def testBlackScholes():
valuation_date = Date(8, 5, 2015)
expiry_date = Date(15, 1, 2016)
strike_price = 130.0
stock_price = 127.62
volatility = 0.20
interest_rate = 0.001
dividend_yield = 0.0163
option_type = OptionTypes.AMERICAN_CALL
euOptionType = OptionTypes.EUROPEAN_CALL
amOption = EquityAmericanOption(expiry_date, strike_price, option_type)
ameuOption = EquityAmericanOption(expiry_date, strike_price, euOptionType)
euOption = EquityVanillaOption(expiry_date, strike_price, euOptionType)
discount_curve = DiscountCurveFlat(valuation_date, interest_rate,
FrequencyTypes.CONTINUOUS,
DayCountTypes.ACT_365F)
dividend_curve = DiscountCurveFlat(valuation_date, dividend_yield,
FrequencyTypes.CONTINUOUS,
DayCountTypes.ACT_365F)
num_steps_per_year = 400
modelTree = BlackScholes(volatility, BlackScholesTypes.CRR_TREE,
num_steps_per_year)
v = amOption.value(valuation_date, stock_price, discount_curve,
dividend_curve, modelTree)
# print(v)
modelApprox = BlackScholes(volatility, BlackScholesTypes.BARONE_ADESI)
v = amOption.value(valuation_date, stock_price, discount_curve,
dividend_curve, modelApprox)
# print(v)
v = ameuOption.value(valuation_date, stock_price, discount_curve,
dividend_curve, modelTree)
# print(v)
v = euOption.value(valuation_date, stock_price, discount_curve,
dividend_curve, modelTree)
# print(v)
amTreeValue = []
amBAWValue = []
euTreeValue = []
euAnalValue = []
volatility = 0.20
def test_FinBinomialTree():
stock_price = 50.0
risk_free_rate = 0.06
dividend_yield = 0.04
volatility = 0.40
valuation_date = Date(1, 1, 2016)
expiry_date = Date(1, 1, 2017)
model = BlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, risk_free_rate)
dividend_curve = DiscountCurveFlat(valuation_date, dividend_yield)
num_steps_list = [100, 500, 1000, 2000, 5000]
strike_price = 50.0
testCases.banner("================== EUROPEAN PUT =======================")
put_option = EquityVanillaOption(expiry_date, strike_price,
OptionTypes.EUROPEAN_PUT)
value = put_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
delta = put_option.delta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
gamma = put_option.gamma(valuation_date, stock_price, discount_curve,
dividend_curve, model)
theta = put_option.theta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
testCases.header("BS Value", "BS Delta", "BS Gamma", "BS Theta")
testCases.print(value, delta, gamma, theta)
payoff = EquityTreePayoffTypes.VANILLA_OPTION
exercise = EquityTreeExerciseTypes.EUROPEAN
params = np.array([-1, strike_price])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_steps_list:
start = time.time()
tree = EquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividend_curve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner("================== AMERICAN PUT =======================")
payoff = EquityTreePayoffTypes.VANILLA_OPTION
exercise = EquityTreeExerciseTypes.AMERICAN
params = np.array([-1, strike_price])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_steps_list:
start = time.time()
tree = EquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividend_curve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner(
"================== EUROPEAN CALL =======================")
call_option = EquityVanillaOption(expiry_date, strike_price,
OptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
delta = call_option.delta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
gamma = call_option.gamma(valuation_date, stock_price, discount_curve,
dividend_curve, model)
theta = call_option.theta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
testCases.header("BS Value", "BS Delta", "BS Gamma", "BS Theta")
testCases.print(value, delta, gamma, theta)
payoff = EquityTreePayoffTypes.VANILLA_OPTION
exercise = EquityTreeExerciseTypes.EUROPEAN
params = np.array([1.0, strike_price])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_steps_list:
start = time.time()
tree = EquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividend_curve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner(
"================== AMERICAN CALL =======================")
payoff = EquityTreePayoffTypes.VANILLA_OPTION
exercise = EquityTreeExerciseTypes.AMERICAN
params = np.array([1.0, strike_price])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_steps_list:
start = time.time()
tree = EquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividend_curve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
def test_EquityVanillaOption():
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 7, 2015)
stock_price = 100
volatility = 0.30
interest_rate = 0.05
dividend_yield = 0.01
model = BlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interest_rate)
dividend_curve = DiscountCurveFlat(valuation_date, dividend_yield)
num_paths_list = [10000, 20000, 40000, 80000, 160000, 320000]
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
for num_paths in num_paths_list:
call_option = EquityVanillaOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
start = time.time()
value_mc = call_option.value_mc(valuation_date, stock_price,
