def test_FinSABR():
strikes = np.linspace(0.01, 0.06, 100)
alpha = 0.060277
beta = 0.5
rho = 0.2097
nu = 0.75091
model1 = FinModelSABR(alpha, beta, rho, nu)
alpha = 0.058484
beta = 0.5
rho = 0.20568
nu = 0.79647
model2 = FinModelSABR(alpha, beta, rho, nu)
f = 0.0350
T = 1.0
vols1 = model1.blackVol(f, strikes, T)
vols2 = model2.blackVol(f, strikes, T)
if PLOT_GRAPHS:
plt.figure()
plt.plot(strikes, vols1)
plt.plot(strikes, vols2)
plt.title("SABR")
def test_SABR_Calibration():
beta = 0.5
rho = -0.09
nu = 0.1
strikeVol = 0.1
f = 0.043
k = 0.050
r = 0.03
texp = 1.0
callOptionType = FinOptionTypes.EUROPEAN_CALL
putOptionType = FinOptionTypes.EUROPEAN_PUT
df = np.exp(-r * texp)
testCases.header("TEST", "CALIBRATION ERROR")
# Make SABR equivalent to lognormal (Black) model
# (i.e. alpha = 0, beta = 1, rho = 0, nu = 0, shift = 0)
modelSABR_01 = FinModelSABR(0.0, 1.0, 0.0, 0.0)
modelSABR_01.setAlphaFromBlackVol(strikeVol, f, k, texp)
impliedLognormalVol = modelSABR_01.blackVol(f, k, texp)
impliedATMLognormalVol = modelSABR_01.blackVol(k, k, texp)
impliedLognormalSmile = impliedLognormalVol - impliedATMLognormalVol
assert impliedLognormalSmile == 0.0, "In lognormal model, smile should be flat"
calibrationError = round(strikeVol - impliedLognormalVol, 12)
testCases.print("LOGNORMAL CASE", calibrationError)
# Volatility: pure SABR dynamics
modelSABR_02 = FinModelSABR(alpha, beta, rho, nu)
modelSABR_02.setAlphaFromBlackVol(strikeVol, f, k, texp)
impliedLognormalVol = modelSABR_02.blackVol(f, k, texp)
impliedATMLognormalVol = modelSABR_02.blackVol(k, k, texp)
impliedLognormalSmile = impliedLognormalVol - impliedATMLognormalVol
calibrationError = round(strikeVol - impliedLognormalVol, 12)
testCases.print("SABR CASE", calibrationError)
# Valuation: pure SABR dynamics
valueCall = modelSABR_02.value(f, k, texp, df, callOptionType)
valuePut = modelSABR_02.value(f, k, texp, df, putOptionType)
assert round(valueCall - valuePut, 12) == round(df*(f - k), 12), \
"The method called 'value()' doesn't comply with Call-Put parity"
