowsAvg = self.cashFlows.mean() * self.notional
pv = self.cashFlows * libor.loc[self.datelist]
self.pv = pv.sum(axis=0) * self.notional
self.pvAvg = np.average(self.pv) * self.notional
return self.pv
# ///// Get the calculated Market to Market based on spread
def getValue(self, spread=1, R=0, buyer=True):
## Assume V(t) = S/2 sum Z(t_i) (Q(t_i) + Q(t_{i-1})) - (1-R)sum Z(t_i) (Q(t_{i-1}) - Q(t_{i}))
## Premium leg = S/2 sum Z(t_i) (Q(t_i) + Q(t_{i-1}))
## Protection leg =sum Z(t_i) (Q(t_i) + Q(t_{i-1}))
premiumLeg = self.getPremiumLegZ()
protectionLeg = self.getProtectionLeg()
mtm = (spread / 2) * premiumLeg - (1 - R) * protectionLeg
if buyer is True:
return mtm
else:
return -mtm
def getSpread(self):
out = self.getProtectionLeg() / self.getPremiumLegZ()
return out.values[0]
def changeGuessForSpread(self, x):
'''
inputs a x list of guesses for the Vasicek simulator than changes the myQ
'''
vasicekMC = MC_Vasicek_Sim(
datelist=[self.referenceDate, self.maturity],
x=x,
simNumber=20,
t_step=t_step)
self.myQ = vasicekMC.getLibor()[0]
self.myQ = pd.DataFrame(self.myQ, index=self.myQ.index)
self.myQ.columns = [self.freq]
spread = self.bootProtec() / self.bootPrem()
return spread.values[0]
def bootProtec(self):
Q1M = self.myQ[self.freq]
Q1M = Q1M.cumprod()
Qminus = np.gradient(Q1M)
zbarProtectionLeg = self.myZ / self.myZ.loc[self.referenceDate]
for i in range(zbarProtectionLeg.shape[0]):
zbarProtectionLeg.iloc[
i] = -Qminus[i] * zbarProtectionLeg.iloc[i] * (1 / 365)
## Calculate the PV of the premium leg using the bond class
zbarProtectionLeg = zbarProtectionLeg.cumsum(axis=0)
zbarProtectionLeg = pd.DataFrame(zbarProtectionLeg, index=Q1M.index)
PVprotectionLeg = (1 - self.R) * zbarProtectionLeg
## Get coupon bond ###
return PVprotectionLeg.loc[self.maturity]
def bootPrem(self):
Q1M = self.myQ[self.freq]
# Q1M = self.myQ["QTranche"]
timed = self.portfolioScheduleOfCF[self.portfolioScheduleOfCF.
index(self.referenceDate):]
Q1M = Q1M.loc[timed]
Q1M = Q1M.cumprod()
zbarPremLeg = self.myZ / self.myZ.loc[self.referenceDate]
zbarPremLeg = zbarPremLeg.loc[timed]
## Calculate Q(t_i) + Q(t_(i-1))
Qplus = []
out = 0
for i in range(1, len(Q1M)):
out = out + (Q1M[(i - 1)] + Q1M[i]) * float(
(timed[i] - timed[i - 1]).days / 365) * zbarPremLeg[i]
## Calculate the PV of the premium leg using the bond class
# zbarPremLeg = zbarPremLeg.cumsum(axis=0)
zbarPremLeg = pd.DataFrame(zbarPremLeg, index=timed)
# print("Premium LEg")
PVpremiumLeg = out * (1 / 2)
# print(PVpremiumLeg)
## Get coupon bond ###
return PVpremiumLeg
observationdate = minDay = date(2005,1,10) # Observation Date
maxDay = date(2010,1,10) # Last Date of the Portfolio
start = date(2005, 3, 30)
maturity = start+ myScheduler.extractDelay("1Y")
referenceDate = date(2005, 5, 3) # 6 months after trim_start
simNumber = 5
R = 0.4
inArrears = True
freq = '3M'
t_step = 1.0/365
simNumber=5
coupon = 0.08
fee= 1.0
xR = [3.0, 0.05, 0.04, 0.03]
datelist = myScheduler.getSchedule(start=start, end=maxDay, freq=freq, referencedate=referenceDate)
myBond = CouponBond(fee=fee, start=start, maturity=maturity, coupon=coupon, freq="3M", referencedate=referenceDate, observationdate = observationdate)
fulllist, datelist = myBond.getScheduleComplete()
myMC = MC_Vasicek_Sim()
myMC.setVasicek(x=xR, minDay=minDay, maxDay=maxDay, simNumber=simNumber, t_step=t_step)
myMC.getLibor()
libor = myMC.getSmallLibor(datelist=fulllist)
myBond.setLibor(libor=libor)
myBond.getExposure(referenceDate)
myBond.getYield(price=1)
print(myBond.getLiborAvg())
a=1
class TestBond(TestCase):