discount_curve, dividend_curve, model,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, value, value_mc, duration)
###############################################################################
stock_prices = range(80, 120, 10)
num_paths = 100000
testCases.header("NUMPATHS", "CALL_VALUE_BS", "CALL_VALUE_MC",
"CALL_VALUE_MC_SOBOL", "TIME")
useSobol = True
for stock_price in stock_prices:
call_option = EquityVanillaOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
start = time.time()
useSobol = False
value_mc1 = call_option.value_mc(valuation_date, stock_price,
discount_curve, dividend_curve, model,
num_paths, useSobol)
useSobol = True
value_mc2 = call_option.value_mc(valuation_date, stock_price,
discount_curve, dividend_curve, model,
num_paths, useSobol)
end = time.time()
duration = end - start
testCases.print(num_paths, value, value_mc1, value_mc2, duration)
###############################################################################
stock_prices = range(80, 120, 10)
num_paths = 100000
testCases.header("NUMPATHS", "PUT_VALUE_BS", "PUT_VALUE_MC",
"PUT_VALUE_MC_SOBOL", "TIME")
for stock_price in stock_prices:
put_option = EquityVanillaOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_PUT)
value = put_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
start = time.time()
useSobol = False
value_mc1 = put_option.value_mc(valuation_date, stock_price,
discount_curve, dividend_curve, model,
num_paths, useSobol)
useSobol = True
value_mc2 = put_option.value_mc(valuation_date, stock_price,
discount_curve, dividend_curve, model,
num_paths, useSobol)
end = time.time()
duration = end - start
testCases.print(num_paths, value, value_mc1, value_mc2, duration)
###############################################################################
stock_prices = range(80, 120, 10)
testCases.header("STOCK PRICE", "CALL_VALUE_BS", "CALL_DELTA_BS",
"CALL_VEGA_BS", "CALL_THETA_BS", "CALL_RHO_BS",
"CALL_VANNA_BS")
for stock_price in stock_prices:
call_option = EquityVanillaOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
delta = call_option.delta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
vega = call_option.vega(valuation_date, stock_price, discount_curve,
dividend_curve, model)
theta = call_option.theta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
rho = call_option.rho(valuation_date, stock_price, discount_curve,
dividend_curve, model)
vanna = call_option.vanna(valuation_date, stock_price, discount_curve,
dividend_curve, model)
testCases.print(stock_price, value, delta, vega, theta, rho, vanna)
###########################################################################
testCases.header("STOCK PRICE", "PUT_VALUE_BS", "PUT_DELTA_BS",
"PUT_VEGA_BS", "PUT_THETA_BS", "PUT_RHO_BS",
"PUT_VANNA_BS")
for stock_price in stock_prices:
put_option = EquityVanillaOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_PUT)
value = put_option.value(valuation_date, stock_price, discount_curve,
dividend_curve, model)
delta = put_option.delta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
vega = put_option.vega(valuation_date, stock_price, discount_curve,
dividend_curve, model)
theta = put_option.theta(valuation_date, stock_price, discount_curve,
dividend_curve, model)
rho = put_option.rho(valuation_date, stock_price, discount_curve,
dividend_curve, model)
vanna = put_option.vanna(valuation_date, stock_price, discount_curve,
dividend_curve, model)
testCases.print(stock_price, value, delta, vega, theta, rho, vanna)
def testImpliedVolatility_NEW():
valuation_date = Date(1, 1, 2015)
stock_price = 100.0
interest_rate = 0.05
dividend_yield = 0.03
discount_curve = DiscountCurveFlat(valuation_date, interest_rate)
dividend_curve = DiscountCurveFlat(valuation_date, dividend_yield)
strikes = np.linspace(50, 150, 11)
timesToExpiry = [0.003, 0.01, 0.1, 0.5, 1.0, 2.0, 5.0]
sigmas = np.arange(1, 100, 5) / 100.0
option_types = [FinOptionTypes.EUROPEAN_CALL, FinOptionTypes.EUROPEAN_PUT]
testCases.header("OPT_TYPE", "TEXP", "STOCK_PRICE", "STRIKE", "INTRINSIC",
"VALUE", "INPUT_VOL", "IMPLIED_VOL")
tol = 1e-5
numTests = 0
numFails = 0
for vol in sigmas:
model = BlackScholes(vol)
for time_to_expiry in timesToExpiry:
expiry_date = valuation_date.add_years(time_to_expiry)
for strike in strikes:
for option_type in option_types:
option = EquityVanillaOption(expiry_date, strike,
option_type)
value = option.value(valuation_date, stock_price,
discount_curve, dividend_curve, model)
intrinsic = option.intrinsic(valuation_date, stock_price,
discount_curve,
dividend_curve)
# I remove the cases where the time value is zero
# This is arbitrary but 1e-10 seems good enough to me
impliedVol = -999
if value - intrinsic > 1e-10:
impliedVol = option.implied_volatility(
valuation_date, stock_price, discount_curve,
dividend_curve, value)
numTests += 1
errVol = np.abs(impliedVol - vol)
if errVol > tol:
testCases.print(option_type, time_to_expiry,
stock_price, strike, intrinsic, value,
vol, impliedVol)
# These fails include ones due to the zero time value
numFails += 1
testCases.print(option_type, time_to_expiry,
stock_price, strike, stock_price,
value, vol, impliedVol)
assert numFails == 694, "Num Fails has changed."
