def setUp(self):
self.curve = YieldCurve(0.03)
mean = 0.03
times = np.array([ 1.0, 2.0, 5.0, 10.0 ])
vols = np.array([ 0.0060, 0.0070, 0.0080, 0.0100 ])
self.modelRiskNeutral = HullWhiteModel(self.curve, mean, times, vols)
self.modelDiscreteFwd = HullWhiteModelWithDiscreteNumeraire(self.curve, mean, times, vols)
def test_CreditHybridModel(self):
# Rates-FX
eurRates = HullWhiteModel(YieldCurve(0.015),0.03,np.array([10.0]),np.array([0.0050]))
usdRates = HullWhiteModel(YieldCurve(0.015),0.03,np.array([10.0]),np.array([0.0050]))
usdFx = AssetModel(1.25,0.15)
hybModel = HybridModel('EUR',eurRates,['USD'],[usdFx],[usdRates],np.eye(3))
# Credit
spreadLevel = 0.05
spreadCurve = YieldCurve(spreadLevel) # use 5% instantanous default probablility
mean = 0.0001 # 1bp
sigma = 0.0100 # 100bp
skew = 0.5*sigma/spreadLevel
#
spreadModel = QuasiGaussianModel(spreadCurve,1,np.array([10.0]),np.array([[sigma]]),
np.array([[skew]]),np.array([[-skew]]),np.array([0.01]),np.array([mean]),np.identity(1))
corr = np.eye(4)
corr[1,3] = -0.85 # credit-FX
corr[3,1] = -0.85
creditModel = CreditModel(hybModel,['CP'],[spreadModel],corr)
# print(creditModel.factorAliases())
#
obsTimes = np.linspace(0.0,10.0,3)
nPaths = 2
seed = 314159265359
mcSim = McSimulation(creditModel,obsTimes,nPaths,seed,True,False)
class TestHullWhiteModel(unittest.TestCase):
# set up the stage for testing the models
def setUp(self):
self.curve = YieldCurve(0.03)
mean = 0.03
times = np.array([1.0, 2.0, 5.0, 10.0])
vols = np.array([0.0060, 0.0070, 0.0080, 0.0100])
self.model = HullWhiteModel(self.curve, mean, times, vols)
def test_zeroBondPrice(self):
obsTime = 10.0
matTime = 20.0
states = [-0.10, -0.05, 0.00, 0.03, 0.07, 0.12]
refResult = [ # reference results checked against QuantLib
1.7178994273756056, 1.1153102854629025, 0.7240918839816156,
0.5587692049384843, 0.39550396436404667, 0.25677267968500767
]
for x, res in zip(states, refResult):
self.assertEqual(self.model.zeroBondPrice(obsTime, matTime, x),
res)
def test_couponBondOption(self):
excTime = 10.0
payTimes = [
11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 20.0
]
cashFlows = [0.025] * 10 + [1.0] # bond cash flows
callOrPut = 1.0 # call
strikes = [0.8, 0.9, 1.0, 1.1, 1.2]
refResult = [ # reference results checked against QuantLib
0.12572604970665557, 0.07466919528750032, 0.039969719617809936,
0.019503405494683164, 0.008804423283331253
]
for strike, res in zip(strikes, refResult):
self.assertEqual(
self.model.couponBondOption(excTime, payTimes, cashFlows,
strike, callOrPut), res)
class TestHullWhiteMonteCarlo(unittest.TestCase):
# set up the stage for testing the models
def setUp(self):
self.curve = YieldCurve(0.03)
mean = 0.03
times = np.array([ 1.0, 2.0, 5.0, 10.0 ])
vols = np.array([ 0.0060, 0.0070, 0.0080, 0.0100 ])
self.modelRiskNeutral = HullWhiteModel(self.curve, mean, times, vols)
self.modelDiscreteFwd = HullWhiteModelWithDiscreteNumeraire(self.curve, mean, times, vols)
def test_monteCarloSimulation(self):
times = np.linspace(0.0, 10.0, 11)
nPaths = 2**11
seed = 1234
# risk-neutral simulation
mcSim = McSimulation(self.modelRiskNeutral,times,nPaths,seed,showProgress=False)
discZeroBonds = np.array([
[ 1.0 / self.modelRiskNeutral.numeraire(t,x) for t,x in zip(times,path) ]
for path in mcSim.X ])
mcZeroBondsRiskNeutral = np.average(discZeroBonds,axis=0)
