def testImpliedVolatility_NEW():
valueDate = FinDate(1, 1, 2015)
stockPrice = 100.0
interestRate = 0.05
dividendYield = 0.03
discountCurve = FinDiscountCurveFlat(valueDate, interestRate)
dividendCurve = FinDiscountCurveFlat(valueDate, dividendYield)
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
optionTypes = [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 = FinModelBlackScholes(vol)
for timeToExpiry in timesToExpiry:
expiryDate = valueDate.addYears(timeToExpiry)
for strike in strikes:
for optionType in optionTypes:
option = FinEquityVanillaOption(expiryDate, strike,
optionType)
value = option.value(valueDate, stockPrice, discountCurve,
dividendCurve, model)
intrinsic = option.intrinsic(valueDate, stockPrice,
discountCurve, dividendCurve)
# 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.impliedVolatility(valueDate,
stockPrice,
discountCurve,
dividendCurve,
value)
numTests += 1
errVol = np.abs(impliedVol - vol)
if errVol > tol:
testCases.print(optionType,
timeToExpiry,
stockPrice,
strike,
intrinsic,
value,
vol,
impliedVol)
# These fails include ones due to the zero time value
numFails += 1
testCases.print(optionType, timeToExpiry, stockPrice,
strike,
stockPrice, value, vol, impliedVol)
assert numFails == 694, "Num Fails has changed."
def test_FinEquityVanillaOption():
valueDate = FinDate(2015, 1, 1)
expiryDate = FinDate(2015, 7, 1)
stockPrice = 100
volatility = 0.30
interestRate = 0.05
dividendYield = 0.01
model = FinEquityModelBlackScholes(volatility)
discountCurve = FinDiscountCurveFlat(valueDate, interestRate)
numPathsList = [10000, 20000, 40000, 80000, 160000, 320000]
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
for numPaths in numPathsList:
callOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = callOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
start = time.time()
valueMC = callOption.valueMC(valueDate, stockPrice, discountCurve,
dividendYield, model, numPaths)
end = time.time()
duration = end - start
testCases.print(numPaths, value, valueMC, duration)
###############################################################################
stockPrices = range(80, 120, 2)
numPaths = 100000
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
useSobol = True
for stockPrice in stockPrices:
callOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = callOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
start = time.time()
useSobol = False
valueMC1 = callOption.valueMC(valueDate, stockPrice, discountCurve,
dividendYield, model, numPaths, useSobol)
useSobol = True
valueMC2 = callOption.valueMC(valueDate, stockPrice, discountCurve,
dividendYield, model, numPaths, useSobol)
end = time.time()
duration = end - start
testCases.print(numPaths, value, valueMC, duration)
###############################################################################
stockPrices = range(80, 120, 2)
numPaths = 100000
testCases.header("STOCK PRICE", "VALUE_BS", "VALUE_MC", "TIME")
for stockPrice in stockPrices:
putOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_PUT)
value = putOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
start = time.time()
valueMC = putOption.valueMC(valueDate, stockPrice, discountCurve,
dividendYield, model, numPaths)
end = time.time()
duration = end - start
testCases.print(stockPrice, value, valueMC, duration)
###############################################################################
stockPrices = range(80, 120, 2)
testCases.header("STOCK PRICE", "VALUE_BS", "DELTA_BS", "VEGA_BS",
"THETA_BS", "RHO_BS")
for stockPrice in stockPrices:
callOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = callOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
delta = callOption.delta(valueDate, stockPrice, discountCurve,
dividendYield, model)
vega = callOption.vega(valueDate, stockPrice, discountCurve,
dividendYield, model)
theta = callOption.theta(valueDate, stockPrice, discountCurve,
dividendYield, model)
# callOption.rho(valueDate,stockPrice, interestRate, dividendYield, modelType, modelParams)
rho = 999
testCases.print(stockPrice, value, delta, vega, theta, rho)
testCases.header("STOCK PRICE", "VALUE_BS", "DELTA_BS", "VEGA_BS",
