def test_RicattiAB(self):
# CIR parameters
r0 = 0.02
chi_ = 0.03
theta_ = 0.05
sigma_ = 0.10
CirModel = CoxIngersollRossModel(r0, chi_, theta_, sigma_)
# Affine Short Rate Parameters
modelTimes = np.array([10.0])
chi = np.array([chi_])
theta = np.array([theta_])
sigma = np.array([sigma_])
alpha = np.array([0.0])
beta = np.array([1.0])
AsrModel = AffineShortRateModel(r0, modelTimes, chi, theta, sigma,
alpha, beta)
#
t = np.linspace(0.0, 10.0, 11)
dt = np.linspace(0.0, 10.0, 11)
#
cirRicattiAB = np.array([
CirModel.ricattiAB(t_, t_ + dt_, 0.0, 1.0) for t_ in t
for dt_ in dt
])
AsrRicattiAB = np.array([
AsrModel.ricattiAB(t_, t_ + dt_, 0.0, 1.0) for t_ in t
for dt_ in dt
])
diff = AsrRicattiAB - cirRicattiAB
# print(diff)
# print(np.max(np.abs(diff)))
self.assertLess(np.max(np.abs(diff)), 1.4e-6)
def test_ModelCurve(self):
# CIR parameters
r0 = 0.02
chi_ = 0.07
theta_ = 0.05
sigma_ = 0.10
CirModel = CoxIngersollRossModel(r0, chi_, theta_, sigma_)
model = CirModel
T = np.linspace(0.0, 10.0, 11)
dt = 1.0 / 365.0
f = np.array([ np.log( \
model.zeroBondPrice(0.0,T_,model.r0) / model.zeroBondPrice(0.0,T_+dt,model.r0)) / dt \
for T_ in T ])
# plt.plot(T,f,label='CIR')
#
curve = YieldCurve(0.03)
model = ShiftedRatesModel(curve, CirModel)
X0 = model.initialValues()
f = np.array([ np.log( \
model.zeroBond(0.0,T_,X0,None) / model.zeroBond(0.0,T_+dt,X0,None)) / dt \
for T_ in T ])
# plt.plot(T,f,label='Shifted')
# plt.legend()
# plt.show()
# print(f - 0.03)
self.assertLess(np.max(np.abs(f - 0.03)), 7.e-14)
def test_SqrtProcessEvolution(self):
# CIR parameters
r0 = 0.02
chi_ = 0.03
theta_ = 0.05
sigma_ = 0.10
model0 = CoxIngersollRossModel(r0, chi_, theta_, sigma_,
fullTruncation)
model1 = CoxIngersollRossModel(r0, chi_, theta_, sigma_,
lognormalApproximation)
model2 = CoxIngersollRossModel(r0, chi_, theta_, sigma_,
quadraticExponential(1.5))
models = [model0, model1, model2]
# MC simulation params
t = 5.0
dt = 1.0
rt = np.linspace(0.0, 0.10, 11)
dw = np.linspace(-1.0, 1.0, 11)
for rt_ in rt:
results = []
for dw_ in dw:
res = np.zeros(3)
for k, model in enumerate(models):
X1 = np.array([0.0, 0.0])
model.evolve(t, np.array([rt_, 0.0]), dt, np.array([dw_]),
X1)
res[k] = X1[0]
results.append(res)
results = np.array(results)
#plt.plot(dw,results[:,0],label='FT')
#plt.plot(dw,results[:,1],label='LN')
#plt.plot(dw,results[:,2],label='QE')
#plt.legend()
#plt.show()
#print(np.max(np.abs(results[:,0]-results[:,1])))
#print(np.max(np.abs(results[:,1]-results[:,2])))
self.assertLess(np.max(np.abs(results[:, 0] - results[:, 1])),
0.0048)
self.assertLess(np.max(np.abs(results[:, 1] - results[:, 2])),
0.0027)
def test_ModelYieldCurve(self):
# CIR parameters
r0 = 0.02
chi_ = 0.07
theta_ = 0.05
sigma_ = 0.10
CirModel = CoxIngersollRossModel(r0, chi_, theta_, sigma_)
model = CirModel
# model = self.model
T = np.linspace(0.0, 10.0, 11)
dt = 1.0 / 365.0
f = np.array([ np.log( \
model.zeroBondPrice(0.0,T_,model.r0) / model.zeroBondPrice(0.0,T_+dt,model.r0)) / dt \
for T_ in T ])
def test_CirSimulation(self):
r0 = 0.02
chi_ = 0.07
theta_ = 0.05
sigma_ = 0.10
modelFT = CoxIngersollRossModel(r0,chi_,theta_,sigma_,fullTruncation)
modelLN = CoxIngersollRossModel(r0,chi_,theta_,sigma_,lognormalApproximation)
modelQE = CoxIngersollRossModel(r0,chi_,theta_,sigma_,quadraticExponential(1.5))
#
dT = 5.0
times = np.linspace(0.0, 10.0, 11)
zcbs = np.array([ modelFT.zeroBondPrice(0.0,T + dT,r0) for T in times ])
#
nPaths = 2**13
seed = 314159265359
# risk-neutral simulation
simFT = McSimulation(modelFT,times,nPaths,seed,showProgress=True)
simLN = McSimulation(modelLN,times,nPaths,seed,showProgress=True)
simQE = McSimulation(modelQE,times,nPaths,seed,showProgress=True)
#
zcbFT = np.mean(np.array([
[ modelFT.zeroBond(times[t],times[t]+dT,simFT.X[p,t,:],None) / modelFT.numeraire(times[t],simFT.X[p,t,:]) for t in range(len(times)) ]
for p in range(nPaths) ]), axis=0)
zcbLN = np.mean(np.array([
[ modelLN.zeroBond(times[t],times[t]+dT,simLN.X[p,t,:],None) / modelLN.numeraire(times[t],simLN.X[p,t,:]) for t in range(len(times)) ]
for p in range(nPaths) ]), axis=0)
zcbQE = np.mean(np.array([
[ modelQE.zeroBond(times[t],times[t]+dT,simQE.X[p,t,:],None) / modelQE.numeraire(times[t],simQE.X[p,t,:]) for t in range(len(times)) ]
for p in range(nPaths) ]), axis=0)
#
results = pd.DataFrame([ times, zcbs, zcbFT, zcbLN, zcbQE ]).T
results.columns = ['times', 'zcbs', 'zcbFT', 'zcbLN', 'zcbQE']
print(results)