def test_HybridSimulation(self):
times = np.concatenate([np.linspace(0.0, 10.0, 11), [10.5]])
nPaths = 2**13
seed = 314159265359
# risk-neutral simulation
print('')
mcSim = McSimulation(self.model, times, nPaths, seed, False)
#
T = 10.0
P = Pay(Fixed(1.0), T)
fw, err = fwd(mcSim, P)
# domestic numeraire
print('1.0 @ %4.1lfy %8.6lf - mc_err = %8.6lf' % (T, fw, err))
# foreign assets
for k, alias in enumerate(self.model.forAliases):
p = Asset(T, alias)
xT = self.model.forAssetModels[k].X0 * \
self.model.forRatesModels[k].yieldCurve.discount(T) / \
self.model.domRatesModel.yieldCurve.discount(T)
fw, err = fwd(mcSim, p)
print(alias +
' @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(T, fw, xT, err))
# domestic Libor rate
Tstart = 10.0
Tend = 10.5
L = Pay(LiborRate(T, Tstart, Tend, alias='EUR'), Tend)
fw, err = fwd(mcSim, L)
Lref = (mcSim.model.domRatesModel.yieldCurve.discount(Tstart) / \
mcSim.model.domRatesModel.yieldCurve.discount(Tend) - 1) / \
(Tend - Tstart)
print('L_EUR @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(T, fw, Lref, err))
# foreign Lbor rates
for k, alias in enumerate(self.model.forAliases):
L = Pay(
LiborRate(T, Tstart, Tend, alias=alias) * Asset(Tend, alias),
Tend)
fw, err = fwd(mcSim, L)
fw *= mcSim.model.domRatesModel.yieldCurve.discount(Tend) / \
mcSim.model.forRatesModels[k].yieldCurve.discount(Tend) / \
mcSim.model.forAssetModels[k].X0
err *= mcSim.model.domRatesModel.yieldCurve.discount(Tend) / \
mcSim.model.forRatesModels[k].yieldCurve.discount(Tend) / \
mcSim.model.forAssetModels[k].X0
Lref = (mcSim.model.forRatesModels[k].yieldCurve.discount(Tstart) / \
mcSim.model.forRatesModels[k].yieldCurve.discount(Tend) - 1) / \
(Tend - Tstart)
print('L_%s @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(alias, T, fw, Lref, err))
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 test_HybridVolAdjusterCalculation(self):
model = copy.deepcopy(self.model)
# model = copy.deepcopy(self.gaussianModel)
hybVolAdjTimes = np.linspace(0.0, 20.0, 21)
model.recalculateHybridVolAdjuster(hybVolAdjTimes)
plt.plot(model.hybAdjTimes, model.hybVolAdj[0], 'r*', label='USD')
plt.plot(model.hybAdjTimes, model.hybVolAdj[1], 'b*', label='GBP')
plt.legend()
#
times = np.linspace(0.0, 20.0, 101)
plt.plot(times, [model.hybridVolAdjuster(0, t) for t in times], 'r-')
plt.plot(times, [model.hybridVolAdjuster(1, t) for t in times], 'b-')
plt.show()
#
# return
times = np.linspace(0.0, 10.0, 11)
nPaths = 2**13
seed = 314159265359
# risk-neutral simulation
print('')
mcSim = McSimulation(model, times, nPaths, seed, False)
#
T = 10.0
for k, alias in enumerate(model.forAliases):
# ATM forward
xT = model.forAssetModels[k].X0 * \
model.forRatesModels[k].yieldCurve.discount(T) / \
model.domRatesModel.yieldCurve.discount(T)
K = Fixed(xT)
Z = Fixed(0.0)
C = Pay(Max(Asset(T, alias) - K, Z), T)
fw, err = fwd(mcSim, C)
vol = BlackImpliedVol(fw, xT, xT, T, 1.0)
vega = BlackVega(xT, xT, vol, T)
err /= vega
volRef = model.forAssetModels[k].sigma
print('C_%s @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(alias, T, vol, volRef, err))
P = Pay(Max(K - Asset(T, alias), Z), T)
fw, err = fwd(mcSim, P)
vol = BlackImpliedVol(fw, xT, xT, T, -1.0)
vega = BlackVega(xT, xT, vol, T)
err /= vega
volRef = model.forAssetModels[k].sigma
print('P_%s @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(alias, T, vol, volRef, err))