# discrete forward measure simulation
mcSim = McSimulation(self.modelDiscreteFwd,times,nPaths,seed,showProgress=False)
discZeroBonds = np.array([
[ 1.0 / self.modelDiscreteFwd.numeraire(t,x) for t,x in zip(times,path) ]
for path in mcSim.X ])
mcZeroBondsDiscreteFwd = np.average(discZeroBonds,axis=0)
# curve
zeroBonds = np.array([ self.curve.discount(t) for t in times ])
print('')
print(' T ZeroRate RiskNeutral DiscreteFwd')
for k, t in enumerate(times[1:]):
zeroRate = -np.log(zeroBonds[k+1])/t
riskNeutral = -np.log(mcZeroBondsRiskNeutral[k+1])/t
discreteFwd = -np.log(mcZeroBondsDiscreteFwd[k+1])/t
print(' %4.1f %6.4lf %6.4lf %6.4lf' % (t, zeroRate, riskNeutral, discreteFwd) )
self.assertAlmostEqual(zeroRate,riskNeutral,3)
self.assertAlmostEqual(zeroRate,discreteFwd,3)
def test_simulationStates(self):
times = np.array([0.0, 2.0, 5.0, 10.0])
nPaths = 2
seed = 1234
mcSim = McSimulation(self.modelRiskNeutral,times,nPaths,seed,False,showProgress=False)
# test exact values
for k, t in enumerate(times):
self.assertListEqual(list(mcSim.state(0,t)),list(mcSim.X[0][k]))
# now we allow interpolation/extrapolation
mcSim.timeInterpolation = True
# test extrapolation
self.assertListEqual(list(mcSim.state(1,-0.5)),list(mcSim.X[1][0]))
self.assertListEqual(list(mcSim.state(1,12.5)),list(mcSim.X[1][3]))
# test interpolation
self.assertListEqual(list(mcSim.state(1,1.0)),list(0.5*(mcSim.X[1][0] + mcSim.X[1][1])))
self.assertListEqual(list(mcSim.state(1,7.0)),list((0.6*mcSim.X[1][2] + 0.4*mcSim.X[1][3])))
def test_pathGeneration(self):
times = np.array([0.0, 2.0, 5.0, 10.0])
nPaths = 2
seed = 1234
mcSim = McSimulation(self.modelRiskNeutral,times,nPaths,seed,True,showProgress=False)
idx = 0
dT = 5.7
path = mcSim.path(idx)
for t in np.linspace(-1.0, 11.0, 13):
s = mcSim.state(idx,t)
self.assertEqual(path.numeraire(t),mcSim.model.numeraire(t,s))
self.assertEqual(path.zeroBond(t,t+dT,None),mcSim.model.zeroBond(t,t+dT,s,None))
def test_liborPayoff(self):
# Libor Rate payoff
liborTimes = np.linspace(0.0, 10.0, 11)
dT0 = 2.0 / 365
dT1 = 0.5
cfs = [ Pay(LiborRate(t,t+dT0,t+dT0+dT1),t+dT0+dT1) for t in liborTimes]
times = set.union(*[ p.observationTimes() for p in cfs ])
times = np.array(sorted(list(times)))
#
nPaths = 2**11
seed = 1234
# risk-neutral simulation
mcSim = McSimulation(self.modelRiskNeutral,times,nPaths,seed,showProgress=False)
#
cfPVs = np.array([
[ p.discountedAt(mcSim.path(idx)) for p in cfs ] for idx in range(nPaths) ])
cfPVs = np.average(cfPVs,axis=0)
discounts0 = np.array([ mcSim.model.yieldCurve.discount(t+dT0) for t in liborTimes ])
discounts1 = np.array([ mcSim.model.yieldCurve.discount(t+dT0+dT1) for t in liborTimes ])
liborsCv = (discounts0/discounts1 - 1.0)/dT1
liborsMC = cfPVs / discounts1
print('')
print(' T LiborRate MnteCarlo')
for k,t in enumerate(liborTimes):
print(' %4.1f %6.4lf %6.4lf' % (t, liborsCv[k], liborsMC[k]) )
self.assertAlmostEqual(liborsCv[k],liborsMC[k],2)
def HWModel(rate=0.01, vol=0.0050, mean=0.03):
curve = YieldCurve(rate)
times = np.array([ 10.0 ])
vols = np.array([ vol ])
return HullWhiteModel(curve, mean, times, vols)
def setUp(self):
self.curve = YieldCurve(0.03)
mean = 0.03
times = np.array([1.0, 2.0, 5.0, 10.0])
vols = np.array([0.0060, 0.0070, 0.0080, 0.0100])
self.model = HullWhiteModel(self.curve, mean, times, vols)