###############################################################################
if 1 == 0:
valuation_date = Date(30, 11, 2021)
expiry_date = valuation_date.add_years(1)
stock_price = 100
volatility = 0.20
model = BlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, 0.05)
dividend_curve = DiscountCurveFlat(valuation_date, 0.0)
call_option = EquityVanillaOption(expiry_date, 100.0,
OptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, 105.0, discount_curve,
dividend_curve, model)
else:
test_EquityVanillaOption()
start = time.time()
testImpliedVolatility_NEW()
end = time.time()
elapsed = end - start
# print("Elapsed:", elapsed)
testCases.compareTestCases()
def test_FinNumbaNumbaParallel(useSobol):
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 7, 2015)
stock_price = 100
volatility = 0.30
interest_rate = 0.05
dividend_yield = 0.01
seed = 2021
model = BlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interest_rate)
useSobolInt = int(useSobol)
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
call_option = EquityVanillaOption(expiry_date, 100.0,
OptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_yield, model)
num_points = 20
v_exact = [value] * num_points
num_paths_list = np.arange(1, num_points+1, 1) * 1000000
NUMBA_ONLY_v = []
NUMBA_ONLY_t = []
print("NUMBA ONLY")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numba_only(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMBA_ONLY_v.append(value_mc)
NUMBA_ONLY_t.append(duration)
NUMBA_PARALLEL_v = []
NUMBA_PARALLEL_t = []
print("NUMBA PARALLEL")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numba_parallel(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMBA_PARALLEL_v.append(value_mc)
NUMBA_PARALLEL_t.append(duration)
###########################################################################
import matplotlib.pyplot as plt
if useSobol:
title = "SOBOL: NUMBA VS NUMBA + PARALLEL"
else:
title = "PSEUDORANDOM: NUMBA VS NUMBA + PARALLEL"
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, NUMBA_ONLY_t, 'o-', label="NUMBA ONLY")
plt.plot(num_paths_list, NUMBA_PARALLEL_t, 'o-', label="NUMBA PARALLEL")
plt.xlabel("Number of Paths")
plt.ylabel("Wall Time (s)")
plt.legend()
plt.title(title)
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, v_exact, label="EXACT")
plt.plot(num_paths_list, NUMBA_ONLY_v, 'o-', label="NUMBA ONLY")
plt.plot(num_paths_list, NUMBA_PARALLEL_v, 'o-', label="NUMBA PARALLEL")
plt.xlabel("Number of Paths")
plt.ylabel("Option Value")
plt.legend()
plt.title(title)
def test_FinNumbaNumpySpeed(useSobol):
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 7, 2015)
stock_price = 100
volatility = 0.30
interest_rate = 0.05
dividend_yield = 0.01
seed = 1999
model = BlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interest_rate)
useSobolInt = int(useSobol)
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
call_option = EquityVanillaOption(expiry_date, 100.0,
OptionTypes.EUROPEAN_CALL)
value = call_option.value(valuation_date, stock_price, discount_curve,
dividend_yield, model)
num_points = 20
v_exact = [value] * num_points
###########################################################################
# DO UP TO 100K AS IT IS SLOW
###########################################################################
num_paths_list = np.arange(1, num_points+1, 1) * 100000
NONUMBA_NONUMPY_v = []
NONUMBA_NONUMPY_t = []
print("PURE PYTHON")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_nonumba_nonumpy(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NONUMBA_NONUMPY_v.append(value_mc)
NONUMBA_NONUMPY_t.append(duration+1e-10)
NUMPY_ONLY_v = []
NUMPY_ONLY_t = []
print("NUMPY ONLY")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numpy_only(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMPY_ONLY_v.append(value_mc)
NUMPY_ONLY_t.append(duration+1e-10)
# speedUp = np.array(NONUMBA_NONUMPY_t)/np.array(NUMPY_ONLY_t)
# print(NUMPY_ONLY_t)
# print(NONUMBA_NONUMPY_t)
# print(speedUp)
if useSobol:
title = "SOBOL: PURE PYTHON VS NUMPY"
