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,
endDate=trim_end,
referenceDate=referenceDate,
effectiveDate=effDay,
rating="AAA",
freq=freq,
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 CDS(object):
def __init__(self,
start,
end,
reference,
recovery,
rating,
notional,
freq="1M"):
self.numSim = 10
self.t_step = 1.0 / 365
#z curve is for discounting
self.zCurve = []
#q curve is for survival prob of the reference entity
self.qCurve = []
self.start = start
self.end = end
self.reference = reference
self.freq = freq
self.rating = rating
self.notional = notional
# mcSim used for simulating default prob, interest rate
# xR should already be calibrated
self.xR = []
# xQ we need to calibrate inside CDS
self.xQ = []
self.mcSim = MC_Vasicek_Sim()
self.mcSimSurvival = MC_Vasicek_Sim()
#self.mcSim.setVasicek(minDay=startDate, maxDay=endDate, x=xR, t_step=1.0 / 365, simNumber=self.simNum)
#self.mcSimSurvival.setVasicek(minDay=startDate, maxDay=endDate, x=xR, t_step=1.0 / 365, simNumber=self.simNum)
self.dateList = pd.date_range(start=start, end=end, freq=freq)
self.recovery = recovery
def setCorpData(self, corpData):
self.corpData = corpData.loc[self.rating, :, "1 MO"]
def setLibor(self, libor):
self.zCurve = libor / libor.loc[self.reference]
def setxR(self, xR):
self.xR = xR
self.mcSim.setVasicek(minDay=self.start,
maxDay=self.end,
x=self.xR,
simNumber=self.numSim,
t_step=self.t_step)
def setxQ(self, xQ):
res = optimize.fmin(func=self.mcSimSurvival.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.mcSimSurvival.setVasicek(minDay=self.start,
maxDay=self.end,
x=self.xQ,
simNumber=self.numSim,
t_step=self.t_step)
def setQCurve(self):
self.qCurve = self.mcSimSurvival.getLibor().loc[:, 0]
return
def getDefaultLegPV(self):
interimSum = 0
for payDates in self.dateList[1:]:
interimSum += self.zCurve.loc[payDates.date(), 0] * (
self.qCurve.loc[(payDates - 1).date()] -
self.qCurve.loc[payDates.date()])
defaultLeg = (1 - self.recovery) * interimSum
return defaultLeg
def getFeeLegPV(self):
delta = (self.dateList[1] - self.dateList[0]).days / 365
interimSum = 0
for payDate in self.dateList[1:]:
interimSum += self.zCurve.loc[payDate.date(), 0] * delta * (
self.qCurve.loc[(payDate - 1).date()] +
self.qCurve.loc[payDate.date()])
feeLeg = 0.5 * interimSum
return feeLeg
def getSpread(self):
spread = self.getDefaultLegPV() / self.getFeeLegPV()
self.spread = spread
return spread
def setCF(self):
feeLegCF = np.ones(len(self.dateList)) * self.spread
defaultLegCF = np.ones(len(self.dateList)) * (
1 - self.recovery) * self.qCurve.loc[self.dateList].values
self.feeLeg = pd.DataFrame(data=feeLegCF, index=self.dateList)
self.defaultLeg = pd.DataFrame(data=defaultLegCF, index=self.dateList)
return
def getExposure(self):
#PV of protection leg - fee leg
#use survivalCurve passed in as the survival prob of the reference entitity
#simulate the default probability of the counterparty - newQcurve
fullDate = pd.date_range(start=self.start,
end=self.end,
freq=self.freq)
EE = np.zeros((len(self.dateList), self.numSim))
for i in range(0, self.numSim):
row = 0
newZCurve = self.mcSim.getLibor()
newQCurve = self.mcSimSurvival.getLibor()
survivalCurve = self.qCurve
for day in fullDate:
if day == fullDate[0]:
#feePV - pay fee as long as counter and reference do not default
feePV = np.transpose(
self.feeLeg.values).ravel() * newZCurve.loc[
self.dateList, 0].values * survivalCurve.loc[
self.dateList].values * newQCurve.loc[
self.dateList, 0].values
#defaultPV - recover a portion of the notional given the refernce defaults and the counterparty does NOT
defaultPV = (1 - self.recovery) * np.transpose(
self.defaultLeg.values).ravel() * self.zCurve.loc[
self.dateList, 0].values * (
np.ones(len(self.dateList)) -
survivalCurve.loc[self.dateList].values
) * newQCurve.loc[self.dateList, 0].values
elif day > fullDate[0] and day < fullDate[-1]:
partialFee = self.feeLeg.loc[day.date():]
partialDefault = self.defaultLeg.loc[day.date():]
feePV = np.transpose(
partialFee.values).ravel() * newZCurve.loc[
partialFee.index, 0].values * survivalCurve.loc[
partialFee.index].values * newQCurve.loc[
partialFee.index, 0].values
defaultPV = (1 - self.recovery) * np.transpose(
partialDefault.values).ravel() * self.zCurve.loc[
partialFee.index, 0].values * (
np.ones(len(partialFee.index)) -
survivalCurve.loc[partialFee.index].values
) * newQCurve.loc[partialFee.index, 0].values
else:
feePV = 0
defaultPV = 0
npv = np.sum(defaultPV - feePV)
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)
def getCVA(self):
self.CVA = self.notional * (
1 - self.recovery) * self.avgExposure.values * self.zCurve.loc[
self.fullDate,
0].values * self.qCurve.loc[self.fullDate].values
return
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
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
myVasicek = MC_Vasicek_Sim()
xOIS = [3.0, 0.07536509, -0.208477, 0.07536509]
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)
]
# For debugging uncomment this to choose a single date for the forward bond
# print(startDates)
startDates = [
date(2005, 3, 10) + SixMonthDelay,
coupon = 0.08
fee = 1.0
xR = [3.0, 0.05, 0.04, 0.03]
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)
class TestBond(TestCase):
def test01_PV(self):
myPV = myBond.getPV(referencedate=referenceDate)
print(myPV)
print(myBond.pv)
def test00_getLiborAvg(self):
print(myBond.getLiborAvg(yieldIn=0.05, datelist=datelist))