def test_put_on_max():
payoff_type = EquityRainbowOptionTypes.PUT_ON_MAXIMUM
payoff_params = [strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
v = rainbowOption.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
assert round(v, 4) == 4.6493
assert round(v_MC, 4) == 4.6839
def test_put_on_nth():
rainboxOptionValues = []
rainbowOptionValuesMC = []
num_paths = 10000
num_assets = 5
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
stock_prices = np.ones(num_assets) * 100
dividend_curves = []
for q in dividend_yields:
dividend_curve = DiscountCurveFlat(valuation_date, q)
dividend_curves.append(dividend_curve)
payoff_type = EquityRainbowOptionTypes.PUT_ON_NTH
expected_results = [
1.4277,
3.9644,
7.6921,
13.2466,
22.3467
]
for n in [1, 2, 3, 4, 5]:
print(n)
payoff_params = [n, strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
assert round(v_MC, 4) == expected_results[n-1]
def test_call_on_nth():
num_paths = 10000
num_assets = 5
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
stock_prices = np.ones(num_assets) * 100
dividend_curves = []
for q in dividend_yields:
dividend_curve = DiscountCurveFlat(valuation_date, q)
dividend_curves.append(dividend_curve)
payoff_type = EquityRainbowOptionTypes.CALL_ON_NTH
expected_results = [
34.1760,
17.8990,
9.6716,
4.7205,
1.6182
]
for n in [1, 2, 3, 4, 5]:
print(n)
payoff_params = [n, strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
assert round(v_MC, 4) == expected_results[n-1]
def test_EquityRainbowOption():
# import matplotlib.pyplot as plt
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 1, 2016)
interest_rate = 0.05
discount_curve = DiscountCurveFlat(valuation_date, interest_rate)
num_assets = 2
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
dividend_curves = []
for q in dividend_yields:
dividend_curve = DiscountCurveFlat(valuation_date, q)
dividend_curves.append(dividend_curve)
stock_prices = np.ones(num_assets) * 100
num_paths_list = [10000]
corrList = np.linspace(0.0, 0.999999, 6)
strike = 100.0
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON MAXIMUM")
testCases.banner(
"===================================================================")
payoff_type = EquityRainbowOptionTypes.CALL_ON_MAXIMUM
payoff_params = [strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
start = time.time()
v = rainbowOption.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON MAX Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON MINIMUM")
testCases.banner(
"===================================================================")
payoff_type = EquityRainbowOptionTypes.CALL_ON_MINIMUM
payoff_params = [strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
start = time.time()
v = rainbowOption.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON MIN Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
###############################################################################
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON MAXIMUM")
testCases.banner(
"===================================================================")
payoff_type = EquityRainbowOptionTypes.PUT_ON_MAXIMUM
payoff_params = [strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
start = time.time()
v = rainbowOption.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "PUT ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "PUT ON MAX Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON MINIMUM")
testCases.banner(
"===================================================================")
payoff_type = EquityRainbowOptionTypes.PUT_ON_MINIMUM
payoff_params = [strike]
rainbowOption = EquityRainbowOption(
expiry_date, payoff_type, payoff_params, num_assets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
start = time.time()
v = rainbowOption.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "PUT ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "PUT ON MIN Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
num_assets = 2
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
stock_prices = np.ones(num_assets) * 100
strike = 100.0
correlation = 0.50
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 1st")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
payoff_type1 = EquityRainbowOptionTypes.CALL_ON_MAXIMUM
payoff_params1 = [strike]
rainbowOption1 = EquityRainbowOption(
expiry_date, payoff_type1, payoff_params1, num_assets)
payoff_type2 = EquityRainbowOptionTypes.CALL_ON_NTH
payoff_params2 = [1, strike]
rainbowOption2 = EquityRainbowOption(
expiry_date, payoff_type2, payoff_params2, num_assets)
start = time.time()
v = rainbowOption1.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption2.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON 1st Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 2nd")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
for num_paths in num_paths_list:
payoff_type1 = EquityRainbowOptionTypes.CALL_ON_MINIMUM
payoff_params1 = [strike]
rainbowOption1 = EquityRainbowOption(
expiry_date, payoff_type1, payoff_params1, num_assets)
payoff_type2 = EquityRainbowOptionTypes.CALL_ON_NTH
payoff_params2 = [2, strike]
rainbowOption2 = EquityRainbowOption(
expiry_date, payoff_type2, payoff_params2, num_assets)
start = time.time()
v = rainbowOption1.value(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix)
v_MC = rainbowOption2.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON 2nd Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 1-5")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
num_paths = 10000
num_assets = 5
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
stock_prices = np.ones(num_assets) * 100
dividend_curves = []
for q in dividend_yields:
dividend_curve = DiscountCurveFlat(valuation_date, q)
dividend_curves.append(dividend_curve)
# plt.figure(figsize=(10,8))
testCases.header(
"NUMPATHS",
"CORRELATION",
"NTD",
"VALUE",
"VALUE_MC",
"TIME")
for n in [1, 2, 3, 4, 5]:
rainboxOptionValues = []
rainbowOptionValuesMC = []
payoff_type2 = EquityRainbowOptionTypes.CALL_ON_NTH
payoff_params2 = [n, strike]
rainbowOption2 = EquityRainbowOption(
expiry_date, payoff_type2, payoff_params2, num_assets)
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
start = time.time()
v_MC = rainbowOption2.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, n, v, v_MC, duration)
rainbowOptionValuesMC.append(v_MC)
# plt.plot(corrList, rainbowOptionValuesMC, 'o-', label = "CALL Rainbow Option MC NTH = " + str(n))
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON 1-5")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
num_paths = 10000
num_assets = 5
volatilities = np.ones(num_assets) * 0.3
dividend_yields = np.ones(num_assets) * 0.01
stock_prices = np.ones(num_assets) * 100
# plt.figure(figsize=(10,8))
testCases.header(
"NUMPATHS",
"CORRELATION",
"NTD",
"VALUE",
"VALUE_MC",
"TIME")
for n in [1, 2, 3, 4, 5]:
rainboxOptionValues = []
rainbowOptionValuesMC = []
payoff_type2 = EquityRainbowOptionTypes.PUT_ON_NTH
payoff_params2 = [n, strike]
rainbowOption2 = EquityRainbowOption(
expiry_date, payoff_type2, payoff_params2, num_assets)
for correlation in corrList:
betas = np.ones(num_assets) * sqrt(correlation)
corr_matrix = beta_vector_to_corr_matrix(betas)
start = time.time()
v_MC = rainbowOption2.value_mc(
valuation_date,
stock_prices,
discount_curve,
dividend_curves,
volatilities,
corr_matrix,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, n, v, v_MC, duration)
rainbowOptionValuesMC.append(v_MC)