"THETA_BS", "RHO_BS")
for stockPrice in stockPrices:
putOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_PUT)
value = putOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
delta = putOption.delta(valueDate, stockPrice, discountCurve,
dividendYield, model)
vega = putOption.vega(valueDate, stockPrice, discountCurve,
dividendYield, model)
theta = putOption.theta(valueDate, stockPrice, discountCurve,
dividendYield, model)
# putOption.rho(valueDate,stockPrice, interestRate, dividendYield,
# modelType, modelParams)
rho = 999
testCases.print(stockPrice, value, delta, vega, theta, rho)
###############################################################################
testCases.header("STOCK PRICE", "VALUE_BS", "VOL_IN", "IMPLD_VOL")
stockPrices = range(60, 150, 2)
for stockPrice in stockPrices:
callOption = FinEquityVanillaOption(expiryDate, 100.0,
FinOptionTypes.EUROPEAN_CALL)
value = callOption.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
impliedVol = callOption.impliedVolatility(valueDate, stockPrice,
discountCurve, dividendYield,
value)
testCases.print(stockPrice, value, volatility, impliedVol)
def testImpliedVolatility():
valueDate = FinDate(1, 1, 2015)
stockPrice = 100
interestRate = 0.05
dividendYield = 0.01
discountCurve = FinDiscountCurveFlat(valueDate, interestRate)
strikes = [10, 20, 50, 100, 150, 200]
timesToExpiry = [0.003, 0.01, 0.1, 0.5, 1.0, 2.0, 5.0]
expiryDates = valueDate.addYears(timesToExpiry)
sigmas = [0.01, 0.10, 0.50, 1.0]
optionTypes = [FinOptionTypes.EUROPEAN_CALL, FinOptionTypes.EUROPEAN_PUT]
testCases.header("OPT_TYPE", "EXP_DATE", "STRIKE", "STOCK_PRICE", "VALUE",
"INPUT_VOL", "IMPLIED_VOL")
tol = 1e-6
numTests = 0
numFails = 0
for vol in sigmas:
model = FinModelBlackScholes(vol)
for expiryDate in expiryDates:
for strike in strikes:
for optionType in optionTypes:
option = FinEquityVanillaOption(expiryDate, 100.0,
optionType)
value = option.value(valueDate, stockPrice, discountCurve,
dividendYield, model)
impliedVol = option.impliedVolatility(
valueDate, stockPrice, discountCurve, dividendYield,
value)
numTests += 1
if np.abs(impliedVol - vol) > tol:
numFails += 1
# print(optionType, expiryDate, strike,
# stockPrice, value, vol, impliedVol)
testCases.print(optionType, expiryDate, strike, stockPrice,
value, vol, impliedVol)
print("Num Tests", numTests, "numFails", numFails)
###############################################################################
K = [10, 20, 50, 100, 150, 200]
T = [0.003, 0.01, 0.1, 0.5, 1.0, 2.0, 5.0]
sigma = [0.01, 0.10, 0.50, 1.0]
optionTypes = [FinOptionTypes.EUROPEAN_CALL, FinOptionTypes.EUROPEAN_PUT]
stockPrice = 100
HOURS_PER_YEAR = 365.25 * 24
convergenceFailure = 0
assertionFailure = 0
noResult = 0
successful = 0
numberTests = 0
totalElapsedTime = 0.
for t in T:
expDate = valueDate.addHours(t * HOURS_PER_YEAR)
for k in K:
for vol in sigma:
bs_model = FinModelBlackScholes(vol)
for type_ in optionTypes:
option = FinEquityVanillaOption(expDate, k, type_)
value = option.value(valueDate, stockPrice, discountCurve,
dividendYield, bs_model)
if value < 1e-10:
continue
try:
start_time = time.time()
impliedVol = option.impliedVolatility_v2(
valueDate, stockPrice, discountCurve,
dividendYield, value)
assert abs(impliedVol - vol) < 0.10
except FinError:
noResult += 1
except AssertionError:
assertionFailure += 1
print("-----------------")
print(
f"Did not converge to expected value: {round(impliedVol, 2)} vs {vol}"
)
print("INPUTS\n", "Type:", type_.name, "ttm:", t,
"strike:", k, "Expected IV:", vol, "BS Price:",
value)
except RuntimeError:
import traceback
traceback.print_exc()
convergenceFailure += 1
print("INPUTS\n", "Type:", type_.name, "ttm:", t,
"strike:", k, "Expected IV:", vol)
except Exception:
import traceback
traceback.print_exc()
noResult += 1
else:
successful += 1
totalElapsedTime += time.time() - start_time
finally:
numberTests += 1
print("\nSuccessful:", successful)
print("Convergence failure:", convergenceFailure)
print("Inaccurate result:", assertionFailure)
print("No result (price too low)", noResult)
print("TOTAL:", numberTests)
print("Mean time:", 1e6 * totalElapsedTime / successful, "us")
