def test_HullWhiteExampleTwo():
# HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3
# Replication may not be exact as I am using dates rather than times
zeroDays = [
0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922,
3287, 3653
]
zero_rates = [
5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733,
6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015
]
times = np.array(zeroDays) / 365.0
zeros = np.array(zero_rates) / 100.0
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiry_date = start_date.add_tenor("3Y")
maturity_date = start_date.add_tenor("9Y")
texp = (expiry_date - start_date) / gDaysInYear
tmat = (maturity_date - start_date) / gDaysInYear
num_time_steps = None
model = HWTree(sigma, a, num_time_steps)
vAnal = model.option_on_zcb(texp, tmat, strike, face, times, dfs)
num_time_steps = 200
model = HWTree(sigma, a, num_time_steps)
model.build_tree(texp, times, dfs)
vTree1 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike, face)
model = HWTree(sigma, a, num_time_steps + 1)
model.build_tree(texp, times, dfs)
vTree2 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike, face)
vTreeCall = (vTree1['call'] + vTree2['call']) / 2.0
vTreePut = (vTree1['put'] + vTree2['put']) / 2.0
assert round(vTreeCall, 4) == 1.0450
assert round(vAnal['call'], 4) == 1.0448
assert round(vTreePut, 4) == 1.8237
assert round(vAnal['put'], 4) == 1.8239
def test_HullWhiteExampleTwo():
# HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3
# Replication may not be exact as I am using dates rather than times
zeroDays = [
0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922,
3287, 3653
]
zero_rates = [
5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733,
6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015
]
times = np.array(zeroDays) / 365.0
zeros = np.array(zero_rates) / 100.0
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiry_date = start_date.add_tenor("3Y")
maturity_date = start_date.add_tenor("9Y")
texp = (expiry_date - start_date) / gDaysInYear
tmat = (maturity_date - start_date) / gDaysInYear
num_time_steps = None
model = HWTree(sigma, a, num_time_steps)
vAnal = model.option_on_zcb(texp, tmat, strike, face, times, dfs)
# Test convergence
num_steps_list = range(100, 500, 100)
analVector = []
treeVector = []
testCases.banner("Comparing option on zero coupon bond analytical vs Tree")
testCases.header("NUMTIMESTEP", "TIME", "VTREE_CALL", "VTREE_PUT",
"VANAL CALL", "VANAL_PUT", "CALLDIFF", "PUTDIFF")
for num_time_steps in num_steps_list:
start = time.time()
model = HWTree(sigma, a, num_time_steps)
model.build_tree(texp, times, dfs)
vTree1 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike,
face)
model = HWTree(sigma, a, num_time_steps + 1)
model.build_tree(texp, times, dfs)
vTree2 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike,
face)
end = time.time()
period = end - start
treeVector.append(vTree1['put'])
analVector.append(vAnal['put'])
vTreeCall = (vTree1['call'] + vTree2['call']) / 2.0
vTreePut = (vTree1['put'] + vTree2['put']) / 2.0
diffC = vTreeCall - vAnal['call']
diffP = vTreePut - vAnal['put']
testCases.print(num_time_steps, period, vTreeCall, vAnal['call'],
vTreePut, vAnal['put'], diffC, diffP)
