def testBachelierImpliedVol(self):
forward = 1.0
bpvol = 0.01
tte = 10.0
r = 0.03
dList = [-3.0, -2.0, -1.0, -0.5, 0.0, 0.5, 1.0, 2.0, 3.0]
for d in dList:
strike = forward + d * bpvol * math.sqrt(tte)
callPrem = bachelierFormula(OptionType.Call, strike, forward,
bpvol * math.sqrt(tte),
math.exp(-r * tte))
impliedBpVol = bachelierFormulaImpliedVol(OptionType.Call, strike,
forward, tte, callPrem,
math.exp(-r * tte))
self.assertAlmostEqual(impliedBpVol, bpvol, 12)
callPrem = bachelierFormula(OptionType.Put, strike, forward,
bpvol * math.sqrt(tte),
math.exp(-r * tte))
impliedBpVol = bachelierFormulaImpliedVol(OptionType.Put, strike,
forward, tte, callPrem,
math.exp(-r * tte))
self.assertAlmostEqual(impliedBpVol, bpvol, 12)
def testBachelierBasics(self):
strike = 1.0
forward = 1.2
discount = 0.95
expected = discount * (forward - strike)
calculated = bachelierFormula(OptionType.Call, strike, forward, 0.0, discount)
self.assertAlmostEqual(expected, calculated, 15)
def testBachelierBasics(self):
strike = 1.0
forward = 1.2
discount = 0.95
expected = discount * (forward - strike)
calculated = bachelierFormula(OptionType.Call, strike, forward, 0.0,
discount)
self.assertAlmostEqual(expected, calculated, 15)
def testBachelierImpliedVol(self):
forward = 1.0
bpvol = 0.01
tte = 10.0
r = 0.03
dList = [-3.0, -2.0, -1.0, -0.5, 0.0, 0.5, 1.0, 2.0, 3.0]
for d in dList:
strike = forward + d * bpvol * math.sqrt(tte)
callPrem = bachelierFormula(OptionType.Call, strike, forward, bpvol * math.sqrt(tte), math.exp(-r * tte))
impliedBpVol = bachelierFormulaImpliedVol(OptionType.Call, strike, forward, tte, callPrem,
math.exp(-r * tte))
self.assertAlmostEqual(impliedBpVol, bpvol, 12)
callPrem = bachelierFormula(OptionType.Put, strike, forward, bpvol * math.sqrt(tte), math.exp(-r * tte))
impliedBpVol = bachelierFormulaImpliedVol(OptionType.Put, strike, forward, tte, callPrem,
math.exp(-r * tte))
self.assertAlmostEqual(impliedBpVol, bpvol, 12)