def test_SpreadSimulation(self):
times = np.linspace(0.0, 10.0, 11)
nPaths = 2**10
seed = 1234
# risk-neutral simulation
print('')
mcSim = McSimulation(self.model,times,nPaths,seed,False)
#
T = 10.0
P = Pay(Fixed(1.0),T)
pv, err = fwd(mcSim,P)
# domestic numeraire
print('1.0 @ %4.1lfy %8.6lf - mc_err = %8.6lf' % (T,pv,err))
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
]
curve = YieldCurve(0.03)
path = DcfModel(curve).path()
cfPVs = np.array([p.discountedAt(path) for p in cfs])
discounts0 = np.array([curve.discount(t + dT0) for t in liborTimes])
discounts1 = np.array(
[curve.discount(t + dT0 + dT1) for t in liborTimes])
liborsCv = (discounts0 / discounts1 - 1.0) / dT1
liborsMC = cfPVs / discounts1
print('')
print(' T LiborRate ModelLibor')
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 test_payoffTimes(self):
L1 = LiborRate(1.0, 1.0, 1.5)
L2 = LiborRate(2.0, 3.0, 3.5)
P = Pay(L1 + L2 + 1.0, 5.0)
self.assertListEqual(list(P.observationTimes()), [0.0, 1.0, 2.0, 5.0])
def test_HybridVolAdjusterCalculation(self):
# we set up a hybrid model consistent to QuantLib
domAlias = 'EUR'
domModel = HWModel(0.01, 0.0050, 0.01)
forAliases = ['USD', 'GBP']
forAssetModels = [AssetModel(1.0, 0.30), AssetModel(2.0, 0.15)]
forRatesModels = [
HWModel(0.02, 0.0060, 0.02),
HWModel(0.02, 0.0070, 0.03)
]
corr = np.identity(2 * len(forAliases) + 1)
# [ EUR, USD-EUR, USD, GBP-EUR, GBP ]
# 0 1 2 3 4
# USD-EUR - EUR
corr[0, 1] = 0.5
corr[1, 0] = 0.5
# USD-EUR - USD
corr[1, 2] = -0.5
corr[2, 1] = -0.5
# EUR - USD
corr[0, 2] = -0.5
corr[2, 0] = -0.5
# GBP-EUR - EUR
corr[0, 3] = -0.5
corr[3, 0] = -0.5
# GBP-EUR - GBP
corr[3, 4] = 0.5
corr[4, 3] = 0.5
# EUR - GBP
corr[0, 4] = -0.8
corr[4, 0] = -0.8
# USD - GBP
corr[2, 4] = 0.0
corr[4, 2] = 0.0
# overwrtite
# corr = np.identity(2 * len(forAliases) + 1)
# print(corr-corr.transpose())
model = HybridModel(domAlias, domModel, forAliases, forAssetModels,
forRatesModels, corr)
hybVolAdjTimes = np.linspace(0.0, 20.0, 21)
model.recalculateHybridVolAdjuster(hybVolAdjTimes)
#plt.plot(model.hybAdjTimes,model.hybVolAdj[0], 'r*')
#plt.plot(model.hybAdjTimes,model.hybVolAdj[1], 'b*')
#
#times = np.linspace(0.0,20.0,101)
#plt.plot(times,[ model.hybridVolAdjuster(0,t) for t in times ] , 'r-')
#plt.plot(times,[ model.hybridVolAdjuster(1,t) for t in times ] , 'b-')
# plt.show()
#
times = np.linspace(0.0, 10.0, 11)
nPaths = 2**13
seed = 314159265359
# risk-neutral simulation
print('')
mcSim = McSimulation(model, times, nPaths, seed, False)
#
T = 10.0
for k, alias in enumerate(model.forAliases):
# ATM forward
xT = model.forAssetModels[k].X0 * \
model.forRatesModels[k].yieldCurve.discount(T) / \
model.domRatesModel.yieldCurve.discount(T)
K = Fixed(xT)
Z = Fixed(0.0)
C = Pay(Max(Asset(T, alias) - K, Z), T)
fw, err = fwd(mcSim, C)
vol = BlackImpliedVol(fw, xT, xT, T, 1.0)
vega = BlackVega(xT, xT, vol, T)
err /= vega
volRef = model.forAssetModels[k].sigma
print('C_%s @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(alias, T, vol, volRef, err))
P = Pay(Max(K - Asset(T, alias), Z), T)
fw, err = fwd(mcSim, P)
vol = BlackImpliedVol(fw, xT, xT, T, -1.0)
vega = BlackVega(xT, xT, vol, T)
err /= vega
volRef = model.forAssetModels[k].sigma
print('P_%s @ %4.1lfy %8.6lf vs %8.6lf (curve) - mc_err = %8.6lf' %
(alias, T, vol, volRef, err))