else:
title = "PSEUDORANDOM: PURE PYTHON VS NUMPY"
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, NONUMBA_NONUMPY_t, 'o-', label="PURE PYTHON")
plt.plot(num_paths_list, NUMPY_ONLY_t, 'o-', label="NUMPY ONLY")
plt.xlabel("Number of Paths")
plt.ylabel("Wall Time (s)")
plt.legend()
plt.title(title)
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, v_exact, label="EXACT")
plt.plot(num_paths_list, NONUMBA_NONUMPY_v, 'o-', label="PURE PYTHON")
plt.plot(num_paths_list, NUMPY_ONLY_v, 'o-', label="NUMPY ONLY")
plt.xlabel("Number of Paths")
plt.ylabel("Option Value")
plt.legend()
plt.title(title)
###########################################################################
# DO UP TO 10 MILLION NOW THAT WE HAVE NUMPY
###########################################################################
num_paths_list = np.arange(1, num_points+1, 1) * 1000000
NUMPY_ONLY_v = []
NUMPY_ONLY_t = []
print("NUMPY ONLY")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numpy_only(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMPY_ONLY_v.append(value_mc)
NUMPY_ONLY_t.append(duration)
NUMBA_NUMPY_v = []
NUMBA_NUMPY_t = []
print("NUMBA+NUMPY")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numpy_numba(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMBA_NUMPY_v.append(value_mc)
NUMBA_NUMPY_t.append(duration)
NUMBA_ONLY_v = []
NUMBA_ONLY_t = []
print("NUMBA ONLY")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numba_only(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMBA_ONLY_v.append(value_mc)
NUMBA_ONLY_t.append(duration)
NUMBA_PARALLEL_v = []
NUMBA_PARALLEL_t = []
print("NUMBA PARALLEL")
for num_paths in num_paths_list:
start = time.time()
value_mc = call_option.value_mc_numba_parallel(valuation_date, stock_price, discount_curve,
dividend_yield, model, num_paths, seed, useSobolInt)
end = time.time()
duration = end - start
print("%10d %9.5f %9.5f %9.6f" %
(num_paths, value, value_mc, duration))
NUMBA_PARALLEL_v.append(value_mc)
NUMBA_PARALLEL_t.append(duration)
# speedUp = np.array(NUMBA_ONLY_t)/np.array(NUMBA_PARALLEL_t)
# print("PARALLEL:", speedUp)
###########################################################################
# COMPUTED USING NUMSTEPS FROM 1M to 10M
###########################################################################
CPP_t = np.array([0.075, 0.155, 0.223, 0.313, 0.359, 0.421, 0.495, 0.556, 0.64, 0.702,
0.765, 0.841, 0.923, 0.982, 1.05, 1.125, 1.195, 1.261, 1.333, 1.408])
CPP_v = np.array([9.30872, 9.29576, 9.29422, 9.29832, 9.29863, 9.30153, 9.2994, 9.3025, 9.29653, 9.29875,
9.29897, 9.29996, 9.29931, 9.29796, 9.29784, 9.2992, 9.3001, 9.30093, 9.29876, 9.29921])
if useSobol:
title = "SOBOL: COMPARING OPTIMISATIONS"
else:
title = "PSEUDORANDOM: COMPARING OPTIMISATIONS"
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, NUMPY_ONLY_t, 'o-', label="NUMPY ONLY")
plt.plot(num_paths_list, NUMBA_NUMPY_t, 'o-', label="NUMBA + NUMPY")
plt.xlabel("Number of Paths")
plt.ylabel("Wall Time (s)")
plt.legend()
plt.title(title)
###########################################################################
if useSobol:
title = "SOBOL: COMPARING OPTIMISATIONS"
else:
title = "PSEUDORANDOM: COMPARING OPTIMISATIONS"
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, NUMPY_ONLY_t, 'o-', label="NUMPY ONLY")
plt.plot(num_paths_list, NUMBA_NUMPY_t, 'o-', label="NUMBA + NUMPY")
plt.plot(num_paths_list, NUMBA_ONLY_t, 'o-', label="NUMBA ONLY")
plt.plot(num_paths_list, NUMBA_PARALLEL_t, 'o-', label="NUMBA PARALLEL")
if useSobol == False:
plt.plot(num_paths_list, CPP_t, 'o-', label="C++")
plt.xlabel("Number of Paths")
plt.ylabel("Wall Time (s)")
plt.legend()
plt.title(title)
###########################################################################
plt.figure(figsize=(8, 6))
plt.plot(num_paths_list, v_exact, label="EXACT")
plt.plot(num_paths_list, NUMBA_ONLY_v, 'o-', label="NUMBA ONLY")
plt.plot(num_paths_list, CPP_v, 'o-', label="C++")
plt.xlabel("Number of Paths")
plt.ylabel("Option Value")
plt.legend()
plt.title(title)